[leetCode]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


主要是递归的思想，大数的分支都是小树组成的，存在组合思想的都可以考虑递归。将一个大数划分为小数的集合，自己写个n=3，n=5的就可以知道了，使用map容器可以极大提高效率

#include <iostream>
#include <map>
using namespace std;
class Solution {
public:
    map<int,int> imap;
    map<int,int> ::iterator iter;
    int numTrees(int n) {
        if(n <= 0)    return 0;
        return pathNumcalc(n);
    }
private:
    int pathNumcalc(int n){
        int left,right,sum;
        left = right = sum = 0;
        iter = imap.find(n);
        if(iter != imap.end()) return iter->second;
        if(n == 0)    sum = 0;
        if(n == 1)  sum = 1;
        for(int i = 1; i <= n; i++){
            left = pathNumcalc(i-1);
            right = pathNumcalc(n-i);
            if(left == 0)        sum+=right;
            else if(right == 0)    sum+=left;
            else sum+=left*right;
        }
        imap.insert(pair<int,int>(n,sum));
        return sum;
    }
};