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35-35.5-3
35
35.5
35.5-3
docs/Chap35/35.5.md
Prove inequality $\text{(35.29)}$.
(Omit!)
[]
false
[]
35-35.5-4
35
35.5
35.5-4
docs/Chap35/35.5.md
How would you modify the approximation scheme presented in this section to find a good approximation to the smallest value not less than $t$ that is a sum of some subset of the given input list?
(Omit!)
[]
false
[]
35-35.5-5
35
35.5
35.5-5
docs/Chap35/35.5.md
Modify the $\text{APPROX-SUBSET-SUM}$ procedure to also return the subset of $S$ that sums to the value $z^\*$.
(Omit!)
[]
false
[]
35-35-1
35
35-1
35-1
docs/Chap35/Problems/35-1.md
Suppose that we are given a set of $n$ objects, where the size $s_i$ of the $i$th object satisfies $0 < s_i < 1$. We wish to pack all the objects into the minimum number of unit-size bins. Each bin can hold any subset of the objects whose total size does not exceed $1$. **a.** Prove that the problem of determining the...
(Omit!)
[]
false
[]
35-35-2
35
35-2
35-2
docs/Chap35/Problems/35-2.md
Let $G = (V, E)$ be an undirected graph. For any $k \ge 1$, define $G^{(k)}$ to be the undirected graph $(V^{(k)}, E^{(k)})$, where $V^{(k)}$ is the set of all ordered $k$-tuples of vertices from $V$ and $E^{(k)}$ is defined so that $(v_1, v_2, \dots, v_k)$ is adjacent to $(w_1, w_2, \dots, w_k)$ if and only if for $i ...
(Omit!)
[]
false
[]
35-35-3
35
35-3
35-3
docs/Chap35/Problems/35-3.md
Suppose that we generalize the set-covering problem so that each set $S_i$ in the family $\mathcal F$ has an associated weight $w_i$ and the weight of a cover $\mathcal C$ is $\sum_{S_i \in \mathcal C} w_i$. We wish to determine a minimum-weight cover. (Section 35.3 handles the case in which $w_i = 1$ for all $i$.) Sh...
(Omit!)
[]
false
[]
35-35-4
35
35-4
35-4
docs/Chap35/Problems/35-4.md
Recall that for an undirected graph $G$, a matching is a set of edges such that no two edges in the set are incident on the same vertex. In Section 26.3, we saw how to find a maximum matching in a bipartite graph. In this problem, we will look at matchings in undirected graphs in general (i.e., the graphs are not requi...
(Omit!)
[]
false
[]
35-35-5
35
35-5
35-5
docs/Chap35/Problems/35-5.md
In the **_parallel-machine-scheduling problem_**, we are given $n$ jobs, $J_1, J_2, \dots, J_n$, where each job $J_k$ has an associated nonnegative processing time of $p_k$. We are also given $m$ identical machines, $M_1, M_2, \dots, M_m$. Any job can run on any machine. A **_schedule_** specifies, for each job $J_k$, ...
(Omit!)
[]
false
[]
35-35-6
35
35-6
35-6
docs/Chap35/Problems/35-6.md
Let $G = (V, E)$ be an undirected graph with distinct edge weights $w(u, v)$ on each edge $(u, v) \in E$. For each vertex $v \in V$, let $\max(v) = \max_{(u, v) \in E} \\{w(u, v)\\}$ be the maximum-weight edge incident on that vertex. Let $S_G = \\{\max(v): v \in V\\}$ be the set of maximum-weight edges incident on eac...
(Omit!)
[]
false
[]
35-35-7
35
35-7
35-7
docs/Chap35/Problems/35-7.md
Recall the knapsack problem from Section 16.2. There are $n$ items, where the $i$th item is worth $v_i$ dollars and weighs $w_i$ pounds. We are also given a knapsack that can hold at most $W$ pounds. Here, we add the further assumptions that each weight $w_i$ is at most $W$ and that the items are indexed in monotonical...
(Omit!)
[]
false
[]
UNKNOWN-index-GettingStart
UNKNOWN
index
Getting Started
docs/index.md
This **[website](https://walkccc.github.io/CLRS/)** contains nearly complete solutions to the bible textbook - [**Introduction to Algorithms** _Third Edition_](https://mitpress.mit.edu/books/introduction-algorithms-third-edition), published by [Thomas H. Cormen](https://mitpress.mit.edu/contributors/thomas-h-cormen), [...
This **[website](https://walkccc.github.io/CLRS/)** contains nearly complete solutions to the bible textbook - [**Introduction to Algorithms** _Third Edition_](https://mitpress.mit.edu/books/introduction-algorithms-third-edition), published by [Thomas H. Cormen](https://mitpress.mit.edu/contributors/thomas-h-cormen), [...
[]
false
[]
UNKNOWN-index-Contributors
UNKNOWN
index
Contributors
docs/index.md
Thanks to the authors of [CLRS Solutions](https://sites.math.rutgers.edu/~ajl213/CLRS/CLRS.html), [Michelle Bodnar](mailto:chellebodnar@gmail.com) (who writes the even-numbered problems) and [Andrew Lohr](mailto:Andrew.Lohr@gmail.com) (who writes the odd-numbered problems), [@skanev](https://github.com/skanev), [@Cyber...
Thanks to the authors of [CLRS Solutions](https://sites.math.rutgers.edu/~ajl213/CLRS/CLRS.html), [Michelle Bodnar](mailto:chellebodnar@gmail.com) (who writes the even-numbered problems) and [Andrew Lohr](mailto:Andrew.Lohr@gmail.com) (who writes the odd-numbered problems), [@skanev](https://github.com/skanev), [@Cyber...
[]
false
[]
UNKNOWN-index-Motivation
UNKNOWN
index
Motivation
docs/index.md
I build this website since I want to help everyone learn algorithms by providing something easy to read on mobile devices.
I build this website since I want to help everyone learn algorithms by providing something easy to read on mobile devices. Therefore, if any adjustment is needed or you have the same motivation to contribute to this work, please don't hesitate to give me your feedback. You can press the "pencil icon" in the upper righ...
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false
[]
UNKNOWN-index-HowIGenerate
UNKNOWN
index
How I Generate the Website?
docs/index.md
I use the static site generator [MkDocs](http://www.mkdocs.org/) and the beautiful theme [Material for MkDocs](https://squidfunk.github.io/mkdocs-material/) to build this website.
I use the static site generator [MkDocs](http://www.mkdocs.org/) and the beautiful theme [Material for MkDocs](https://squidfunk.github.io/mkdocs-material/) to build this website. As for rendering math equations, I use [KaTeX](https://katex.org/), which is fast and beautiful. I also add `overflow-x: auto` to prevent ...
[]
false
[]
UNKNOWN-index-MoreInformat
UNKNOWN
index
More Information
docs/index.md
For a clear commit history, I rebase my repository regularly. Therefore, if you have forked the repository before, consider re-forking it again.
For a clear commit history, I rebase my repository regularly. Therefore, if you have forked the repository before, consider re-forking it again. For more information, please visit [**my GitHub**](https://github.com/walkccc). Updated to this new page on April 13, 2018, at 04:48 [(GMT+8)](https://time.is/GMT+8). Revis...
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false
[]
UNKNOWN-index-License
UNKNOWN
index
License
docs/index.md
Licensed under the MIT License.
Licensed under the MIT License.
[]
false
[]