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CF618F, CF1836E, and the Beijing College Entrance Exam
By dfsof, history, 12 months ago, In English

These three problems are almost the same.

CF618F [Double Knapsack]: https://codeforces.com/problemset/problem/618/F

CF1836E [Twin Cluster]: https://codeforces.com/contest/1836/problem/E

Beijing College Entrance Exam:

Given two positive integer arrays $$$A$$$ and $$$B$$$, such that:

$$$len(A) = len(B) = n$$$

and

$$$\forall 1 \leq i \leq n$$$, $$$1 \leq a_i, b_i \leq n$$$.

Prove there are subsegments $$$[x, y] \subseteq [1, n]$$$, $$$[z, w] \subseteq [1, n]$$$ such that $$$\sum\limits_{i=x}^y A[i] = \sum\limits_{j=z}^w B[j]$$$. For example, $$$n=4, A=[1,2,3,4], B=[4,4,4,4]$$$, then $$$x=4, y=4, z=1, w=1$$$ is a solution.

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12 months ago, # |
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I think twin cluster is pretty different, unless you consider every problem that considers pigeon hole principle the same (it is all same mindset but setup and realization is different).

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    12 months ago, # ^ |
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    But twin cluster is also prefix sum + pigeon hole?

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      12 months ago, # ^ |
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      So is half other pigeonhole problems.

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12 months ago, # |
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I agree that Twin Cluster should not be grouped with the others. Anyway, see Putnam 1993 A4 as well.

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