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MinimumPathSum.java
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MinimumPathSum.java
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package Leetcode;
/**
* @author kalpak
*
* 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.
*
*
* Example 1:
* Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
* Output: 7
* Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.
*
* Example 2:
* Input: grid = [[1,2,3],[4,5,6]]
* Output: 12
*
* Constraints:
*
* m == grid.length
* n == grid[i].length
* 1 <= m, n <= 200
* 0 <= grid[i][j] <= 100
*
*/
public class MinimumPathSum {
public static int minPathSum(int[][] grid) {
if(grid.length == 0 || grid == null)
return 0;
int[][] dp = new int[grid.length][grid[0].length];
dp[0][0] = grid[0][0];
for(int i = 1; i < grid.length; i++) {
dp[i][0] = dp[i - 1][0] + grid[i][0];
}
for(int i = 1; i < grid[0].length; i++) {
dp[0][i] = dp[0][i - 1] + grid[0][i];
}
for(int i = 1; i < grid.length; i++) {
for(int j = 1; j < grid[0].length; j++) {
dp[i][j] = grid[i][j] + Math.min(dp[i - 1][j], dp[i][j - 1]);
}
}
return dp[grid.length - 1][grid[0].length - 1];
}
public static void main(String[] args) {
}
}