[LeetCode] 96. Unique Binary Search Trees

轉自LeetCode

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

<Solution>

這題就是要專有的公式解，叫做 Catalan Number

Catalan Number 除了可以來計算由 1 到 n 個正整數組成的 unique BST 外

還有其他題目也可以應用，詳情請看連結

主要要把這個公式記下來



code 如下

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

view raw uniqueBinarySearchTree.cpp hosted with ❤ by GitHub