Description
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
The original problem is here.
The original code is here.
My Solution
I solve this problem in C++, as below:
/*
*Unique Binary Search Trees
*Author: shuaijiang
*Email: zhaoshuaijiang8@gmail.com
*/
#include<iostream>
#include<vector>
#include<stdlib.h>
class Solution {
public:
int numTrees(int n) {
vector<int> nums;
nums.push_back(1);
for(int i=1;i<=n;i++){
nums.push_back(0);
if(i<=2)
nums[i] = i;
else{
for(int j=1;j<=i;j++){
nums[i] += nums[j-1]*nums[i-j];
}
}
}
return nums[n];
}
};
Note
Dynamic programming is used. For n, the number of trees is the sum of all j-1 and n-j.