leetcode 96. Unique Binary Search Trees

Given n, how many structurally unique BST's (binary search trees) that store values 1...n?

For example,
Given n = 3, there are a total of 5 unique BST's.

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3


class Solution {
public:
    int numTrees(int n) {
        int dp[n + 1] = {0};
        dp[0] = 1;
        dp[1] = 1;
        for(int i = 2; i <= n; i++) {
            for(int j = 1; j <= i; j++) {
                dp[i] += dp[j - 1] * dp[i - j];
            }
        }

        return dp[n];
    }
};

可以根据左右对称性对问题做进一步优化。

呼呼呼山(http://code4fun.me)
2 May 2017 7:32 PM