How many structurally unique combinations of binary tree given N values

Can anyone please help me with this, I cannot understand the solution to this problem, I really have been looking at this with a nine mile stare and the combination of recursion and for loop is devastating my brain. Is there a step by step explanation that one forum user can explain to me that walks me through this dawnting code?

Quote:

Suppose you are building an N node binary search tree with the values 1..N. How many structurally different

binary search trees are there that store those values? Write a recursive function that, given the number of distinct

values, computes the number of structurally unique binary search trees that store those values. For example, countTrees(4) should return 14, since there are 14 structurally unique binary search trees that store 1, 2, 3, and 4.

Code:

`/*`

For the key values 1...numKeys, how many structurally unique

binary search trees are possible that store those keys.

Strategy: consider that each value could be the root.

Recursively find the size of the left and right subtrees.

*/

int countTrees(int numKeys) {

if (numKeys <=1) {

return(1);

}

else {

// there will be one value at the root, with whatever remains

// on the left and right each forming their own subtrees.

// Iterate through all the values that could be the root...

int sum = 0;

int left, right, root;

for (root=1; root<=numKeys; root++) {

left = countTrees(root - 1);

right = countTrees(numKeys - root);

// number of possible trees with this root == left*right

sum += left*right;

}

return(sum);

}

}