[DP] 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.

分析：符合DP求解条件。

递推关系：dp[i][j] = grid[i][j] + max{dp[i][j - 1], [i - 1][j]}

public class Solution {
public int minPathSum(int[][] grid) {
int row = grid.length;
int column = grid[0].length;
if (row == 0 || column == 0) {
return 0;
}

int[][] dp = new int[row][column];;
for (int i = 0; i < row; ++i) {
for (int j = 0; j < column; ++j) {
if (i == 0 && j != 0) {
dp[0][j] = dp[0][j - 1] + grid[0][j];
} else if (i != 0 && j == 0) {
dp[i][0] = dp[i-1][0] + grid[i][0];
} else if (i == 0 && j == 0) {
dp[0][0] = grid[0][0];
} else {
dp[i][j] = grid[i][j] + Math.min(dp[i][j - 1], dp[i - 1][j]);
}
}
}
return dp[row - 1][column - 1];
}
}