https://leetcode.com/problems/unique-binary-search-trees/
Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?
Example:
Input: 3 Output: 5 Explanation: 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
代码:
class Solution { public: int numTrees(int n) { vector<int> dp(n + 1, 0); dp[0] = 1; dp[1] = 1; for(int i = 2; i <= n; i ++) { for(int j = 0; j < i; j ++) dp[i] += dp[j] * dp[i - j - 1]; } return dp[n]; } };
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
#include <bits/stdc++.h> using namespace std; long long mod = 1e9 + 7; int main() { int n; long long sum; long long dp[3005]; dp[0] = 1; dp[1] = 1; dp[2] = 2; dp[3] = 5; for(int i = 4; i <= 3000; i ++) { int tem = i; int cnt = tem / 2; sum = 0; for(int j = 0; j < cnt; j ++) sum += (dp[j] * dp[tem - 1 - j] * 2) % mod; if(tem % 2 == 1) sum += (dp[cnt] * dp[cnt]) % mod; dp[i] += sum % mod; } while(~scanf("%d", &n)) printf("%lld ", dp[n]); return 0; }
卡特兰数 人生中第二次遇见 好吧我还是认不出