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A vertex cover of an undirected graph is a subset of its vertices such that for every edge (u, v) of the graph, either ‘u’ or ‘v’ is in vertex cover.

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Consider a game where a player can score 3 or 5 or 10 points in a move. Given a total score n, find number of ways to reach the given score.

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Given N jobs where every job is represented by following three elements of it. 1) Start Time 2) Finish Time. 3) Profit or Value Associated.

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Given a string ‘str’ of digits, find length of the longest substring of ‘str’, such that the length of the substring is 2k digits and sum of left k digits is equal to the sum of right k digits.

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A triangulation of a convex polygon is formed by drawing diagonals between non-adjacent vertices (corners) such that the diagonals never intersect.

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Given the mobile numeric keypad. You can only press buttons that are up, left, right or down to the current button. You are not allowed to press bottom row corner buttons (i.e. * and # ).

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Given a directed and two vertices ‘u’ and ‘v’ in it, find shortest path from ‘u’ to ‘v’ with exactly k edges on the path.

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Given a directed graph and two vertices ‘u’ and ‘v’ in it, count all possible walks from ‘u’ to ‘v’ with exactly k edges on the walk.

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Let 1 represent ‘A’, 2 represents ‘B’, etc. Given a digit sequence, count the number of possible decodings of the given digit sequence.

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Given a positive integer N, count all possible distinct binary strings of length N such that there are no consecutive 1’s.

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Catalan numbers are a sequence of natural numbers that occurs in many interesting counting problems like following.

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Given an unsorted array, trim the array such that twice of minimum is greater than maximum in the trimmed array. Elements should be removed either end of the array.

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The problem is to count all the possible paths from top left to bottom right of a mXn matrix with the constraints that from each cell you can either move only to right or down

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Travelling Salesman Problem (TSP): Given a set of cities and distance between every pair of cities, the problem is to find the shortest p

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