解决思路

排列组合

动态规划

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];
}

优化2：空间复杂度 O(n)

 public int uniquePaths(int m, int n) {
        int[] cur = new int[n];
        Arrays.fill(cur,1);
        for (int i = 1; i < m;i++){
            for (int j = 1; j < n; j++){
                cur[j] += cur[j-1] ;
            }
        }
        return cur[n-1];
    }