leetcode 力扣 62 不同路径

动态规划，填表即可很好理解

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][j - 1] + dp[i - 1][j];
            }
        }

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

空间优化，由于dp[i]只与左边的数和上边的数有关，所以可以用一维数组代替。左边的数当然就是dp[j - 1]了，上边的数就是dp[j]自己

public int uniquePaths(int m, int n) {
        int[] dp = new int[n];

        for (int i = 0; i < n; i++) {
            dp[i] = 1;
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[j] += dp[j - 1];
            }
        }

        return dp[n - 1];
    }