279. Perfect Squares

1. Description

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.

2. Example

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

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

3. Constraints

• 1 <= n <= n <= $10^4$

4. Solutions

Dynamic Programming

n
Time complexity: O($n\sqrt{n}$)
Space complexity: O(n)

class Solution {
public:
    int numSquares(int n) {
        vector<int> min_squares(n + 1);
        for (int i = 1; i <= n; ++i) {
            min_squares[i] = i;
            for (int j = 1; j <= sqrt(i); ++j) {
                min_squares[i] = min(min_squares[i], min_squares[i - j * j] + 1);
            }
        }

        return min_squares[n];
    }
};