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MinimumPathSum.java

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/**

* Given a m x n grid filled with non-negative numbers, find a path from top

* left to bottom right which minimizes the sum of all numbers along its path.

*

* Note: You can only move either down or right at any point in time.

*/

public class MinimumPathSum {

public int minPathSum(int[][] grid) {

int[][] path = new int[grid.length][grid[0].length];

path[0][0] = grid[0][0];

for (int i = 1; i < grid.length; i++) {

path[i][0] = path[i - 1][0] + grid[i][0];

}

for (int j = 1; j < grid[0].length; j++) {

path[0][j] = path[0][j - 1] + grid[0][j];

}

for (int i = 1; i < grid.length; i++)

for (int j = 1; j < grid[0].length; j++) {

path[i][j] = Math.min(path[i - 1][j], path[i][j - 1])

+ grid[i][j];

}

return path[grid.length - 1][grid[0].length - 1];

}

}