LeetCode 57 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

分析：

递归，每一个作为根，对左右递归求子树个数，左右是组合关系，所以总数应该是相乘，而每个数作为根是相加关系。

public class Solution {
public int numTrees(int n) {

return numTrees(1, n);
}

public int numTrees(int start, int end){
if(start >= end)
return 1;
int total = 0;
for(int i=start; i<=end; i++)
total = total + numTrees(start, i-1)*numTrees(i+1, end);
return total;
}
}