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bridges_5x5_solver_traces_sft

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problem stringlengths 29 29	solution stringlengths 29 29	solution_path stringlengths 520 3.03k	difficulty stringclasses 1 value	gridsize stringclasses 1 value	filename stringlengths 26 26	puzzlename stringclasses 1 value	solver_stats stringclasses 244 values
3.2.1 ..... 4...2 ..... 3...1	3=2.1 \|...\| 4---2 ".... 3---1	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(4,4)H min=1 Current grid: 3-2.1 \|.... 4...2...	easy	5x5	bridges_5x5dm_72ca013e.txt	bridges	{"propagation_steps": 14, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2.1.2 ..... 4...3 ..... 4...2	2-1.2 \|..." 4---3 ".... 4===2	[Step 1] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(4,4)H to 2 [Step 2] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 [Step 3] Island (4,4) count=2 complete (2 bridges). Set (4,2)-(4,4)V max=0 Current grid: 2.1.2 ..... 4...3 ".... 4===2 [Step 4] Island (4,2) count=3 nee...	easy	5x5	bridges_5x5dm_d6b62be8.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
2..1. ..... 3...2 ..... 2.1.1	2--1. \|.... 3---2 \|...\| 2-1.1	[Step 1] Island (3,0) count=1 needs 1, 1 active edges, must connect all. Set (0,0)-(3,0)H min=1 [Step 2] Island (3,0) count=1 complete (1 bridges). Set (0,0)-(3,0)H max=1 [Step 3] Subgroup isolation: (2,4)-(4,4)H at 1 bridges would isolate component. Set max=0 Current grid: 2--1. ..... 3...2 ..... 2.1.1 [Step 4] Isla...	easy	5x5	bridges_5x5dm_bab0d338.txt	bridges	{"propagation_steps": 7, "search_nodes": 4, "backtracks": 3, "max_depth": 3, "time_ms": 0.6}
..2.1 2.... ....1 ..... 4.4.2	..2-1 2.\|.. ".\|.1 ".\|.\| 4=4-2	[Step 1] Island (0,1) count=2 needs 2, has 0 with 2 spaces. Fill (0,1)-(0,4)V to 2 [Step 2] Island (0,4) count=4 needs 4, has 2 with 2 spaces. Fill (0,4)-(2,4)H to 2 [Step 3] Subgroup isolation: (2,0)-(2,4)V at 2 bridges would isolate component. Set max=1 Current grid: ..2.1 2.... "...1 ".... 4=4.2 [Step 4] Subgroup ...	easy	5x5	bridges_5x5dm_de60c4eb.txt	bridges	{"propagation_steps": 11, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
3.4.2 ..... ....1 ..... 1.3.2	3=4-2 \|.\|.\| \|.\|.1 \|.\|.. 1.3=2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,4)V min=1 [Step 3] Island (0,4) count=1 complete (1 bridges). Set (0,4)-(2,4)H max=0 Current grid: 3-4.2 \|.... \|...1 \|.... 1.3.2 [Step 4...	easy	5x5	bridges_5x5dm_000ad1b6.txt	bridges	{"propagation_steps": 14, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
1.4.3 ..... 2.... ....1 3.2..	1-4=3 ..\|.\| 2.\|.\| ".\|.1 3-2..	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,3)V min=1 [Step 3] Island (4,3) count=1 complete (1 bridges). Set (4,0)-(4,3)V max=1 Current grid: 1.4-3 ....\| 2...\| ....1 3.2.. [Step 4...	easy	5x5	bridges_5x5dm_c86ec02c.txt	bridges	{"propagation_steps": 10, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
2.1.. ....1 2.... ..... 3.4.3	2-1.. \|...1 2...\| \|...\| 3=4=3	[Step 1] Island (4,1) count=1 needs 1, 1 active edges, must connect all. Set (4,1)-(4,4)V min=1 [Step 2] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(2,4)H min=1 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(0,4)V min=1 Current grid: 2.1.. ....1 2...\|...	easy	5x5	bridges_5x5dm_89961429.txt	bridges	{"propagation_steps": 13, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2.1.2 ..... 3...3 ..... .1..2	2.1-2 "...\| 3---3 ....\| .1--2	[Step 1] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(4,2)H min=1 [Step 2] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (1,4) count=1 needs 1, 1 active edges, must connect all. Set (1,4)-(4,4)H min=1 Current grid: 2.1.2 \|.... 3---3...	easy	5x5	bridges_5x5dm_00381dfe.txt	bridges	{"propagation_steps": 8, "search_nodes": 4, "backtracks": 2, "max_depth": 3, "time_ms": 0.6}
2.6.4 ..... 1.... ..2.. 3...4	2=6=4 .."." 1."." \|.2." 3===4	[Step 1] Island (2,0) count=6 needs 6, has 0 with 6 spaces. Fill (0,0)-(2,0)H to 2 [Step 2] Island (2,0) count=6 needs 6, has 0 with 6 spaces. Fill (2,0)-(4,0)H to 2 [Step 3] Island (2,0) count=6 needs 6, has 0 with 6 spaces. Fill (2,0)-(2,3)V to 2 Current grid: 2=6=4 ..... 1.... ..2.. 3...4 [Step 4] Island (4,0) cou...	easy	5x5	bridges_5x5de_9b255cd4.txt	bridges	{"propagation_steps": 9, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
1.1.2 ..... 4...2 ..... 4..2.	1.1-2 \|...\| 4---2 ".... 4==2.	[Step 1] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(3,4)H to 2 [Step 2] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 [Step 3] Subgroup isolation: (0,0)-(2,0)H at 1 bridges would isolate component. Set max=0 Current grid: 1.1.2 ..... 4...2 ".... 4==2. [Step 4] Subgroup ...	easy	5x5	bridges_5x5dm_53ab5104.txt	bridges	{"propagation_steps": 11, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
4..2. ..... 4.2.1 ..... 3...2	4==2. ".... 4-2-1 \|.... 3===2	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(3,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,2)V to 2 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(4,4)H min=1 Current grid: 4==2. ".... 4.2.1 ..... 3...2 [Step 4] Isl...	easy	5x5	bridges_5x5dm_142af3bf.txt	bridges	{"propagation_steps": 11, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
