# 279. Perfect Squares

Question link is here.

# Question

Given an integer n, return the least number of perfect square numbers that sum to n.

A perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 1, 4, 9, and 16 are perfect squares while 3 and 11 are not.

Example 1:

Input: n = 12
Output: 3
Explanation: 12 = 4 + 4 + 4.

Example 2:

Input: n = 13
Output: 2
Explanation: 13 = 4 + 9. 

# Solution

This is obviously a greedy problem.

For 1 to n, we try to find the smallest i that the n can be the sum of exactly i square numbers.

And order to check whether a number is square number, we can use a HashSet to store those number.

# Java

class Solution {
    HashSet<Integer> candidates = new HashSet<Integer>();
    int res;
    public int numSquares(int n) {
        for(int i = 1; i* i <= n; i++) {
            candidates.add(i*i);
        }
        int i = 1;
        for(i = 1; i <= n; i++) {
            if(helper(n, i))
                return i;
        }
        return i;
    }
    
    public boolean helper(int n, int level) {
        if(level == 1) {
            return candidates.contains(n);
        }
        for(Integer i : candidates) {
            if(helper(n - i, level - 1))
                return true;
        }
        return false;
    }
}

# Python

class Solution:
    def numSquares(self, n: int) -> int:
        candidates = set()
        for i in range(1, int(n ** 0.5) + 1):
            candidates.add(i * i)
        
        def helper(n, level):
            if level == 1:
                return n in candidates
            for num in candidates:
                if helper(n - num, level-1):
                    return True
            return False
        
        for i in range(1, n+1):
            if helper(n, i):
                return i
        

Time Complexity $O(n^{\frac{h}{2}})$.