int minPathSum(vector<vector<int>>& grid) {

// Start typing your C/C++ solution below

// DO NOT write int main() function

int m = grid.size();

if (m == 0) return 0;

int n = grid[0].size();

vector<vector<int>> dp(m, vector<int>(n, 0));

dp[0][0] = grid[0][0];

for (int i = 1; i < m; i++)

dp[i][0] = dp[i-1][0] + grid[i][0];

for (int j = 1; j < n; j++)

dp[0][j] = dp[0][j-1] + grid[0][j];

for (int i = 1; i < m; i++) {

for (int j = 1; j < n; j++)

dp[i][j] = min(dp[i-1][j], dp[i][j-1]) + grid[i][j];

}

return dp[m-1][n-1];

}

int minPathSum(vector<vector<int> > &grid) {

if (grid.empty()) {

return 0;

}

int m = grid.size();

int n = grid[0].size();

vector<vector<int>> dp(2, vector<int>(n, 0));

int T1 = 1;

int T2 = 0;

for (int i = 0; i < m; i++) {

T1 ^= 1;

T2 ^= 1;

dp[T2][0] = dp[T1][0] + grid[i][0];

for (int j = 1; j < n; j++) {

if (i == 0) {

dp[T2][j] = dp[T2][j-1] + grid[i][j];

} else {

dp[T2][j] = grid[i][j] + min(dp[T1][j], dp[T2][j-1]);

}

}

}

return dp[T2][n-1];

}