Programming Test - Codility - Dominator

Question

I just had a codility problem give me a hard time and I'm still trying to figure out how the space and time complexity constraints could have been met.

The problem is as follows: A dominant member in the array is one that occupies over half the positions in the array, for example:

{3, 67, 23, 67, 67}

67 is a dominant member because it appears in the array in 3/5 (>50%) positions.

Now, you are expected to provide a method that takes in an array and returns an index of the dominant member if one exists and -1 if there is none.

Easy, right? Well, I could have solved the problem handily if it were not for the following constraints:

• Expected time complexity is O(n)
• Expected space complexity is O(1)

I can see how you could solve this for O(n) time with O(n) space complexities as well as O(n^2) time with O(1) space complexities, but not one that meets both O(n) time and O(1) space.

I would really appreciate seeing a solution to this problem. Don't worry, the deadline has passed a few hours ago (I only had 30 minutes), so I'm not trying to cheat. Thanks.

Answer 1

Googled "computing dominant member of array", it was the first result. See the algorithm described on page 3.

element x;
int count ← 0;
For(i = 0 to n − 1) {
  if(count == 0) { x ← A[i]; count++; }
  else if (A[i] == x) count++;
  else count−−;
}
Check if x is dominant element by scanning array A

Basically observe that if you find two different elements in the array, you can remove them both without changing the dominant element on the remainder. This code just keeps tossing out pairs of different elements, keeping track of the number of times it has seen the single remaining unpaired element.

Answer 2

Find the median with BFPRT, aka median of medians (O(N) time, O(1) space). Then scan through the array -- if one number dominates, the median will be equal to that number. Walk through the array and count the number of instances of that number. If it's over half the array, it's the dominator. Otherwise, there is no dominator.

Answer 3

Adding a Java 100/100 O(N) time with O(1) space:

https://codility.com/demo/results/demoPNG8BT-KEH/

class Solution {
  public int solution(int[] A) {
        int indexOfCandidate = -1;
        int stackCounter = 0, candidate=-1, value=-1, i =0;

        for(int element: A ) {
            if (stackCounter == 0) {
                value = element;
                ++stackCounter;
                indexOfCandidate = i;
            } else {
                if (value == element) {
                    ++stackCounter;
                } else {
                    --stackCounter;
                }
            }
            ++i;
        }

        if (stackCounter > 0 ) {
            candidate = value;
        } else {
            return -1;
        }

        int countRepetitions = 0;
        for (int element: A) {
            if( element == candidate) {
                ++countRepetitions;

            }
            if(countRepetitions > (A.length / 2)) {
                return indexOfCandidate;
            }
        }
        return -1;
    }
}

If you want to see the Java source code it's here, I added some test cases as comments as the beginning of the file.

Answer 4

Java solution with score 100%

public  int solution(int[] array) {

    int candidate=0;
    int counter = 0;

    // Find candidate for leader
    for(int i=0; i<array.length; i++){

        if(counter == 0) candidate = i;

        if(array[i] == array[candidate]){
            counter++;
        }else {
            counter--;
        }
    }

    // Count candidate occurrences in array
    counter = 0;
    for(int i=0; i<array.length; i++){
        if(array[i] == array[candidate]) counter++;
    }

    // Check that candidate occurs more than array.lenght/2
    return counter>array.length/2 ? candidate : -1;
}

Answer 5

Here's my C solution which scores 100%

int solution(int A[], int N) {

    int candidate;
    int count = 0;
    int i;

    // 1. Find most likely candidate for the leader
    for(i = 0; i < N; i++){

        // change candidate when count reaches 0
        if(count == 0) candidate = i;

        // count occurrences of candidate
        if(A[i] == A[candidate]) count++;
        else count--;          
    }

    // 2. Verify that candidate occurs more than N/2 times
    count = 0;
    for(i = 0; i < N; i++) if(A[i] == A[candidate]) count++;

    if (count <= N/2) return -1;
    return candidate; // return index of leader
}

Answer 6

100%

import java.util.HashMap;
import java.util.Map;

class Solution {
    public static int solution(int[] A) {
        final int N = A.length;
        Map<Integer, Integer> mapOfOccur = new HashMap((N/2)+1);

        for(int i=0; i<N; i++){
            Integer count = mapOfOccur.get(A[i]);
            if(count == null){
                count = 1;
                mapOfOccur.put(A[i],count);
            }else{
                mapOfOccur.replace(A[i], count, ++count);
            }
            if(count > N/2)
                return i;

