# Question

Given a positive integer n, find the least number of perfect square numbers (for example, `1, 4, 9, 16, ...`

) which sum to n.

Example 1:

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

Example 2:

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

# BFS Solution

Populate numbers that can be summed with 1, 2, 3, … perfect square numbers. It also uses an array to store results for 1, 2, …, n so it’s sort of a DP solution too.

```
from collections import deque
class Solution(object):
def numSquares(self, n):
"""
:type n: int
:rtype: int
"""
perfectSqrs = list()
i = 0
while i * i <= n:
perfectSqrs.append(i * i)
i += 1
counts = [0] * (n + 1)
q = deque()
count = 1
for sqr in perfectSqrs:
counts[sqr] = count
q.append(sqr)
if counts[-1] == 1:
return 1
while True:
newQ = deque()
count += 1
while len(q) > 0:
m = q.popleft()
for sqr in perfectSqrs:
s = m + sqr
if s < n and counts[s] == 0:
counts[s] = count
newQ.append(s)
elif s == n:
return count
elif s > n:
break
q = newQ
```