# Perfect Squares Problem

## Description

LeetCode Problem 279.

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:

``````1
2
3
Input: n = 12
Output: 3
Explanation: 12 = 4 + 4 + 4.
``````

Example 2:

``````1
2
3
Input: n = 13
Output: 2
Explanation: 13 = 4 + 9.
``````

Constraints:

• 1 <= n <= 10^4

## Sample C++ Code

``````1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
class Solution {
public:
int numSquares(int n) {
vector<int> squares;
int i = 1;
while (i*i <= n) {
squares.push_back(i*i);
i ++;
}

queue<int> bfsQ;
bfsQ.push(n);

int len, curr, threshold = 0;
int level = 0;
while (!bfsQ.empty()) {
len = bfsQ.size();
for (int i = 0; i < len; i ++) {
curr = bfsQ.front();
bfsQ.pop();
if (curr == 0)
return level;
threshold = curr / 3;
for (int j = squares.size() - 1; j >= 0; j --) {
if (squares[j] > curr)
continue;
bfsQ.push(curr - squares[j]);
if (squares[j] < threshold)
break;
}
}
level ++;
}
return level;
}
};
``````