【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;
}