Leetcode:Unique Binary Search Trees
2015-02-10 10:50:06      个评论    来源：Luis的个人博客

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```

```/**
* Taking 1~n as root respectively:
*      1 as root: # of trees = F(0) * F(n-1)  // F(0) == 1
*      2 as root: # of trees = F(1) * F(n-2)
*      3 as root: # of trees = F(2) * F(n-3)
*      ...
*      n-1 as root: # of trees = F(n-2) * F(1)
*      n as root:   # of trees = F(n-1) * F(0)
*
* So, the formulation is:
*      F(n) = F(0) * F(n-1) + F(1) * F(n-2) + F(2) * F(n-3) + ... + F(n-2) * F(1) + F(n-1) * F(0)
*/
class Solution {
public:
int numTrees(int n) {
int dp[n+1];
dp = dp = 1;
for (int i=2; i<=n; i++) {
dp[i] = 0;
for (int j=1; j<=i; j++) {
dp[i] += dp[j-1] * dp[i-j];
}
}
return dp[n];
}
};```