1...2 ..... 4.2.2 ..... 4...3	1---2 ....\| 4=2.2 "...\| 4===3	[Step 1] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(4,4)H to 2 [Step 2] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 Current grid: 1...2 ..... 4.2.2 ".... 4===3 [Step 4] Isl...	easy	5x5	bridges_5x5dm_6fdb02b7.txt	bridges	{"propagation_steps": 9, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2...2 ..... 1.1.4 ..... .1..3	2---2 \|...\| 1.1-4 ...." .1--3	[Step 1] Island (1,4) count=1 needs 1, 1 active edges, must connect all. Set (1,4)-(4,4)H min=1 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 [Step 3] Island (1,4) count=1 complete (1 bridges). Set (1,4)-(4,4)H max=1 Current grid: 2...2 ..... 1.1.4 ....\| .1--3 [Step 4...	easy	5x5	bridges_5x5dm_e3dfb982.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
..2.1 ..... 2...2 ..... 4.4.3	..2-1 ..\|.. 2.\|.2 ".\|." 4=4-3	[Step 1] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(2,4)H to 2 [Step 2] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 Current grid: ..2.1 ..... 2...2 ".... 4=4.3 [Step 4] Isl...	easy	5x5	bridges_5x5dm_0256d4f6.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.5}
1...3 ..... 1.2.4 ..... 1...2	1---3 ...." 1-2-4 ....\| 1---2	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (0,0) count=1 complete (1 bridges). Set (0,0)-(4,0)H max=1 Current grid: 1---3 ....\| 1.2.4 ..... 1...2 [Step 4...	easy	5x5	bridges_5x5dm_7768e9bb.txt	bridges	{"propagation_steps": 14, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
1.4.2 ..... 2.... ..... 2.4.1	1.4=2 \|.".. 2.".. \|.".. 2-4-1	[Step 1] Subgroup isolation: (0,2)-(0,4)V at 2 bridges would isolate component. Set max=1 [Step 2] Island (0,2) count=2 needs 2 more, only 1 available without (0,0)-(0,2)V. Set min=1 [Step 3] Island (0,4) count=2 needs 2 more, only 1 available without (0,4)-(2,4)H. Set min=1 Current grid: 1.4.2 \|.... 2.... ..... 2.4.1...	easy	5x5	bridges_5x5dm_1fbb4034.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
2.1.2 ..... 4...5 ..... 4...4	2-1.2 \|..." 4---5 "..." 4===4	[Step 1] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(4,2)H min=1 [Step 2] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (4,2)-(4,4)V min=1 Current grid: 2.1.2 ....\| 4---5...	easy	5x5	bridges_5x5dm_9c68d6b0.txt	bridges	{"propagation_steps": 10, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
1.3.1 ..... ....2 ..... 2.5.2	1-3.1 ..".\| ..".2 ..".\| 2=5-2	[Step 1] Island (2,4) count=5 needs 5, 3 active edges, must connect all. Set (0,4)-(2,4)H min=1 [Step 2] Island (2,4) count=5 needs 5, 3 active edges, must connect all. Set (2,4)-(4,4)H min=1 [Step 3] Island (2,4) count=5 needs 5, 3 active edges, must connect all. Set (2,0)-(2,4)V min=1 Current grid: 1.3.1 ..... ....2...	easy	5x5	bridges_5x5dm_a96f4e44.txt	bridges	{"propagation_steps": 14, "search_nodes": 5, "backtracks": 2, "max_depth": 3, "time_ms": 0.8}
2...4 ..... 2...4 ..... 2.1.1	2===4 ...." 2---4 \|...\| 2-1.1	[Step 1] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(4,0)H to 2 [Step 2] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (4,0)-(4,2)V to 2 [Step 3] Island (0,0) count=2 complete (2 bridges). Set (0,0)-(0,2)V max=0 Current grid: 2===4 ...." 2...4 ..... 2.1.1 [Step 4] Subgroup isolation: (0,2...	easy	5x5	bridges_5x5dm_705082fc.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
1.1.. ....1 ..2.. ..... 2.4.3	1.1.. \|.\|.1 \|.2.\| \|.\|.\| 2-4=3	[Step 1] Island (4,1) count=1 needs 1, 1 active edges, must connect all. Set (4,1)-(4,4)V min=1 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 [Step 3] Island (4,1) count=1 complete (1 bridges). Set (4,1)-(4,4)V max=1 Current grid: 1.1.. ....1 ..2.\| ....\| 2.4-3 [Step 4...	easy	5x5	bridges_5x5dm_fc70a221.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
1.2.2 ..... 3...3 ..... 3.2..	1-2-2 ....\| 3===3 \|.... 3=2..	[Step 1] Island (4,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(4,2)H min=1 [Step 2] Island (4,2) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(2,4)H min=1 Current grid: 1.2.2 ....\| 3---3...	easy	5x5	bridges_5x5dm_a9ff4b9a.txt	bridges	{"propagation_steps": 13, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
3.5.2 ..... 1...2 ..... ..2.1	3=5-2 \|.".\| 1.".2 ..".\| ..2.1	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (2,0) count=5 needs 5, 3 active edges, must connect all. Set (2,0)-(4,0)H min=1 Current grid: 3-5.2 \|.... 1...2...	easy	5x5	bridges_5x5dm_63636d96.txt	bridges	{"propagation_steps": 10, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.5}
4...3 ..... 4.2.4 ..... 1...2	4===3 "...\| 4-2-4 \|..." 1...2	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(4,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,2)V to 2 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 Current grid: 4===3 ".... 4.2.4 ..... 1...2 [Step 4] Isl...	easy	5x5	bridges_5x5dm_361df35c.txt	bridges	{"propagation_steps": 9, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.7}
2.2.. ....1 1.... ..... 1.4.3	2-2.. \|.\|.1 1.\|.\| ..\|.\| 1-4=3	[Step 1] Island (4,1) count=1 needs 1, 1 active edges, must connect all. Set (4,1)-(4,4)V min=1 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 [Step 3] Island (4,1) count=1 complete (1 bridges). Set (4,1)-(4,4)V max=1 Current grid: 2.2.. ....1 1...\| ....\| 1.4-3 [Step 4...	easy	5x5	bridges_5x5dm_5df9db79.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
