LeetCode - Unique Binary Search Trees
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Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
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
http://oj.leetcode.com/problems/unique-binary-search-trees/
Consider from 0. If n = 0, res = 1; n = 1, res = 1; n = 2, res = 2; n = 3, res = 5. Use dp method.
Assume there is a count[] that count[n] means the number of unique BSTs that {1, ..., n} can create.
count[2] = num of BST with root 1 + num of BST with root 2, which is count[0] * count[1] + count[1] * count[0].
count[3] = num of BST with root 1 + num of BST with root 2 + num of BST with root 3, which is count[0] * count[2] + count[1] * count[1] + count[2] * count[0].
Obviously we find that count[j] = sum(count[0, ..., i-1] * count[i-1, .., 0]).
Another way if you are familiar with combinatorial mathematics, this is catalan number. http://en.wikipedia.org/wiki/Catalan_number
In that case it is much simpler.
https://github.com/starcroce/leetcode/blob/master/unique_binary_search_trees.cpp
// 4 ms for 14 test cases// Given n, how many structurally unique BST's (binary search trees) that store values 1...n?class Solution {public: int numTrees(int n) { // Note: The Solution object is instantiated only once and is reused by each test case. int count[n]; for(int i = 0; i <= n; i++) { count[i] = 0; } count[0] = 1; count[1] = 1; for(int i = 2; i <= n; i++) { for(int j = 0; j < i; j++) { count[i] += count[j] * count[i-j-1]; } } return count[n]; }};
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