[914] card group (X of a Kind in a Deck of Cards)

Given a deck of cards, each card are written on an integer.

At this point, you need to select a digital X, so that we can be full decks of cards according to the following rules into one or more groups:

• Each group has X cards.
• Within the group are written the same integer on all the cards.

> = 2 returns true only if you optional X.

Example 1:

Input: [1,2,3,4,4,3,2,1]
Output: true
interpretation: grouping is possible [1,1], [2,2], [3,3], [4,4 ]

Example 2:

Input: [1,1,1,2,2,2,3,3]
Output: false
interpretation: the packet does not satisfy the requirements.

Personal ideas: to get an array, the first step must be to count the number of each value is assumed 1有a个，2有b个，3有c个，4有d个to satisfy the conditions of the subject, its essence is to find a,b,c,dthere is no number (except 1) of the Convention.
E.g. Example 1, corresponding to that a=2,b=2,c=2,d=2, it has a common divisor is 2True

C#

public bool HasGroupsSizeX(int[] deck) 
{
    //1:总长度小于2直接返回
    if (deck.Length < 2) 
        return false;

    //2:统计每个数出现的次数
    //Key：该数字。   Value：该数字出现的次数
    Dictionary<int, int> NumcntDic = new Dictionary<int, int>();
    //遍历数组
    for (int i = 0; i < deck.Length; i++)
    {
        //字典键中是否包含当前数，包含，即该数已存在，则加一，不包含，即不存在，则赋值为1
        NumcntDic[deck[i]] = NumcntDic.ContainsKey(deck[i]) ? NumcntDic[deck[i]] + 1 : 1;
    }

    //3:找到字典值集合中的最小值
    int minCnt = NumcntDic.Values.Min();
    //如果最小值小于二，则返回false
    if (minCnt < 2) 
        return false;

    //若最小则是a，其他值是b
    //若满足条件，则a和b中有一个大于1的公约数
    //eg:如果最小值a=6，其他值b=15。因为a=6=2*3，b=15=3*5，存在一个大于1的公约数3
    //所以可以每组分配3个，符合条件，返回true

    //4:找到最小值a的约数大于1的集合
    //公约数集合
    List<int> comList = new List<int>();
    //从1开始，到minCnt的算术平方根结束
    for (int i = 1; i <= Math.Sqrt(minCnt); i++) 
    {
        //取余等于0
        if (minCnt % i == 0) 
        {
            //只记录大于1的约数
            if (i > 1)
                comList.Add(i);
            //若i与其对应的约数不同，则添加
            if (i != minCnt / i) 
                comList.Add(minCnt / i);
        }
    }
    //遍历所有其他值b
    foreach (int curCnt in NumcntDic.Values)
    {
        //相同不用计算
        if (curCnt != minCnt) 
        {
            //遍历最小值约数集合
            //由于遍历时，移除元素不方便
            //所以规定：集合中已舍去的约数用-1代替
            for (int i = 0; i < comList.Count; i++)
            {
                if (comList[i] != -1)
                {
                    //当前约数是公约数，则继续查找
                    if (curCnt % comList[i] == 0)
                        continue;
                    //当前约数不是公约数，则舍去，赋值为-1
                    comList[i] = -1;
                }
            }
        }
    }

    //最后检查约数集合里是否含有非-1值
    return comList.Any(com => com != -1);
}