        }
        return -1;
    }
}

Answer 7

Does it have to be a particularly good algorithm? ;-)

static int dominant(final int... set) {
  final int[] freqs = new int[Integer.MAX_VALUE];
  for (int n : set) {
    ++freqs[n];
  }
  int dom_freq = Integer.MIN_VALUE;
  int dom_idx = -1;
  int dom_n = -1;
  for (int i = set.length - 1; i >= 0; --i) {
    final int n = set[i];
    if (dom_n != n) {
      final int freq = freqs[n];
      if (freq > dom_freq) {
        dom_freq = freq;
        dom_n = n;
        dom_idx = i;
      } else if (freq == dom_freq) {
        dom_idx = -1;
      }
    }
  }
  return dom_idx;
}

(this was primarily meant to poke fun at the requirements)

Answer 8

In python, we are lucky some smart people have bothered to implement efficient helpers using C and shipped it in the standard library. The collections.Counter is useful here.

>>> data = [3, 67, 23, 67, 67]
>>> from collections import Counter
>>> counter = Counter(data)  # counter accepts any sequence/iterable
>>> counter  # dict like object, where values are the occurrence 
Counter({67: 3, 3: 1, 23: 1})
>>> common = counter.most_common()[0]
>>> common
(67, 3)
>>> common[0] if common[1] > len(data) / 2.0 + 1 else -1
67
>>>

If you prefer a function here is one ...

>>> def dominator(seq):
        counter = Counter(seq)
        common = counter.most_common()[0]
        return common[0] if common[1] > len(seq) / 2.0 + 1 else -1
...
>>> dominator([1, 3, 6, 7, 6, 8, 6])
-1
>>> dominator([1, 3, 6, 7, 6, 8, 6, 6])
6

Answer 9

This question looks hard if a small trick does not come to the mind :). I found this trick in this document of codility : https://codility.com/media/train/6-Leader.pdf.

The linear solution is explained at the bottom of this document.

I implemented the following java program which gave me a score of 100 on the same lines.

public int solution(int[] A) {

    Stack<Integer> stack = new Stack<Integer>();

    for (int i =0; i < A.length; i++)
    {
        if (stack.empty())
            stack.push(new Integer(A[i]));
        else
        {
            int topElem = stack.peek().intValue();
            if (topElem == A[i])
            {
                stack.push(new Integer(A[i]));
            }
            else
            {
                stack.pop();
            }
        }            
    }

    if (stack.empty())
        return -1;

    int elem = stack.peek().intValue();
    int count = 0;
    int index = 0;
    for (int i = 0; i < A.length; i++)
    {
        if (elem == A[i])
        {
            count++;
            index = i;
        }
    }

    if (count > ((double)A.length/2.0))
        return index;
    else
        return -1;
}

Answer 10

Consider this 100/100 solution in Ruby:

# Algorithm, as described in https://codility.com/media/train/6-Leader.pdf:
#
# * Iterate once to find a candidate for dominator.
# * Count number of candidate occurences for the final conclusion.
def solution(ar)
  n_occu = 0
  candidate = index = nil

  ar.each_with_index do |elem, i|
    if n_occu < 1
      # Here comes a new dominator candidate.
      candidate = elem
      index = i
      n_occu += 1
    else
      if candidate == elem
        n_occu += 1
      else
        n_occu -= 1
      end
    end # if n_occu < 1
  end

  # Method result. -1 if no dominator.
  # Count number of occurences to check if candidate is really a dominator.
  if n_occu > 0 and ar.count {|_| _ == candidate} > ar.size/2
    index
  else
    -1
  end
end

#--------------------------------------- Tests

def test
  sets = []
  sets << ["4666688", [1, 2, 3, 4], [4, 6, 6, 6, 6, 8, 8]]
  sets << ["333311", [0, 1, 2, 3], [3, 3, 3, 3, 1, 1]]
  sets << ["313131", [-1], [3, 1, 3, 1, 3, 1]]
  sets << ["113333", [2, 3, 4, 5], [1, 1, 3, 3, 3, 3]]

  sets.each do |name, one_of_expected, ar|
    out = solution(ar)
    raise "FAILURE at test #{name.inspect}: #{out.inspect} not in #{expected.inspect}" if not one_of_expected.include? out
  end

  puts "SUCCESS: All tests passed"
end

Answer 11

Here is an easy to read, 100% score version in Objective-c

  if (A.count > 100000)
    return -1;
NSInteger occur = 0;
NSNumber *candidate = nil;
for (NSNumber *element in A){
    if (!candidate){
        candidate = element;
        occur = 1;
        continue;
    }

    if ([candidate isEqualToNumber:element]){
        occur++;
    }else{
        if (occur == 1){
            candidate = element;
            continue;
        }else{
            occur--;
        }
    }
}
if (candidate){
    occur = 0;
    for (NSNumber *element in A){
        if ([candidate isEqualToNumber:element])
            occur++;
    }
    if (occur > A.count / 2)
        return [A indexOfObject:candidate];
}
return -1;

