LeetCode-64. Minimum Path Sum [C++][Java]

LeetCode-64. Minimum Path SumLevel up your coding skills and quickly land a job. This is the best place to expand your knowledge and get prepared for your next interview.https://leetcode.com/problems/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 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]
Output: 7
Explanation: Because the path 1 → 3 → 1 → 1 → 1 minimizes the sum.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]
Output: 12

Constraints:

m == grid.lengthn == grid[i].length1 <= m, n <= 2000 <= grid[i][j] <= 100

class Solution {
public:
    int minPathSum(vector>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector> dp(m, vector(n, 0));
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; j++) {
                if (i == 0 && j == 0) {
                    dp[i][j] = grid[i][j];
                } else if (i == 0) {
                    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];
    }
};

压缩一下空间

class Solution {
public:
    int minPathSum(vector>& grid) {
        int m = grid.size(), n = grid[0].size();
        vector dp(n, 0);
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; j++) {
                if (i == 0 && j == 0) {
                    dp[j] = grid[i][j];
                } else if (i == 0) {
                    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];
    }
};

class Solution {
    public int minPathSum(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        int[] dp = new int[n];
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; j++) {
                if (i == 0 && j == 0) {
                    dp[j] = grid[i][j];
                } else if (i == 0) {
                    dp[j] = dp[j-1] + grid[i][j];
                } else if (j == 0) {
                    dp[j] = dp[j] + grid[i][j];
                } else {
                    dp[j] = Math.min(dp[j], dp[j-1]) + grid[i][j];
                }
            }
        }
        return dp[n-1];
    }
}