62. Unique Paths

DP

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
class Solution {
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        dp[0][0] = 1;
        for (int j = 1; j < n; j++) {
            dp[0][j] = 1;
        }
        for (int i = 1; i < m; i++) {
            dp[i][0] = 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];
    }
}

DP

1
2
3
4
5
6
7
8
9
10
11
12
13
14
class Solution {
    public int uniquePaths(int m, int n) {
        int[] dp = new int[n];
        dp[0] = 1;

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

        return dp[n - 1];
    }
}

References

62. Unique Paths
剑指 Offer II 098. 路径的数目