Answer 12

100% score JavaScript solution. Technically it's O(nlogn) but still passed.

function solution(A) {
  if (A.length == 0)
    return -1;

  var S = A.slice(0).sort(function(a, b) {
    return a - b;
  });

  var domThresh = A.length/2;
  var c = S[Math.floor(domThresh)];
  var domCount = 0;

  for (var i = 0; i < A.length; i++) {
    if (A[i] == c)
      domCount++;

    if (domCount > domThresh)
      return i;
  }

  return -1;
}

Answer 13

This is the solution in VB.NET with 100% performance.

Dim result As Integer = 0
        Dim i, ladderVal, LadderCount, size, valCount As Integer
        ladderVal = 0
        LadderCount = 0
        size = A.Length
        If size > 0 Then


            For i = 1 To size - 1
                If LadderCount = 0 Then
                    LadderCount += 1
                    ladderVal = A(i)
                Else
                    If A(i) = ladderVal Then
                        LadderCount += 1
                    Else
                        LadderCount -= 1
                    End If
                End If
            Next
            valCount = 0
            For i = 0 To size - 1
                If A(i) = ladderVal Then
                    valCount += 1
                End If
            Next
            If valCount <= size / 2 Then
                result = 0
            Else
                LadderCount = 0
                For i = 0 To size - 1
                    If A(i) = ladderVal Then
                        valCount -= 1
                        LadderCount += 1
                    End If
                    If LadderCount > (LadderCount + 1) / 2 And (valCount > (size - (i + 1)) / 2) Then
                        result += 1
                    End If
                Next
            End If
        End If
        Return result

See the correctness and performance of the code

Answer 14

Below solution resolves in complexity O(N).

public int solution(int A[]){
    int dominatorValue=-1;
    if(A != null && A.length>0){
        Hashtable<Integer, Integer> count=new Hashtable<>();
        dominatorValue=A[0];
        int big=0;
        for (int i = 0; i < A.length; i++) {
            int value=0;
            try{
                value=count.get(A[i]);
                value++;
            }catch(Exception e){
            }
            count.put(A[i], value);
            if(value>big){
                big=value;
                dominatorValue=A[i];
            }
        }
    }
    return dominatorValue;
}

Answer 15

100% in PHP https://codility.com/demo/results/trainingVRQGQ9-NJP/

function solution($A){

    if (empty($A)) return -1;

    $copy = array_count_values($A);  // 3 => 7, value => number of repetition

    $max_repetition = max($copy); // at least 1 because the array is not empty

    $dominator = array_search($max_repetition, $copy);

    if ($max_repetition > count($A) / 2) return array_search($dominator, $A); else return -1;

}

Answer 16

i test my code its work fine in arrays lengths between 2 to 9

public static int sol (int []a)
{
    int count = 0 ;
    int candidateIndex = -1;
    for (int i = 0; i <a.length ; i++)
    {
        int nextIndex = 0;
        int nextOfNextIndex = 0;

        if(i<a.length-2)
        {
            nextIndex = i+1;
            nextOfNextIndex = i+2;
        }
        if(count==0)
        {
            candidateIndex = i;
        }
        if(a[candidateIndex]== a[nextIndex])
        {
            count++;

        }
        if (a[candidateIndex]==a[nextOfNextIndex])
        {
            count++;

        }


    }
    count -- ;
    return count>a.length/2?candidateIndex:-1;
}

Answer 17

Adding a Java 100/100 O(N) time with O(1) space:

// you can also use imports, for example:
import java.util.Stack;

// you can write to stdout for debugging purposes, e.g.
// System.out.println("this is a debug message");

class Solution {
    public int solution(int[] A) {
        // write your code in Java SE 8
        int count = 0;
        Stack<Integer> integerStack = new Stack<Integer>();
        for (int i = 0; i < A.length; i++) {
            if (integerStack.isEmpty()) {
                integerStack.push(A[i]);
            } else if (integerStack.size() > 0) {
                if (integerStack.peek() == A[i])
                    integerStack.push(A[i]);
                else
                    integerStack.pop();
            }
        }
        if (!integerStack.isEmpty()) {
            for (int i = 0; i < integerStack.size(); i++) {
                for (int j = 0; j < A.length; j++) {
                    if (integerStack.get(i) == A[j])
                        count++;
                    if (count > A.length / 2)
                        return j;
                }
                count = 0;
            }
        }
        return -1;
    }
}

Here is test result from codility.

