96. Unique Binary Search Trees

• Difficulty: Medium

• Topics: Dynamic Programming, Tree

• Similar Questions:

  • Unique Binary Search Trees II

Problem:

Given n, how many structurally unique BST's (binary search trees) that store values 1 ... n?

Example:

Input: 3
Output: 5
Explanation:
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

Solutions:

class Solution {
public:
    int numTrees(int n) {
        map<pair<int, int>, int> cache;
        return helper(1, n, cache);
    }

    int helper(int left, int right, map<pair<int, int>, int>& cache) {
        if (left > right)   return 1; // return 1!
        if (left == right)  return 1;
        auto range = make_pair(left, right);
        if (cache.count(range) != 0)    return cache[range];
        int count = 0;
        for (int num = left; num <= right; ++num) {
            count += helper(left, num - 1, cache) * helper(num + 1, right, cache);
        }

        cache[range] = count;
        return count;
    }
};