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.
经典动态规划。
状态方程: dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
public class Solution {
public int minPathSum(int[][] grid) {
if(grid == null) {
return 0;
}
int rows = grid.length;
int cols = grid[0].length;
int[][] dp = new int[rows][cols];
dp[0][0] = grid[0][0];
// initialize the first row
for(int i = 1; i < cols; i++) {
dp[0][i] = dp[0][i - 1] + grid[0][i];
}
//initialize the first col
for(int i = 1; i < rows; i++) {
dp[i][0] = dp[i - 1][0] + grid[i][0];
}
for(int i = 1; i < rows; i++) {
for(int j = 1; j < cols; j++) {
dp[i][j] = Math.min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
}
}
return dp[rows - 1][cols - 1];
}
}