2.4.1 ..... ....2 ..... 1.4.2	2=4.1 ..".\| ..".2 ..".\| 1-4-2	[Step 1] Subgroup isolation: (4,2)-(4,4)V at 2 bridges would isolate component. Set max=1 [Step 2] Island (4,2) count=2 needs 2 more, only 1 available without (4,0)-(4,2)V. Set min=1 [Step 3] Island (4,4) count=2 needs 2 more, only 1 available without (2,4)-(4,4)H. Set min=1 Current grid: 2.4.1 ....\| ....2 ..... 1.4.2...	easy	5x5	bridges_5x5dm_489ce117.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
1.1.. ..... ..2.3 ..... 2.3.4	1.1.. \|.\|.. \|.2-3 \|..." 2-3=4	[Step 1] Island (4,2) count=3 needs 3, 2 active edges, must connect all. Set (2,2)-(4,2)H min=1 [Step 2] Island (4,2) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 [Step 3] Island (4,4) count=4 needs 4, has 1 with 3 spaces. Fill (2,4)-(4,4)H to 2 Current grid: 1.1.. ..... ..2-3 ....\| 2.3.4 ...	easy	5x5	bridges_5x5dm_63bc84ba.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
2.3.2 ..... ..3.. 1.... ..2.1	2-3-2 \|.\|.\| \|.3.\| 1.".\| ..2.1	[Step 1] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(2,2)V min=1 [Step 2] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,2)-(2,4)V min=1 [Step 3] Island (0,3) count=1 needs 1, 1 active edges, must connect all. Set (0,0)-(0,3)V min=1 Current grid: 2.3.2 ..\|.. ..3.....	easy	5x5	bridges_5x5dm_5fde3c14.txt	bridges	{"propagation_steps": 8, "search_nodes": 4, "backtracks": 2, "max_depth": 3, "time_ms": 0.5}
4...4 .2.3. ..... ....2 4..3.	4===4 "2=3" "..\|" "..\|2 4==3.	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(4,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,4)V to 2 [Step 3] Island (4,0) count=4 needs 4, has 2 with 2 spaces. Fill (4,0)-(4,3)V to 2 Current grid: 4===4 "2.3. ".... "...2 4..3. [Step 4] Island (1,1) cou...	easy	5x5	bridges_5x5de_5760c765.txt	bridges	{"propagation_steps": 7, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
3...3 ..... 6...5 ..... 3.1.1	3---3 "..." 6===5 "...\| 3-1.1	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(4,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 Current grid: 3---3 \|.... 6...5...	easy	5x5	bridges_5x5de_608f4afa.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
3.4.1 ..... ..2.. ..... 2...2	3=4.1 \|.".\| \|.2.\| \|...\| 2---2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,4)V min=1 [Step 3] Island (2,2) count=2 needs 2, has 0 with 2 spaces. Fill (2,0)-(2,2)V to 2 Current grid: 3-4.1 \|.... \|.2.. \|.... 2...2 ...	easy	5x5	bridges_5x5dm_fdba71c4.txt	bridges	{"propagation_steps": 10, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.4}
.2..3 ..... 3...3 ..... 2.1.2	.2==3 ....\| 3---3 "...\| 2.1-2	[Step 1] Island (1,0) count=2 needs 2, has 0 with 2 spaces. Fill (1,0)-(4,0)H to 2 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(4,2)H min=1 Current grid: .2==3 ....\| 3...3 ..... 2.1.2 ...	easy	5x5	bridges_5x5dm_822a9a43.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.5}
4.4.3 ..... ....2 ..... 2.2.1	4=4-3 ".\|." ".\|.2 ".\|.. 2.2-1	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(2,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,4)V to 2 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 Current grid: 4=4.3 ".... "...2 ".... 2.2.1 [Step 4] Isl...	easy	5x5	bridges_5x5dm_8e436daa.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
1.2.. ..... 1...1 ..... 2.3.2	1-2.. ..\|.. 1.\|.1 \|.\|.\| 2-3-2	[Step 1] Subgroup isolation: (0,0)-(0,2)V at 1 bridges would isolate component. Set max=0 [Step 2] Subgroup isolation: (0,2)-(4,2)H at 1 bridges would isolate component. Set max=0 [Step 3] Island (0,0) count=1 needs 1, 1 active edges, must connect all. Set (0,0)-(2,0)H min=1 Current grid: 1.2.. ..... 1...1 ..... 2.3.2...	easy	5x5	bridges_5x5dm_a50c8eb9.txt	bridges	{"propagation_steps": 8, "search_nodes": 4, "backtracks": 3, "max_depth": 3, "time_ms": 0.7}
..2.1 ..... 4.4.. ..... 3.2.2	..2.1 ..".\| 4=4.\| "...\| 3-2-2	[Step 1] Island (0,2) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(2,2)H to 2 [Step 2] Island (0,2) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(2,4)H min=1 Current grid: ..2.1 ..... 4=4.. ".... 3.2.2 [Step 4] Isl...	easy	5x5	bridges_5x5dm_a72ed1f3.txt	bridges	{"propagation_steps": 8, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.5}
2..1. ..... 4.3.2 ..... 4..2.	2--1. \|.... 4-3=2 ".... 4==2.	[Step 1] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 2] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,2)-(4,2)H min=1 [Step 3] Island (4,2) count=2 needs 2, has 1 with 1 spaces. Fill (2,2)-(4,2)H to 2 Current grid: 2..1. ..... 4-3-2 ..... 4..2. ...	easy	5x5	bridges_5x5de_6e29bbd7.txt	bridges	{"propagation_steps": 8, "search_nodes": 2, "backtracks": 1, "max_depth": 1, "time_ms": 0.2}
3..1. ..... 4...2 ..... 1.1.2	3--1. ".... 4---2 \|...\| 1.1-2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(3,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (3,0) count=1 complete (1 bridges). Set (0,0)-(3,0)H max=1 Current grid: 3--1. \|.... 4...2 ..... 1.1.2 [Step 4...	easy	5x5	bridges_5x5dm_e86e5ed0.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
.2..4 ..... 3...4 ..... 2.2.1	.2==4 ...." 3===4 \|.... 2-2-1	[Step 1] Island (1,0) count=2 needs 2, has 0 with 2 spaces. Fill (1,0)-(4,0)H to 2 [Step 2] Island (4,0) count=4 needs 4, has 2 with 2 spaces. Fill (4,0)-(4,2)V to 2 [Step 3] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(4,2)H min=1 Current grid: .2==4 ...." 3...4 ..... 2.2.1 [Step 4] Isl...	easy	5x5	bridges_5x5dm_491a0ecc.txt	bridges	{"propagation_steps": 11, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2...1 ..... 5.2.4 ..... 2...2	2...1 "...\| 5-2-4 "..." 2...2	[Step 1] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 2] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(0,4)V min=1 Current grid: 2...1 \|.... 5-2.4...	easy	5x5	bridges_5x5dm_4a351e88.txt	bridges	{"propagation_steps": 10, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.5}
