【leetcode】96. Unique Binary Search Trees

动态规划问题入门，分解成左右两颗子树。

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

/**
* @param {number} n
* @return {number}
*/
var numTrees = function(n) {
var dp = new Array(n);
dp[0]=1;
dp[1]=1;
if(n==1){
return 1;
}
for(var i=2;i<=n;i++){
dp[i]=0;
for(var j=0;j<i;j++){
dp[i] += dp[j]*dp[i-j-1];
}
}
return dp
;
};