279. Perfect Squares

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.

// Dynamic programming
int numSquares(int n) { // time: O(n^1.5); space: O(n)
    if (n <= 0) return 0;
    vector<int> dp(n + 1, 1e8);
    dp[0] = 0;
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j * j <= i; ++j) {
            dp[i] = min(dp[i], dp[i - j * j] + 1);
        }
    }
    return dp.back();
}

// Math
int numSquares(int n) {
    while (n % 4 == 0) n /= 4;
    if (n % 8 == 7) return 4;
    for (int a = 0; a * a <= n; ++a) {
        int b = sqrt(n - a * a);
        if (a * a + b * b == n) {
            return !!a + !!b;
        }
    }
    return 3;
}