2.1.1 ..... 2...4 ..... ..2.4	2-1.1 \|...\| 2---4 ...." ..2=4	[Step 1] Island (4,4) count=4 needs 4, has 0 with 4 spaces. Fill (2,4)-(4,4)H to 2 [Step 2] Island (4,4) count=4 needs 4, has 0 with 4 spaces. Fill (4,2)-(4,4)V to 2 [Step 3] Island (2,4) count=2 complete (2 bridges). Set (2,0)-(2,4)V max=0 Current grid: 2.1.1 ..... 2...4 ...." ..2=4 [Step 4] Subgroup isolation: (0,0...	easy	5x5	bridges_5x5dm_1ec24180.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
2..1. ..... 4...1 ..... 4.4.2	2--1. \|.... 4---1 ".... 4=4=2	[Step 1] Island (3,0) count=1 needs 1, 1 active edges, must connect all. Set (0,0)-(3,0)H min=1 [Step 2] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(2,4)H to 2 [Step 3] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 Current grid: 2--1. ..... 4...1 ..... 4=4.2 [Step 4] Isl...	easy	5x5	bridges_5x5de_2f58954b.txt	bridges	{"propagation_steps": 8, "search_nodes": 2, "backtracks": 1, "max_depth": 1, "time_ms": 0.2}
1.2.. ....2 1.... ..... 3.5.4	1-2.. ..\|.2 1.\|." \|.\|." 3=5=4	[Step 1] Island (4,1) count=2 needs 2, has 0 with 2 spaces. Fill (4,1)-(4,4)V to 2 [Step 2] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(2,4)H min=1 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(0,4)V min=1 Current grid: 1.2.. ....2 1..." ...." 3-5.4 ...	easy	5x5	bridges_5x5de_c615543b.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
3.3.1 ..... ..3.. 2.... ..2.2	3-3.1 ".".\| ".3.\| 2.\|.\| ..2-2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,3)V min=1 [Step 3] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(2,2)V min=1 Current grid: 3-3.1 \|.... \|.3.....	easy	5x5	bridges_5x5dm_ef560fbe.txt	bridges	{"propagation_steps": 13, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2...2 ..... 4...5 ..... 1.2.2	2...2 "..." 4===5 ....\| 1-2-2	[Step 1] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(4,2)H min=1 [Step 2] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (4,2)-(4,4)V min=1 Current grid: 2...2 ....\| 4---5...	easy	5x5	bridges_5x5dm_8491f4e1.txt	bridges	{"propagation_steps": 17, "search_nodes": 6, "backtracks": 3, "max_depth": 3, "time_ms": 0.8}
..2.3 2.... ....2 ..... 3.3.1	..2-3 2.\|." ".\|.2 ".\|.. 3-3-1	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (0,1) count=2 needs 2, has 0 with 2 spaces. Fill (0,1)-(0,4)V to 2 Current grid: ..2-3 2...\| ....2 ..... 3.3.1 ...	easy	5x5	bridges_5x5dm_f1f37a77.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
1.2.3 ..... 4...2 ..... 3..1.	1.2=3 \|...\| 4---2 ".... 3--1.	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(3,4)H min=1 Current grid: 1.2-3 ....\| 4...2...	easy	5x5	bridges_5x5dm_e0409f23.txt	bridges	{"propagation_steps": 13, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2.2.1 ..... ..1.. ..... 3.4.3	2-2.1 \|.\|.\| \|.1.\| \|...\| 3=4=3	[Step 1] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(2,4)H min=1 [Step 2] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,4)V min=1 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 Current grid: 2.2.1 \|.... \|.1.....	easy	5x5	bridges_5x5dm_b43a8d74.txt	bridges	{"propagation_steps": 14, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
1.1.2 ..... 2...4 ..... .1..3	1.1-2 \|...\| 2---4 ...." .1--3	[Step 1] Island (1,4) count=1 needs 1, 1 active edges, must connect all. Set (1,4)-(4,4)H min=1 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 [Step 3] Island (1,4) count=1 complete (1 bridges). Set (1,4)-(4,4)H max=1 Current grid: 1.1.2 ..... 2...4 ....\| .1--3 [Step 4...	easy	5x5	bridges_5x5dm_e73c79a1.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
3.4.2 ..... ..1.. ..... 1.2.3	3=4-2 \|.\|.\| \|.1.\| \|...\| 1.2=3	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,4)V min=1 [Step 3] Island (0,4) count=1 complete (1 bridges). Set (0,4)-(2,4)H max=0 Current grid: 3-4.2 \|.... \|.1.. \|.... 1.2.3 [Step 4...	easy	5x5	bridges_5x5dm_91cb8715.txt	bridges	{"propagation_steps": 14, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
1.1.2 ..... 4...2 ..... 3.1..	1.1-2 \|...\| 4---2 ".... 3-1..	[Step 1] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(2,4)H min=1 [Step 2] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(0,4)V min=1 [Step 3] Island (2,4) count=1 complete (1 bridges). Set (0,4)-(2,4)H max=1 Current grid: 1.1.2 ..... 4...2 \|.... 3-1.. [Step 4...	easy	5x5	bridges_5x5dm_2b6c1b46.txt	bridges	{"propagation_steps": 14, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
3.1.1 ..... 5...3 ..... 2.1..	3-1.1 "...\| 5===3 \|.... 2-1..	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (2,0) count=1 complete (1 bridges). Set (0,0)-(2,0)H max=1 Current grid: 3-1.1 \|.... 5...3 ..... 2.1.. [Step 4...	easy	5x5	bridges_5x5de_5476bd5d.txt	bridges	{"propagation_steps": 14, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
