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.
class Solution {
public int minPathSum(int[][] grid) {
int row = grid.length;
int col = grid[0].length;
int[][] paths = new int[row][col];
paths[0][0] = grid[0][0];
// start from 1 should include the current grid value and prev value
for (int i = 1; i < row; i++) {
paths[i][0] = grid[i][0] + paths[i - 1][0];
}
for (int i = 1; i < col; i++) {
paths[0][i] = grid[0][i] + paths[0][i - 1];
}
for (int i = 1; i < row; i++) {
for (int j = 1; j < col; j++) {
paths[i][j] = Math.min(paths[i - 1][j], paths[i][j - 1]) + grid[i][j];
}
}
return paths[row - 1][col - 1];
}
}