# 64. 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.

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(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];
for (int j = 1; j < n; ++j) dp[0][j] = grid[0][j] + dp[0][j - 1];
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]);
}
}
return dp[m - 1][n - 1];
}
};
``````

``````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<int> dp(n, INT_MAX);
dp[0] = 0;
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) {
if (j == 0) dp[j] += grid[i][j];
else dp[j] = grid[i][j] + min(dp[j], dp[j - 1]);
}
}
return dp[n - 1];
}
};
``````

``````class Solution {
public:
int minPathSum(vector<vector<int>>& grid) {
if (grid.empty() || grid[0].empty()) return 0;
for (int i = 0; i < grid.size(); ++i) {
for (int j = 0; j < grid[i].size(); ++j) {
if (i == 0 && j == 0) continue;
if (i == 0) grid[0][j] += grid[0][j - 1];
else if (j == 0) grid[i][0] += grid[i - 1][0];
else grid[i][j] += min(grid[i - 1][j], grid[i][j - 1]);
}
}
return grid.back().back();
}
};
``````

``````class Solution {
public:
int minPathSum(vector<vector<int>>& grid) {
if (grid.empty() || grid[0].empty()) return 0;
for (int i = 0; i < grid.size(); ++i) {
for (int j = 0; j < grid[i].size(); ++j) {
if (i == 0 && j == 0) continue;
int up = (i == 0) ? INT_MAX : grid[i - 1][j];
int left = (j == 0) ? INT_MAX : grid[i][j - 1];
grid[i][j] += min(up, left);
}
}
return grid.back().back();
}
};
``````

Github 同步地址：

https://github.com/grandyang/leetcode/issues/64

Unique Paths

Dungeon Game

Cherry Pickup

https://leetcode.com/problems/minimum-path-sum/

https://leetcode.com/problems/minimum-path-sum/discuss/23457/C%2B%2B-DP

https://leetcode.com/problems/minimum-path-sum/discuss/23617/C%2B%2B-solution-beat-98.59

https://leetcode.com/problems/minimum-path-sum/discuss/23611/My-Java-clean-code-DP-no-extra-space

https://leetcode.com/problems/minimum-path-sum/discuss/23678/C%2B%2B-easy-solution-using-dp.-space-compexity-%3A-O(1)

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