Answer 18

I think this question has already been resolved somewhere. The "official" solution should be :

  public int dominator(int[] A) {
    int N = A.length;

    for(int i = 0; i< N/2+1; i++)
    {
        int count=1;
        for(int j = i+1; j < N; j++)
        {
            if (A[i]==A[j]) {count++; if (count > (N/2)) return i;}
        }
    }

    return -1;
  }

Answer 19

How about sorting the array first? You then compare middle and first and last elements of the sorted array to find the dominant element.

public Integer findDominator(int[] arr) {
    int[] arrCopy = arr.clone();

    Arrays.sort(arrCopy);

    int length = arrCopy.length;
    int middleIndx = (length - 1) /2;

    int middleIdxRight;
    int middleIdxLeft = middleIndx;

    if (length % 2 == 0) {
        middleIdxRight = middleIndx+1;
    } else {
        middleIdxRight = middleIndx;
    }

    if (arrCopy[0] == arrCopy[middleIdxRight]) {
        return arrCopy[0];
    }

    if (arrCopy[middleIdxLeft] == arrCopy[length -1]) {
        return arrCopy[middleIdxLeft];
    }

    return null;
}

Answer 20

C#

int dominant = 0;
        int repeat = 0;
        int? repeatedNr = null;
        int maxLenght = A.Length;
        int halfLenght = A.Length / 2;
        int[] repeations = new int[A.Length];

        for (int i = 0; i < A.Length; i++)
        {
            repeatedNr = A[i];
            for (int j = 0; j < A.Length; j++)
            {
                if (repeatedNr == A[j])
                {
                    repeations[i]++;
                }
            }
        }
        repeatedNr = null;
        for (int i = 0; i < repeations.Length; i++)
        {
            if (repeations[i] > repeat)
            {
                repeat = repeations[i];
                repeatedNr = A[i];
            }
        }
        if (repeat > halfLenght)
            dominant = int.Parse(repeatedNr.ToString());

Answer 21

class Program
{
    static void Main(string[] args)
    {
        int []A= new int[] {3,6,2,6};
        int[] B = new int[A.Length];
        Program obj = new Program();
        obj.ABC(A,B);

    }

    public int ABC(int []A, int []B)
    { 
        int i,j;

        int n= A.Length;
        for (j=0; j<n ;j++)
        {
            int count = 1;
            for (i = 0; i < n; i++)
            {
                if ((A[j]== A[i] && i!=j))
                {
                    count++;

                }

             }
           int finalCount = count;
            B[j] = finalCount;// to store the no of times a number is repeated 

        }
       // int finalCount = count / 2;
        int finalCount1 = B.Max();// see which number occurred max times
        if (finalCount1 > (n / 2))
        { Console.WriteLine(finalCount1); Console.ReadLine(); }

        else
        { Console.WriteLine("no number found"); Console.ReadLine(); }
        return -1;
    }
}

Answer 22

In Ruby you can do something like

def dominant(a)
  hash = {}
  0.upto(a.length) do |index|
    element = a[index]
    hash[element] = (hash[element] ? hash[element] + 1 : 1)
  end

  res = hash.find{|k,v| v > a.length / 2}.first rescue nil
  res ||= -1
  return res
end

Answer 23

@Keith Randall solution is not working for {1,1,2,2,3,2,2}

his solution was:

element x;
int count ← 0;
For(i = 0 to n − 1) {
  if(count == 0) { x ← A[i]; count++; }
  else if (A[i] == x) count++;
  else count−−;
}
Check if x is dominant element by scanning array A

I converted it into java as below:

int x = 0;
int count = 0;

for(int i = 0; i < (arr.length - 1); i++) {

    if(count == 0) {
        x = arr[i];
        count++;
    }
    else if (arr[i] == x)
        count++;

    else count--;
}

return x;

Out put : 3 Expected: 2

Answer 24

This is my answer in Java: I store a count in seperate array which counts duplicates of each of the entries of the input array and then keeps a pointer to the array position that has the most duplicates. This is the dominator.

private static void dom(int[] a) {
        int position = 0;
        int max = 0;
        int score = 0;
        int counter = 0;
        int[]result = new int[a.length];

        for(int i = 0; i < a.length; i++){
            score = 0;
            for(int c = 0; c < a.length;c++){

                if(a[i] == a[c] && c != i ){
                    score = score + 1;
                    result[i] = score; 
                    if(result[i] > position){
                        position = i;
                    }
            }

            }
        }


                 //This is just to facilitate the print function and MAX = the number of times that dominator number was found in the list.

        for(int x = 0 ; x < result.length-1; x++){
            if(result[x] > max){
                max = result[x] + 1;
            }

        }




  System.out.println(" The following number is the dominator " + a[position] +  " it appears a total of " + max);





}