Jun 122012

Given a Matrix of positive integers and 2 cells A & B. You have to reach from A to B covering cells such that the sum of elements in path is minimum. You can travel in forward, downward and diagonally. For example: If the given Matrix is as below:

1 2 3 4 8 2 1 5 3

and you want to move from (0,0) to (2,2). Then you have to travel the following elements:

1 2 3 4 8 2 1 5 3

**Path:** 1->2->2->3

### Solution:

It is easy to visualize it recursively. If we start from the destination point and move backward. Then

Minimum Path to reach a point = Current Cell value + Minimum of paths from (top, left & top-left diagonal)

/** Print the min sum path in a matrix. if the matrix is * { {1, 2, 3}, * {4, 8, 2}, * {1, 5, 3} } *then path from (0,0) to (2,2) will be via 1->2->2->3 * * (m,n) is the last cell where we want to reach. */ int printMinPath(int arr[R][C], int m, int n) { if(m<0 || n<0) return POSOTIVE_INFINITY; if(n==0 && m==0) return arr[m][n]; // since array has only positive numbers else { int a = printMinPath(arr, m-1, n); int b = printMinPath(arr, m, n-1); int c = printMinPath(arr, m-1, n-1); return getMinimum(a, b, c) + arr[m][n]; } }

Function getMinimum(int, int, int); is a simple function which accepts 3 int values and return the minimum of them.

### One Response to “Minimum path sum in a matrix”

Comments (1)

What if the shortest path is a snake that ca go in all 8 directions?

1 1 1 1 1 1 1 1 9 9 9 9 9 9

0 0 0 0 0 0 0 1 0 0 0 0 0 9

1 1 1 1 1 1 0 1 0 0 0 0 0 9

1 0 0 0 0 1 0 1 0 0 0 0 0 9

1 0 0 1 1 1 0 1 0 0 0 0 0 9

1 0 0 1 0 0 0 1 0 0 0 0 0 9

1 0 0 1 1 1 1 1 0 0 0 0 0 9

1 0 0 0 0 0 0 0 0 0 0 0 0 9

1 1 1 1 1 1 1 1 1 1 1 1 1 1

your prgm will show only the 9 patn but not the ones path

could you pls update the correct prgm bcos i really wanted it and google search got me here

thank you.