// Name:  Rushil Umaretiya
// Date: 08/26/19

public class Modes
{
    public static void main (String[] args)
    {
        int[] tally = {0,0,10,5,10,0,7,1,0,6,0,10,3,0,0,1};
        display(tally);
        int[] modes = calculateModes(tally);
        display(modes);
        int sum = 0;
        for(int k = 0; k < tally.length; k++)
            sum += tally[k];
        System.out.println("kth \tindex"); 
        for(int k = 1; k <= sum; k++)
            System.out.println(k + "\t\t" + kthDataValue(tally, k));
}
      
   /**
    * precondition: tally.length > 0
    * postcondition: returns an int array that contains the modes(s);
    *                the array's length equals the number of modes.
    */
    public static int[] calculateModes(int[] tally)
    {
        int maxValue = findMax(tally);
        int modeCount = 0;
        for (int x = 0; x<tally.length;x++) 
            if (maxValue == tally[x]) 
               modeCount++;
            
        
        int index = 0;
        int[] modeArray = new int[modeCount];
        for (int x = 0; x<tally.length;x++) {
            if (maxValue == tally[x]) {
               modeArray[index] = x;
               index++;
            }
        }
        
        return modeArray;
        
    }
      
   /**  
    * precondition:  tally.length > 0
    * 	             0 < k <= total number of values in data collection
    * postcondition: returns the kth value in the data collection
    *                represented by tally
    */
    public static int kthDataValue(int[] tally, int k)
    {
        int dataLength = 0;
        for (int x = 0; x<tally.length; x++)
            dataLength += tally[x];
        int[] frequencyArray = new int[dataLength];
        int index = 0;
        for(int x = 0; x<tally.length; x++) {
            int frequency = tally[x];
            for (int y = 0; y<frequency; y++) {
               frequencyArray[index] = x;
               index++;
            }
        }
        return frequencyArray[k-1];
    }
      
   /**
    * precondition:  nums.length > 0
    * postcondition: returns the maximal value in nums
    */
    public static int findMax(int[] nums)
    {
        int pos = 0;
        for(int k = 1; k < nums.length; k++)
            if(nums[k] > nums[pos])
                pos = k;
            return nums[pos];
    }
    
    public static void display(int[] args)
    {
        for(int k = 0; k < args.length; k++)
            System.out.print(args[k] + " ");
        System.out.println();
        System.out.println();
    }
}