LintCode: Minimum Path Sum

class Solution {
public:
/**
* @param grid: a list of lists of integers.
* @return: An integer, minimizes the sum of all numbers along its path
*/
int minPathSum(vector<vector<int> > &grid) {
// write your code here
int m = grid.size(), n = grid[0].size();
vector<vector<int> > dp(m, vector<int>(n));
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i == 0) {
if (j == 0) {
dp[i][j] = grid[i][j];
} else {
dp[i][j] = dp[i][j-1] + grid[i][j];
}
} else if (j == 0) {
dp[i][j] = dp[i-1][j] + grid[i][j];
} else {
dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
}
}
}
return dp[m-1][n-1];
}
};

class Solution {
public:
/**
* @param grid: a list of lists of integers.
* @return: An integer, minimizes the sum of all numbers along its path
*/
int minPathSum(vector<vector<int> > &grid) {
// write your code here
int m = grid.size(), n = grid[0].size();
vector<int> dp(n);
for (int i = 0; i < m; i++) {
for (int j = 0; j < n; j++) {
if (i == 0) {
if (j == 0) {
dp[j] = grid[i][j];
} else {
dp[j] = dp[j-1] + grid[i][j];
}
} else if (j == 0) {
dp[j] = dp[j] + grid[i][j];
} else {
dp[j] = min(dp[j], dp[j - 1]) + grid[i][j];
}
}
}
return dp[n-1];
}
};