2...1 ..... 3..1. ..... 2...1	2---1 \|.... 3--1. \|.... 2---1	[Step 1] Island (3,2) count=1 needs 1, 1 active edges, must connect all. Set (0,2)-(3,2)H min=1 [Step 2] Island (3,2) count=1 complete (1 bridges). Set (0,2)-(3,2)H max=1 [Step 3] Subgroup isolation: (0,0)-(0,2)V at 2 bridges would isolate component. Set max=1 Current grid: 2...1 ..... 3--1. ..... 2...1 [Step 4] Subg...	easy	5x5	bridges_5x5dm_06d4df23.txt	bridges	{"propagation_steps": 11, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
3.4.. ..... 3.4.3 ..... 1...2	3=4.. \|.".. 3-4-3 \|..." 1...2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (2,0) count=4 needs 4, has 1 with 3 spaces. Fill (0,0)-(2,0)H to 2 Current grid: 3-4.. \|.... 3.4.3 ..... 1...2 ...	easy	5x5	bridges_5x5dm_2c029a6a.txt	bridges	{"propagation_steps": 11, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
1.2.2 ..... 3...5 ..... 2...3	1-2-2 ....\| 3===5 \|..." 2---3	[Step 1] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(4,2)H min=1 [Step 2] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (4,2) count=5 needs 5, 3 active edges, must connect all. Set (4,2)-(4,4)V min=1 Current grid: 1.2.2 ....\| 3---5...	easy	5x5	bridges_5x5dm_1cd3788e.txt	bridges	{"propagation_steps": 12, "search_nodes": 6, "backtracks": 3, "max_depth": 4, "time_ms": 0.9}
1.3.1 ..... ....2 ..... 1.4.2	1-3.1 ..".\| ..".2 ..".\| 1-4-2	[Step 1] Subgroup isolation: (0,0)-(0,4)V at 1 bridges would isolate component. Set max=0 [Step 2] Subgroup isolation: (4,2)-(4,4)V at 2 bridges would isolate component. Set max=1 [Step 3] Island (0,0) count=1 needs 1, 1 active edges, must connect all. Set (0,0)-(2,0)H min=1 Current grid: 1.3.1 ..... ....2 ..... 1.4.2...	easy	5x5	bridges_5x5dm_dda3e009.txt	bridges	{"propagation_steps": 13, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
3.1.. .2..3 ..... ..... 4.4.3	3-1.. "2==3 "...\| "...\| 4=4=3	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,4)V min=1 [Step 3] Island (2,0) count=1 complete (1 bridges). Set (0,0)-(2,0)H max=1 Current grid: 3-1.. \|2..3 \|.... \|.... 4.4.3 [Step 4...	easy	5x5	bridges_5x5de_e3512f89.txt	bridges	{"propagation_steps": 10, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
..2.4 ..... 3...4 ..... 2.1.2	..2=4 ...." 3---4 "...\| 2.1-2	[Step 1] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (2,0)-(4,0)H to 2 [Step 2] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (4,0)-(4,2)V to 2 [Step 3] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(4,2)H min=1 Current grid: ..2=4 ...." 3...4 ..... 2.1.2 [Step 4] Isl...	easy	5x5	bridges_5x5dm_aac6c742.txt	bridges	{"propagation_steps": 8, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.5}
2...3 .2.3. ..... 2..2. ....2	2---3 \|2=3" \|..\|" 2--2" ....2	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,4)V min=1 [Step 3] Island (1,1) count=2 needs 2, has 0 with 2 spaces. Fill (1,1)-(3,1)H to 2 Current grid: 2---3 .2.3\| ....\| 2..2\| ....2 ...	easy	5x5	bridges_5x5de_df3967a0.txt	bridges	{"propagation_steps": 7, "search_nodes": 3, "backtracks": 2, "max_depth": 2, "time_ms": 0.3}
1...2 ..... 2.3.4 ..... 1...3	1---2 ....\| 2=3-4 ...." 1---3	[Step 1] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 2] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,2)-(4,2)H min=1 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(4,4)H min=1 Current grid: 1...2 ..... 2-3-4...	easy	5x5	bridges_5x5dm_35cbea62.txt	bridges	{"propagation_steps": 14, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
..1.2 2.... ..2.. ..... 4.4.3	..1.2 2.\|." ".2." ".\|." 4=4-3	[Step 1] Island (0,1) count=2 needs 2, has 0 with 2 spaces. Fill (0,1)-(0,4)V to 2 [Step 2] Island (0,4) count=4 needs 4, has 2 with 2 spaces. Fill (0,4)-(2,4)H to 2 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 Current grid: ..1.2 2.... ".2.. ".... 4=4.3 [Step 4] Isl...	easy	5x5	bridges_5x5dm_cbacf773.txt	bridges	{"propagation_steps": 8, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
3.2.1 ..... 4...2 ..... 4...2	3=2.1 \|...\| 4---2 ".... 4===2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(4,4)H to 2 Current grid: 3-2.1 \|.... 4...2 ..... 4...2 ...	easy	5x5	bridges_5x5dm_122c1721.txt	bridges	{"propagation_steps": 12, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.4}
.2..4 ..... .2..6 ..... 2.3.3	.2==4 ...." .2==6 ...." 2=3-3	[Step 1] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (1,0)-(4,0)H to 2 [Step 2] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (4,0)-(4,2)V to 2 [Step 3] Island (4,2) count=6 needs 6, has 2 with 4 spaces. Fill (1,2)-(4,2)H to 2 Current grid: .2==4 ...." .2..6 ..... 2.3.3 [Step 4] Island (4,2) cou...	easy	5x5	bridges_5x5de_52aaffed.txt	bridges	{"propagation_steps": 8, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
2.4.4 ..... 3.... ....2 2.1..	2-4=4 \|.\|." 3.\|." ".\|.2 2.1..	[Step 1] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (2,0)-(4,0)H to 2 [Step 2] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (4,0)-(4,3)V to 2 [Step 3] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 Current grid: 2.4=4 ...." 3..." ....2 2.1.. [Step 4] Isl...	easy	5x5	bridges_5x5dm_0d46fab0.txt	bridges	{"propagation_steps": 8, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
