Tuesday, April 7, 2015

LeetCode [96] Unique Binary Search Trees

 96. Unique Binary Search Trees

Medium

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

 

Constraints:

  • 1 <= n <= 19
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//C++: Recursive TLE
class Solution {
public:
    int numTrees(int n) {
        if(n==0||n==1) return 1;
        int res = 0;
        for(int i=1; i<=n; ++i){
            res += numTrees(i-1)*numTrees(n-i);
        }
        return res;
    }
};

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

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