# LeetCode 279. Perfect Squares

## Description

https://leetcode.com/problems/perfect-squares/

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

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.
```

Constraints:

• `1 <= n <= 104`

## Explanation

Dynamic programming dp[i] means what is the minimum number of square numbers to add up to equal to i.

## Python Solution

``````class Solution:
def numSquares(self, n: int) -> int:

square_nums = [i**2 for i in range(0, int(sqrt(n)) + 1)]

dp = [float('inf')] * (n + 1)

dp[0] = 0

for i in range(1, n + 1):
for square in square_nums:
if i < square:
break

dp[i] = min(dp[i], dp[i - square] + 1)

return dp[n]``````
• Time Complexity: O(N).
• Space Complexity: O(N).

where Q is the length of queries and N is the length of colors.