279. Perfect Squares.js

/**
 * @param {number} n
 * @return {number}
 */
var numSquares = function (n) {

    function isPerfectSquare(N) {
        let floorSqrt = Math.floor(Math.sqrt(N));
        return (N == floorSqrt * floorSqrt);
    }

    function legendreFunction(N) {
        // Factor out the powers of 4
        while (N % 4 == 0) N = Math.floor(N / 4);

        // N is NOT of the
        // form 4^a * (8b + 7)
        if (N % 8 != 7) return true;
        else return false;
    }

    function minSquares(N) {

        // If N is perfect square
        if (isPerfectSquare(N)) return 1;

        // If N is sum of 2 perfect squares
        for (let i = 1; i * i < N; i++)  if (isPerfectSquare(N - i * i)) return 2;


        // If N is sum of 3 perfect squares
        if (legendreFunction(N)) return 3;

        // Otherwise, N is the
        // sum of 4 perfect squares
        return 4;
    }

    return minSquares(n)
};

console.log(numSquares(n = 12));
console.log(numSquares(n = 13));