class Solution {

    public int[] solution(int brown, int yellow) {
        int[] answer = new int[2];
        
        int sum = brown + yellow; // 12
        int hori, verti = 0;
        
        // find the possibility of hori and verti
        // condition : hori >= verti -> so i--
        for (int i = sum / 2; i > 2; i--) {
            if (sum % i == 0) {
                hori = i;
                if (check(hori, brown, yellow)) {
                    answer[0] = hori;
                    answer[1] = sum / hori;
                    break;
                }
            }
        }
        return answer;
    }
    
    private boolean check(int hori, int brown, int yellow) {
        int y_hori = hori - 2;
        
        if (yellow % y_hori != 0) return false;
        
        return true;
    }
}
/**
[Question]
return { horizontal length, vertical length }

[Condition]
- 8 <= brown <= 5000
- 1 <= yellow <= 2,000,000
- horizontal length >= vertical length

[Algorithm]
- Brute-force search : dfs (recursion)

[Logic]
- the goal : get hori, verti
- it's okay only know one variable, hori or verti
- brown must be 2 * hori + (verti - 2)
- yello must be hori - 2
**/