LintCode: Minimum Path Sum

C++,

time: O(m*n)

space: O(m*n)

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];
    }
};

C++,

time: O(m*n)

space: O(m)

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];
    }
};