代码随想录算法训练营第三十九天|动态规划part02|62.不同路径 ● 63. 不同路径 II

62.不同路径  Unique Paths - LeetCode

dp[i - 1][j] + 1 从00出发到i- 1，j这里有多少不同的路径

dp[i][j - 1] + 1 从00出发到i，j - 1这里有多少不同的路径

dp[i][j] = dp[i - 1][j] + dp[i][j - 1]

dp[0][j] = 1;

dp[i][0] = 1;

class Solution {
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        for (int i = 0; i < m; i++) dp[i][0] = 1;
        for (int j = 0; j < n; j++) dp[0][j] = 1;
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m - 1][n - 1];
    }
}

63. 不同路径 II Unique Paths II - LeetCode

for (int i = 0; i < m && dp[i][0] == 0; i++)

        dp[i][0] = 1;

class Solution {
    public int uniquePathsWithObstacles(int[][] obstacleGrid) {
        int m = obstacleGrid.length;
        int n = obstacleGrid[0].length;
        int[][] dp = new int[m][n];

        for (int i = 0; i < m && obstacleGrid[i][0] == 0; i++) {
            dp[i][0] = 1;
        }
        for (int j = 0; j < n && obstacleGrid[0][j] == 0; j++) {
            dp[0][j] = 1;
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                if (obstacleGrid[i][j] == 1) continue;
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m - 1][n - 1];
    }
}