Sunday, September 1, 2013

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

int calc(int n)
{
if(n <= 1)
return 1;
int total = 0;
for(int i = 1; i <= n; i++)
{
int left = calc(i-1);
int right  = calc(n - i);
total = total + left * right;
}
    return total;
}
int numTrees(int n) {
if(n <= 1)
return n;
return calc(n);
}

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