dynamic programming

The Coin Change Problem

Given a set of coins S with values { S1, S2, ..., Sm }, find the number of ways of making the change to a certain value N. There is an infinite quantity of coins and the order of the coins doesn't matter. This real life problem can be solved by Dynamic Programming in

dynamic programming

Box stacking Problem

Given a set of n types of 3D rectangular boxes, find the maximum height that can be reached stacking instances of these boxes. This problem can be solved efficiently by using Dynamic programming in O(N^2) time complexity and linear O(N) space complexity.

dynamic programming

0-1 Knapsack Problem

Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack.

catalan number

Catalan Numbers

Catalan Numbers are one of the widest used and evident number patterns. They are named after the Belgian mathematician Eugène Charles Catalan. A sequence of natural numbers that occur in various counting problems. The Catalan numbers are: 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786,

graph algorithm

Floyd-Warshall Algorithm: Shortest path between all pair of nodes

Floyd-Warshall Algorithm is an algorithm based on dynamic programming technique to compute the shortest path between all pair of nodes in a graph. The credit of Floyd-Warshall Algorithm goes to Robert Floyd, Bernard Roy and Stephen Warshall.