3.2.1 ..... 4...2 ..... 4...2	3=2.1 \|...\| 4---2 ".... 4===2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(4,4)H to 2 Current grid: 3-2.1 \|.... 4...2 ..... 4...2 ...	easy	5x5	bridges_5x5dm_8725d49e.txt	bridges	{"propagation_steps": 12, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2...2 ..... 3.5.6 ..... ..2.2	2...2 "..." 3-5=6 .."." ..2.2	[Step 1] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 2] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (2,2) count=5 needs 5, 3 active edges, must connect all. Set (2,2)-(4,2)H min=1 Current grid: 2...2 \|.... 3-5.6...	easy	5x5	bridges_5x5de_52cd8168.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
2.3.2 ..... 1...4 ..... ..1.3	2=3-2 ....\| 1---4 ...." ..1-3	[Step 1] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 [Step 3] Island (2,4) count=1 complete (1 bridges). Set (2,4)-(4,4)H max=1 Current grid: 2.3.2 ..... 1...4 ....\| ..1-3 [Step 4...	easy	5x5	bridges_5x5dm_2766287a.txt	bridges	{"propagation_steps": 14, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
4.6.2 ..... 4.... ..2.. 3..1.	4=6=2 ".".. 4.".. ".2.. 3--1.	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(2,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,2)V to 2 [Step 3] Island (2,0) count=6 needs 6, has 2 with 4 spaces. Fill (2,0)-(4,0)H to 2 Current grid: 4=6.2 ".... 4.... ..2.. 3..1. [Step 4] Island (2,0) cou...	easy	5x5	bridges_5x5de_af848014.txt	bridges	{"propagation_steps": 7, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
3...3 ..... 4..1. ..... 2...3	3---3 "..." 4--1" \|..." 2---3	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(4,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,4)V min=1 Current grid: 3---3 \|.... 4..1....	easy	5x5	bridges_5x5dm_5b44d4ab.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.3}
3...3 .1.3. ..... 3..4. ....1	3===3 \|1-3\| \|.."\| 3==4\| ....1	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(4,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,3)V min=1 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,4)V min=1 Current grid: 3---3 \|1.3. \|.......	easy	5x5	bridges_5x5de_8837895a.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
2..1. ..... 4.2.3 ..... 2...2	2--1. \|.... 4-2-3 "..." 2...2	[Step 1] Island (3,0) count=1 needs 1, 1 active edges, must connect all. Set (0,0)-(3,0)H min=1 [Step 2] Island (4,2) count=3 needs 3, 2 active edges, must connect all. Set (2,2)-(4,2)H min=1 [Step 3] Island (4,2) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 Current grid: 2--1. ..... 4.2-3...	easy	5x5	bridges_5x5dm_9222519a.txt	bridges	{"propagation_steps": 7, "search_nodes": 4, "backtracks": 2, "max_depth": 3, "time_ms": 0.5}
..3.2 ..... 2...1 ..... 4.4.2	..3=2 ..\|.. 2.\|.1 ".\|.\| 4=4-2	[Step 1] Island (2,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 [Step 2] Island (2,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(2,4)V min=1 [Step 3] Island (0,2) count=2 needs 2, has 0 with 2 spaces. Fill (0,2)-(0,4)V to 2 Current grid: ..3-2 ..\|.. 2.\|.1 ..\|.. 4.4.2 ...	easy	5x5	bridges_5x5dm_8a73a094.txt	bridges	{"propagation_steps": 11, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2...1 ..... 5.2.2 ..... 4..2.	2...1 "...\| 5-2-2 ".... 4==2.	[Step 1] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 2] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(0,4)V min=1 Current grid: 2...1 \|.... 5-2.2...	easy	5x5	bridges_5x5dm_c9b49a71.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
1.2.3 ..... ..1.. ..... 2.3.4	1.2-3 \|.\|." \|.1." \|..." 2-3=4	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,4)V min=1 [Step 3] Island (4,4) count=4 needs 4, has 1 with 3 spaces. Fill (2,4)-(4,4)H to 2 Current grid: 1.2-3 ....\| ..1.\| ....\| 2.3.4 ...	easy	5x5	bridges_5x5dm_595a3c63.txt	bridges	{"propagation_steps": 10, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.6}
2...1 ..... 3.4.2 ..... ..4.2	2...1 "...\| 3-4-2 ..".. ..4=2	[Step 1] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 2] Island (0,2) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (2,4) count=4 needs 4, has 0 with 4 spaces. Fill (2,4)-(4,4)H to 2 Current grid: 2...1 \|.... 3-4.2 ..... ..4.2 ...	easy	5x5	bridges_5x5dm_f17843cb.txt	bridges	{"propagation_steps": 9, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
2...2 ..... 5.2.1 ..... 4..2.	2---2 \|...\| 5=2.1 ".... 4==2.	[Step 1] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 2] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (0,2) count=5 needs 5, 3 active edges, must connect all. Set (0,2)-(0,4)V min=1 Current grid: 2...2 \|.... 5-2.1...	easy	5x5	bridges_5x5dm_65bae5f5.txt	bridges	{"propagation_steps": 12, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.4}
2...3 ..... 2.1.3 ..... ..2.3	2---3 \|..." 2-1.3 ....\| ..2=3	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 Current grid: 2---3 ....\| 2.1.3...	easy	5x5	bridges_5x5dm_14630a4a.txt	bridges	{"propagation_steps": 11, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.5}
.1..2 ..... 2.3.3 ..... 1...2	.1--2 ....\| 2=3-3 ....\| 1---2	[Step 1] Island (1,0) count=1 needs 1, 1 active edges, must connect all. Set (1,0)-(4,0)H min=1 [Step 2] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(2,2)H min=1 [Step 3] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,2)-(4,2)H min=1 Current grid: .1--2 ..... 2-3.3...	easy	5x5	bridges_5x5dm_d0721a8c.txt	bridges	{"propagation_steps": 11, "search_nodes": 6, "backtracks": 6, "max_depth": 3, "time_ms": 0.7}
3.2.3 ..... .2... 2.... .3..3	3-2-3 "..." "2.." 2".." .3--3	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,3)V min=1 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 Current grid: 3-2.3 \|.... \|2......	easy	5x5	bridges_5x5de_5a1c3333.txt	bridges	{"propagation_steps": 11, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
