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UniqueBinarySearchTrees.swift
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UniqueBinarySearchTrees.swift
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//
// UniqueBinarySearchTrees.swift
// LeetCode
//
// Created by 榛庤档澶儙 on 28/11/2017.
// Copyright 漏 2017 lizhaotailang. All rights reserved.
//
//
// 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
//
// Accepted. See [UniqueBinarySearchTreesTests](./LeetCodeTests/UniqueBinarySearchTreesTests.swift) for test cases.
//
import Foundation
class UniqueBinarySearchTrees {
// Recursive solution. Time limit exceeded.
// func numTrees(_ n: Int) -> Int {
// if n == 0 || n == 1 {
// return 1
// }
//
// var r = 0
// for i in 1...n {
// r += numTrees(i - 1) * numTrees(n - i)
// }
//
// return r
// }
// Dynamic programming. Accepted.
func numTrees(_ n: Int) -> Int {
var array = Array<Int>.init(repeating: 0, count: n + 2)
array[0] = 1
array[1] = 1
var i = 2
while i < (n + 1) {
for j in 0...(i - 1) {
array[i] += array[j] * array[i - j - 1]
}
i += 1
}
return array[n]
}
}