# Category: DP

## Rod Cutting

Given a rod of length n and list of prices of rod of length i where 1 < = i

## Minimum Sum Partition problem

Given a set of positive integers S, partition the set S into two subsets S1, S2 such that the difference between the sum of elements in S1 and the sum of elements in S2 is minimized.

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## Subset sum problem

Given a set of positive integers and an integer s, is there any non-empty subset whose sum to s.

## Partition problem

Given a set of positive integers, find if it can be divided into two subsets with equal sum.

## Maximize value of the expression

Given an array A, maximize value of the expression (A[s] – A[r] + A[q] – A[p]) where l, k, j and i are indexes of the input array and s > r > q > p.

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## 0-1 Knapsack problem

Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. Items are indivisible; you either take an item or …

## Count number of paths in a matrix with given cost to reach destination cell

Given a M x N matrix where each cell have non-negative cost associated with it, count number of paths to reach last cell (M-1, N-1) of the matrix from its first cell (0, 0) such that path has given cost. We can only move one unit right or one unit down from any cell. i.e. …

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## Find longest sequence formed by adjacent numbers in the matrix

Given a N x N matrix where each cell has distinct value in the 1 to N * N. Find the longest sequence formed by adjacent numbers in the matrix such that for each number, the number on the adjacent neighbor is +1 its value.

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## Find the minimum cost to reach last cell of the matrix from its first cell

Given a M x N matrix where each cell has a cost associated with it, find the minimum cost to reach last cell (M-1, N-1) of the matrix from its first cell (0, 0). We can only move one unit right or one unit down from any cell. i.e. from cell (i, j), we can …

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## The Levenshtein distance (Edit distance) problem

Edit distance is a way of quantifying how dissimilar two strings are to one another by counting the minimum number of operations required to transform one string into the other.

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## Increasing Subsequence with Maximum Sum

Find a subsequence of a given sequence such that subsequence sum is as high as possible and subsequence’s elements are in sorted order, from lowest to highest. This subsequence is not necessarily contiguous, or unique.

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