23. Perfect Squares

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: (DP)

Approach: Base case:- n = 1 = 1 n = 2 = 2 n = 3 = 3 Checking for all values greater than 4 by creating square breakpoints

class Solution
{
public:
    int numSquares(int n)
    {

        vector<int> v(n + 1);
        for (int i = 1; i <= n; i++)
        {
            v[i] = i;
        }

        for (int i = 4; i <= n; i++)
        {

            for (int j = 1; j * j <= i; j++)
            {
                v[i] = min(v[i], 1 + v[i - j * j]);
            }
        }

        return v[n];
    }
};

Time Complexity: O(n sqrt(n) )