【树】Unique Binary Search Trees II

题目：

Given n, generate all structurally unique BST's (binary search trees) that store values 1...n.

For example,
Given n = 3, your program should return all 5 unique BST's shown below.

   1         3     3      2      1
    \       /     /      / \      \
     3     2     1      1   3      2
    /     /       \                 \
   2     1         2                 3

思路：

找到一个数作为根结点，剩余的数分别划入左子树或者右子树。需设置一个变量来记录左右子树能够生成的所有数。

/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {number} n
 * @return {TreeNode[]}
 */
var generateTrees = function(n) {
    if(n==0){
        return [];
    }
    return createTrees(1,n);
};
function createTrees(start,end){
    var results=[];
    if(start>end){
        results.push(null);
        return results;
    }

    for(var i=start;i<=end;i++){
        var left=createTrees(start,i-1);
        var right=createTrees(i+1,end);
        for(var j=0;j<left.length;j++){
            for(var k=0;k<right.length;k++){
                var root=new TreeNode(i);
                root.left=left[j];
                root.right=right[k];
                results.push(root);
            }
        }
    }

    return results;
}