3.1.. ..... 4...3 ..... 1.2.2	3-1.. ".... 4===3 ....\| 1-2-2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (2,0) count=1 complete (1 bridges). Set (0,0)-(2,0)H max=1 Current grid: 3-1.. \|.... 4...3 ..... 1.2.2 [Step 4...	easy	5x5	bridges_5x5dm_90e3f01b.txt	bridges	{"propagation_steps": 14, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
..2.2 ..... 2...1 ..... 4.4.1	..2-2 ..\|.\| 2.\|.1 ".\|.. 4=4-1	[Step 1] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(2,4)H to 2 [Step 2] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 [Step 3] Island (0,2) count=2 complete (2 bridges). Set (0,2)-(4,2)H max=0 Current grid: ..2.2 ..... 2...1 ".... 4=4.1 [Step 4] Subgroup isolation: (2,0...	easy	5x5	bridges_5x5dm_17511139.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
1...2 ..... .1..3 ..... 1...2	1---2 ....\| .1--3 ....\| 1---2	[Step 1] Island (1,2) count=1 needs 1, 1 active edges, must connect all. Set (1,2)-(4,2)H min=1 [Step 2] Island (1,2) count=1 complete (1 bridges). Set (1,2)-(4,2)H max=1 [Step 3] Subgroup isolation: (0,0)-(0,4)V at 1 bridges would isolate component. Set max=0 Current grid: 1...2 ..... .1--3 ..... 1...2 [Step 4] Subg...	easy	5x5	bridges_5x5dm_41e79ca2.txt	bridges	{"propagation_steps": 11, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
2...1 ..... .2..4 ..... 2...3	2---1 \|.... \|2==4 \|..." 2---3	[Step 1] Island (1,2) count=2 needs 2, has 0 with 2 spaces. Fill (1,2)-(4,2)H to 2 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(4,4)H min=1 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 Current grid: 2...1 ..... .2==4 ..... 2---3 ...	easy	5x5	bridges_5x5dm_6a9e05f6.txt	bridges	{"propagation_steps": 7, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
3.4.2 ..... ..... ..1.. 3...3	3=4-2 \|.\|.\| \|.\|.\| \|.1.\| 3===3	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,4)V min=1 [Step 3] Island (2,3) count=1 needs 1, 1 active edges, must connect all. Set (2,0)-(2,3)V min=1 Current grid: 3-4.2 \|.... \|.......	easy	5x5	bridges_5x5dm_b773735f.txt	bridges	{"propagation_steps": 11, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.3}
4.4.2 ..... ..2.. ..... 2.1.1	4=4-2 ".\|.\| ".2.\| ".\|.\| 2.1.1	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(2,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,4)V to 2 [Step 3] Island (0,4) count=2 complete (2 bridges). Set (0,4)-(2,4)H max=0 Current grid: 4=4.2 ".... ".2.. ".... 2.1.1 [Step 4] Subgroup isolation: (2,0...	easy	5x5	bridges_5x5dm_b5d7508c.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
4...3 ...1. ....3 4..3. ....2	4===3 "..1\| "..\|3 4==3" ....2	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(4,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,3)V to 2 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 Current grid: 4===3 "..1. "...3 4..3. ....2 [Step 4] Isl...	easy	5x5	bridges_5x5de_a4b955d9.txt	bridges	{"propagation_steps": 9, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
2...3 ..... 2.1.4 ..... .2..4	2---3 \|..." 2-1.4 ...." .2==4	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (1,4) count=2 needs 2, has 0 with 2 spaces. Fill (1,4)-(4,4)H to 2 Current grid: 2---3 ....\| 2.1.4 ..... .2..4 ...	easy	5x5	bridges_5x5dm_83abe13f.txt	bridges	{"propagation_steps": 8, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
..2.1 ..... 2.2.. ..... 4.5.2	..2-1 ..\|.. 2.2.. ".\|.. 4=5=2	[Step 1] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,4)-(2,4)H to 2 [Step 2] Island (0,4) count=4 needs 4, has 0 with 4 spaces. Fill (0,2)-(0,4)V to 2 [Step 3] Island (2,4) count=5 needs 5, 3 active edges, must connect all. Set (2,4)-(4,4)H min=1 Current grid: ..2.1 ..... 2.2.. ".... 4=5.2 [Step 4] Isl...	easy	5x5	bridges_5x5dm_42eed4b3.txt	bridges	{"propagation_steps": 12, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
3.2.2 ..... 2...4 ..... .1..2	3=2.2 \|..." 2---4 ....\| .1--2	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,2)V min=1 [Step 3] Island (1,4) count=1 needs 1, 1 active edges, must connect all. Set (1,4)-(4,4)H min=1 Current grid: 3-2.2 \|.... 2...4...	easy	5x5	bridges_5x5dm_806b09dd.txt	bridges	{"propagation_steps": 11, "search_nodes": 5, "backtracks": 3, "max_depth": 3, "time_ms": 0.6}
.2..3 4..4. ..... ...2. 4...3	.2==3 4==4\| ".."\| "..2\| 4===3	[Step 1] Island (1,0) count=2 needs 2, has 0 with 2 spaces. Fill (1,0)-(4,0)H to 2 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,4)V min=1 [Step 3] Island (0,1) count=4 needs 4, has 0 with 4 spaces. Fill (0,1)-(3,1)H to 2 Current grid: .2==3 4..4\| ....\| ...2\| 4...3 [Step 4] Isl...	easy	5x5	bridges_5x5de_bcd34123.txt	bridges	{"propagation_steps": 7, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
.3..4 ..... .1..3 ..... 1...2	.3==4 .\|.." .1..3 ....\| 1---2	[Step 1] Island (1,0) count=3 needs 3, 2 active edges, must connect all. Set (1,0)-(4,0)H min=1 [Step 2] Island (1,0) count=3 needs 3, 2 active edges, must connect all. Set (1,0)-(1,2)V min=1 [Step 3] Island (4,0) count=4 needs 4, has 1 with 3 spaces. Fill (1,0)-(4,0)H to 2 Current grid: .3--4 .\|... .1..3 ..... 1...2 ...	easy	5x5	bridges_5x5de_7c258e8c.txt	bridges	{"propagation_steps": 10, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
