[LeetCode][JavaScript]Unique Binary Search Trees

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

https://leetcode.com/problems/unique-binary-search-trees/

 

 

 

 

 

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生成n个节点的二叉排序树，只要求出个数。

从1到n遍历，选当前的点为根，比根小的在左子树，比根大的在右子树。

如果用递归，有很多重复计算的子树会TLE，改用DP，记住之前算过的节点。

/**
 * @param {number} n
 * @return {number}
 */
var numTrees = function(n) {
    var dp = [1, 1, 2], i, j, left, right, sum;
    for(i = 3; i <= n; i++){
        sum = 0;
        for(j = 0; j < i; j++){
            left = dp[j];
            right = dp[i - j - 1];
            sum += left * right;
        }
        dp[i] = sum;
    }
    return dp[n];
};

TLE:

/**
 * @param {number} n
 * @return {number}
 */
var numTrees_TLE = function(n) {
    var target = [];
    for(var i = 1; i <= n; i++){
        target.push(i);
    }
    return getNum(target);

    function getNum(arr){
        var sum = 0, left, right;
        if(arr.length === 2){
            return 2;
        }else if(arr.length <= 1){
            return 1;
        }
        for(var i = 0; i < arr.length; i++){
            left = getNum(arr.slice(0, i));
            right = getNum(arr.slice(i + 1, arr.length));
            sum += left * right;
        }
        return sum;
    }
};