The longest common subsequence (LCS) problem is the problem of finding the longest subsequence common to all sequences in a set of sequences (often just two sequences).

Graph Coloring is a way of coloring the vertices of a undirected graph such that no two adjacent vertices share the same color.

Subset sum problem is to find subset of elements that are selected from a given set whose sum adds up to a given number K.

The n queens puzzle is the problem of placing eight chess queens on an n×n chessboard so that no two queens threaten each other. Thus, a solution requires that no two queens share the same row, column, or diagonal.

The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a mass 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.

In 0-1 Knapsack, the restriction is that, one cannot select fraction of any item. He/She must select either whole item or try with alternate one.

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All pair shortest path algorithm is used to find shortest distance between each pair of vertices.