4.4.1 ..... ..2.. ..... 2.2.1	4=4-1 ".\|.. ".2.. ".\|.. 2.2-1	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(2,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,4)V to 2 [Step 3] Island (0,4) count=2 complete (2 bridges). Set (0,4)-(2,4)H max=0 Current grid: 4=4.1 ".... ".2.. ".... 2.2.1 [Step 4] Subgroup isolation: (2,0...	easy	5x5	bridges_5x5dm_a9377d9f.txt	bridges	{"propagation_steps": 12, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.2}
.1..2 ..... 2.2.4 ..... 3...2	.1--2 ....\| 2.2=4 "...\| 3---2	[Step 1] Island (1,0) count=1 needs 1, 1 active edges, must connect all. Set (1,0)-(4,0)H min=1 [Step 2] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(4,4)H min=1 [Step 3] Island (0,4) count=3 needs 3, 2 active edges, must connect all. Set (0,2)-(0,4)V min=1 Current grid: .1--2 ..... 2.2.4...	easy	5x5	bridges_5x5dm_ff891475.txt	bridges	{"propagation_steps": 7, "search_nodes": 4, "backtracks": 2, "max_depth": 3, "time_ms": 0.6}
2.3.2 ..... 1...1 ..... ..2.1	2-3-2 \|.\|.\| 1.\|.1 ..\|.. ..2-1	[Step 1] Subgroup isolation: (0,2)-(4,2)H at 1 bridges would isolate component. Set max=0 [Step 2] Subgroup isolation: (4,2)-(4,4)V at 1 bridges would isolate component. Set max=0 [Step 3] Island (0,2) count=1 needs 1, 1 active edges, must connect all. Set (0,0)-(0,2)V min=1 Current grid: 2.3.2 ..... 1...1 ..... ..2.1...	easy	5x5	bridges_5x5dm_6745c561.txt	bridges	{"propagation_steps": 8, "search_nodes": 4, "backtracks": 3, "max_depth": 3, "time_ms": 0.6}
3.4.4 ..... ..2.. ....2 2.1..	3-4=4 ".\|." ".2." ".\|.2 2.1..	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,4)V min=1 [Step 3] Island (4,0) count=4 needs 4, has 0 with 4 spaces. Fill (2,0)-(4,0)H to 2 Current grid: 3-4.4 \|.... \|.2.. \|...2 2.1.. ...	easy	5x5	bridges_5x5dm_4f8f1656.txt	bridges	{"propagation_steps": 8, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}
1.3.2 ..... 2...1 ..... 2.3..	1.3-2 \|.".\| 2.".1 \|.".. 2-3..	[Step 1] Island (2,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(2,4)H min=1 [Step 2] Island (2,4) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(2,4)V min=1 [Step 3] Island (4,2) count=1 needs 1, 1 active edges, must connect all. Set (4,0)-(4,2)V min=1 Current grid: 1.3.2 ..\|.. 2.\|.1...	easy	5x5	bridges_5x5dm_39b0bbcc.txt	bridges	{"propagation_steps": 8, "search_nodes": 4, "backtracks": 2, "max_depth": 3, "time_ms": 0.6}
..2.1 2.... ..3.. ..... 4.4.2	..2.1 2.".\| ".3.\| ".\|.\| 4=4-2	[Step 1] Island (0,1) count=2 needs 2, has 0 with 2 spaces. Fill (0,1)-(0,4)V to 2 [Step 2] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(2,2)V min=1 [Step 3] Island (2,2) count=3 needs 3, 2 active edges, must connect all. Set (2,2)-(2,4)V min=1 Current grid: ..2.1 2.\|.. ".3.. ".... 4.4.2 ...	easy	5x5	bridges_5x5dm_92312db2.txt	bridges	{"propagation_steps": 11, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
2...2 ..... ..2.. ..... 1.4.3	2---2 \|...\| \|.2.\| \|.".\| 1.4=3	[Step 1] Island (2,2) count=2 needs 2, has 0 with 2 spaces. Fill (2,2)-(2,4)V to 2 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (2,4)-(4,4)H min=1 [Step 3] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,4)V min=1 Current grid: 2...2 ..... ..2.. ..".. 1.4-3 ...	easy	5x5	bridges_5x5dm_8f22fc10.txt	bridges	{"propagation_steps": 10, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.4}
1...2 ..... 1.2.4 ..... 1...3	1---2 ....\| 1-2-4 ...." 1---3	[Step 1] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (0,4)-(4,4)H min=1 [Step 2] Island (4,4) count=3 needs 3, 2 active edges, must connect all. Set (4,2)-(4,4)V min=1 [Step 3] Island (0,4) count=1 complete (1 bridges). Set (0,4)-(4,4)H max=1 Current grid: 1...2 ..... 1.2.4 ....\| 1---3 [Step 4...	easy	5x5	bridges_5x5dm_115c8945.txt	bridges	{"propagation_steps": 14, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.3}
3.4.2 ..... ..1.. 1.... ..2.3	3=4-2 \|.\|.\| \|.1.\| 1...\| ..2=3	[Step 1] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(2,0)H min=1 [Step 2] Island (0,0) count=3 needs 3, 2 active edges, must connect all. Set (0,0)-(0,3)V min=1 [Step 3] Island (0,3) count=1 complete (1 bridges). Set (0,0)-(0,3)V max=1 Current grid: 3-4.2 \|.... \|.1.. 1.... ..2.3 [Step 4...	easy	5x5	bridges_5x5dm_3163227e.txt	bridges	{"propagation_steps": 13, "search_nodes": 4, "backtracks": 2, "max_depth": 2, "time_ms": 0.5}
4...3 ..... .2..4 3..1. ....1	4===3 "...\| "2==4 3--1\| ....1	[Step 1] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(4,0)H to 2 [Step 2] Island (0,0) count=4 needs 4, has 0 with 4 spaces. Fill (0,0)-(0,3)V to 2 [Step 3] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 Current grid: 4===3 ".... "2..4 3..1. ....1 [Step 4] Isl...	easy	5x5	bridges_5x5de_34e71202.txt	bridges	{"propagation_steps": 9, "search_nodes": 0, "backtracks": 0, "max_depth": 0, "time_ms": 0.1}
..2.3 1.... ....2 ..... 3.4.1	..2-3 1.\|." \|.\|.2 \|.\|.. 3=4-1	[Step 1] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (2,0)-(4,0)H min=1 [Step 2] Island (4,0) count=3 needs 3, 2 active edges, must connect all. Set (4,0)-(4,2)V min=1 [Step 3] Island (0,1) count=1 needs 1, 1 active edges, must connect all. Set (0,1)-(0,4)V min=1 Current grid: ..2-3 1...\| ....2...	easy	5x5	bridges_5x5dm_9d79e0d7.txt	bridges	{"propagation_steps": 10, "search_nodes": 3, "backtracks": 1, "max_depth": 2, "time_ms": 0.4}

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