description:
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:
Example:
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.
answer:
class Solution {
public:
int minPathSum(vector<vector<int>>& grid) {
if (grid.empty() || grid[0].empty()) return 0;
int m = grid.size(), n = grid[0].size();
vector<vector<int>> dp(m, vector<int>(n));
dp[0][0] = grid[0][0];
for (int i = 1; i < m; ++i) dp[i][0] = grid[i][0] + dp[i - 1][0]; // 边界
for (int j = 1; j < n; ++j) dp[0][j] = grid[0][j] + dp[0][j - 1]; // 边界
for (int i = 1; i < m; ++i) {
for (int j = 1; j < n; ++j) {
dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1]); // 更新条件
}
}
return dp[m - 1][n - 1];
}
};
relative point get√：
hint :
动态规划，边界情况，更新条件