Saturday, January 10, 2015

LeetCode 96: 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
public class Solution {
    public int numTrees(int n) {
        // DP problem
        // Supposed one node is root, if there is m nodes on the left, then there is n-m-1 on the right
        // The number of combination is combi(m) * combi(n-m-1)
        
        if (n < 1)
            return 0;
        
        int[] combi = new int[n+1];
        combi[0] = 1;
        
        for (int i = 1; i <= n; i++)
            for (int j = 0; j < i; j++)
                combi[i] += combi[j] * combi[i-j-1];
                
        return combi[n];
    }
}

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