64. Minimum Path Sum

64. Minimum Path Sum

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:

Input:
[
  [1,3,1],
  [1,5,1],
  [4,2,1]
]
Output: 7
Explanation: Because the path 1→3→1→1→1 minimizes the sum.

solution

class Solution {
   public int minPathSum(int[][] grid) {
        int rows = grid.length;
        int cols = grid[0].length;
        int[][] minValue = new int[rows][cols];

        minValue[0][0] = grid[0][0];
        //这里和求最大值不一样，需要将第一排和第一列单独进行计算
        for(int i = 1; i < rows; i++){
            minValue[i][0] = minValue[i-1][0] + grid[i][0];
        }
        for(int j = 1; j < cols; j++){
            minValue[0][j] = minValue[0][j-1] + grid[0][j];
        }

        for(int i = 1; i < rows; i ++){
            for(int j = 1; j < cols; j++){
                minValue[i][j] = Math.min(minValue[i-1][j] , minValue[i][j-1] ) + grid[i][j];
            }
        }
        return minValue[rows-1][cols-1];
    }
}