# Category: Dynamic Programming

## 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 …

## Matrix Chain Multiplication using Dynamic Programming

Matrix chain multiplication problem: Determine the optimal parenthesization of a product of n matrices.

## Find size of largest square sub-matrix of 1’s present in given binary matrix

Given a M x N binary matrix, find the size of largest square sub-matrix of 1’s present in it.

## 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.

## 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.

## Longest Bitonic Subsequence

The longest bitonic subsequence problem is to find a subsequence of a given sequence in which the subsequence’s elements are first sorted in in increasing order, then in decreasing order, and the subsequence is as long as possible.

## Longest Increasing Subsequence using Dynamic Programming

The longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence’s elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible. This subsequence is not necessarily contiguous, or unique.

## Shortest Common Supersequence using LCS

The shortest common supersequence (SCS) is the problem of finding the shortest supersequence Z of given sequences X and Y such that both X & Y are subsequences of Z.

## Shortest Common Supersequence | Finding all SCS

The shortest common supersequence (SCS) is the problem of finding the shortest supersequence Z of given sequences X and Y such that both X & Y are subsequences of Z.

## Shortest Common Supersequence | Introduction & SCS Length

The shortest common supersequence (SCS) is the problem of finding the shortest supersequence Z of given sequences X and Y such that both X & Y are subsequences of Z.

## Longest Repeated Subsequence Problem

The longest repeated subsequence (LRS) problem is the problem of finding the longest subsequences of a string that occurs at least twice.

## Longest Palindromic Subsequence using Dynamic Programming

The Longest Palindromic Subsequence (LPS) problem is the problem of finding the longest subsequences of a string that is also a palindrome.