【leetcode】 Unique Binary Search Trees

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From : https://leetcode.com/problems/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

任选一个结点作为根结点，那么这棵树的组合为其左边树的组合数目乘以右边的组合数目，即

num[i] = Σ num[k-1]*num[i-k] (1<=k<=i)

那么从小到大求可以依次求出num[i[, 最后返回num[n]即可。

class Solution {public:    int numTrees(int n) {if(n < 1) return 0;if(n < 3) return n;        vector<int> num(n+1);        num[0] = 1;        num[1] = 1;        num[2] = 2;        for(int i=3; i<=n; i++){for(int j=1; j<=i; j++)num[i] += num[j-1]*num[i-j];        }        return num[n];    }};

public class Solution {public int numTrees(int n) {if (n < 1) {return 0;}if (n < 3) {return n;}int[] num = new int[n + 1];num[0] = 1;num[1] = 1;num[2] = 2;for (int i = 3; i <= n; i++) {// length = ifor (int j = 1; j <= i; j++) {// root is jnum[i] += num[j - 1] * num[i - j];}}return num[n];}}

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