[leetcode][DP] Minimum Path Sum

题目：

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.

class Solution {
public:
int minPathSum(vector<vector<int>>& grid) {
if (grid.empty()) return 0;
int m = grid.size();
int n = grid[0].size();
//创建table
vector<int> dummy(n);
vector<vector<int> > table(m);
for (int i = 0; i < m; ++i){
table[i] = dummy;
}
//初始化
table[0][0] = grid[0][0];
for (int i = 1; i < n; ++i){
table[0][i] = table[0][i - 1] + grid[0][i];
}
for (int i = 1; i < m; ++i){
table[i][0] = table[i - 1][0] + grid[i][0];
}
//可能有两种方式到达(i, j),从start到此位置的最小路径是两者中的较小值
for (int i = 1; i < m; ++i){
for (int j = 1; j < n; ++j){
table[i][j] = grid[i][j] + (table[i - 1][j] < table[i][j - 1] ? table[i - 1][j] : table[i][j - 1]);
}
}
return table[m - 1][n - 1];
}
};