Counting Sort Algorithm in DSA Javascript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Counting Sort on a small array

What is the output of the following counting sort implementation on the array [4, 2, 2, 8, 3, 3, 1]?

DSA Javascript

function countingSort(arr) {
  const max = Math.max(...arr);
  const count = new Array(max + 1).fill(0);
  for (const num of arr) {
    count[num]++;
  }
  let sortedIndex = 0;
  for (let i = 0; i < count.length; i++) {
    while (count[i] > 0) {
      arr[sortedIndex++] = i;
      count[i]--;
    }
  }
  return arr;
}

console.log(countingSort([4, 2, 2, 8, 3, 3, 1]));

A [1, 2, 3, 4, 8]

B [1, 2, 2, 3, 3, 4, 8]

C [8, 4, 3, 3, 2, 2, 1]

D [1, 1, 2, 2, 3, 3, 4, 8]

💡 Hint

Counting sort counts how many times each number appears and then rebuilds the array in order.

The counting sort counts the frequency of each number and then places them back in sorted order. The input array has one 1, two 2s, two 3s, one 4, and one 8. So the sorted array is [1, 2, 2, 3, 3, 4, 8].

🧠 Conceptual

intermediate

Counting Sort Stability Property

Which statement correctly describes the stability of counting sort?

A Counting sort is unstable because it uses a hash map internally.

B Counting sort is unstable because it rearranges equal elements randomly.

C Counting sort is stable only if the input array is already sorted.

D Counting sort is stable because it preserves the relative order of equal elements.

💡 Hint

Think about whether equal numbers keep their original order after sorting.

Counting sort is stable because it places elements in the output array in the order they appear in the input, preserving the relative order of equal elements.

🔧 Debug

advanced

Identify the error in this counting sort code

What error will this code produce when run on the array [3, 1, 2]?

DSA Javascript

function countingSort(arr) {
  const max = Math.max(...arr);
  const count = new Array(max).fill(0);
  for (const num of arr) {
    count[num]++;
  }
  let sortedIndex = 0;
  for (let i = 0; i < count.length; i++) {
    while (count[i] > 0) {
      arr[sortedIndex++] = i;
      count[i]--;
    }
  }
  return arr;
}

console.log(countingSort([3, 1, 2]));

A TypeError: Cannot read property '3' of undefined

B RangeError: Maximum call stack size exceeded

C Output: [1, 2, 3]

D ReferenceError: max is not defined

💡 Hint

Check how the count array is created and accessed.

The count array is created with length max (3), so indices 0,1,2 exist. But the code tries to access count[3] which is undefined, causing a TypeError when incrementing count[3].

🚀 Application

advanced

Counting Sort with Negative Numbers

Given the array [-5, -10, 0, -3, 8, 5, -1, 10], which approach correctly adapts counting sort to handle negative numbers?

A Convert all numbers to strings and sort lexicographically.

B Ignore negative numbers and sort only positive numbers using counting sort.

C Shift all numbers by adding the absolute value of the minimum number before sorting, then shift back after sorting.

D Use counting sort directly without changes; it handles negatives automatically.

💡 Hint

Counting sort uses array indices as counts, so negative indices are invalid.

Counting sort cannot use negative indices. Shifting all numbers by adding the absolute value of the minimum number makes all numbers non-negative, allowing counting sort to work. After sorting, shift back to original values.

❓ Predict Output

expert

Output of Counting Sort with Frequency Array

What is the output of this code snippet?

DSA Javascript

function countingSort(arr) {
  const max = Math.max(...arr);
  const count = new Array(max + 1).fill(0);
  for (const num of arr) {
    count[num]++;
  }
  const result = [];
  for (let i = 0; i < count.length; i++) {
    for (let j = 0; j < count[i]; j++) {
      result.push(i);
    }
  }
  return result;
}

const input = [2, 5, 3, 0, 2, 3, 0, 3];
console.log(countingSort(input));

A [0, 0, 2, 2, 3, 3, 3, 5]

B [0, 0, 2, 3, 3, 3, 5]

C [0, 0, 2, 3, 3, 5]

D [0, 0, 2, 3, 5]

💡 Hint

Count how many times each number appears and list them in order.

The input has two 0s, two 2s, three 3s, and one 5. So the sorted output is [0, 0, 2, 2, 3, 3, 3, 5].

Practice

1. What is the main idea behind the Counting Sort Algorithm?

easy

A. Swap adjacent elements if they are in wrong order repeatedly

B. Compare each element with every other element to sort

C. Count the occurrences of each element and use counts to place elements in order

D. Divide the array into halves and sort recursively

Solution

1. Step 1: Understand Counting Sort principle

   Counting sort counts how many times each value appears in the input array.

2. Step 2: Use counts to place elements

   Using these counts, it calculates positions to place each element in the sorted output.

3. Final Answer:

   Count the occurrences of each element and use counts to place elements in order -> Option C

4. Quick Check:

   Counting elements = Counting Sort [OK]

Hint: Counting sort counts elements, no comparisons needed [OK]

Common Mistakes:

• Thinking counting sort compares elements like bubble sort
• Confusing counting sort with divide and conquer methods
• Assuming counting sort works on all data types

2. Which of the following is the correct way to initialize the count array in Counting Sort for input array arr with maximum value maxVal in JavaScript?

easy

A. const count = new Array().fill(maxVal + 1);

B. const count = new Array(maxVal).fill(0);

C. const count = new Array(arr.length).fill(0);

D. const count = new Array(maxVal + 1).fill(0);

Solution

1. Step 1: Determine size of count array

   The count array must cover all values from 0 to maxVal, so size is maxVal + 1.

2. Step 2: Initialize count array with zeros

   Use new Array(maxVal + 1).fill(0) to create and fill with zeros.

3. Final Answer:

   const count = new Array(maxVal + 1).fill(0); -> Option D

4. Quick Check:

   Count array size = maxVal + 1 [OK]

Hint: Count array length = max value + 1 [OK]

Common Mistakes:

• Using maxVal instead of maxVal + 1 for array size
• Using input array length instead of maxVal
• Incorrectly filling array with maxVal + 1 instead of zeros

3. What will be the output of the following JavaScript code using Counting Sort?

function countingSort(arr) {
  const maxVal = Math.max(...arr);
  const count = new Array(maxVal + 1).fill(0);
  for (const num of arr) count[num]++;
  let sorted = [];
  for (let i = 0; i <= maxVal; i++) {
    while (count[i] > 0) {
      sorted.push(i);
      count[i]--;
    }
  }
  return sorted;
}

console.log(countingSort([4, 2, 2, 8, 3, 3, 1]));

medium

A. [1, 2, 2, 3, 3, 4, 8]

B. [8, 4, 3, 3, 2, 2, 1]

C. [1, 2, 3, 4, 8]

D. [4, 2, 2, 8, 3, 3, 1]

Solution

1. Step 1: Count occurrences of each number

   Count array after counting: count[1]=1, count[2]=2, count[3]=2, count[4]=1, count[8]=1.

2. Step 2: Build sorted array using counts

   Push each number count[i] times in ascending order: 1, 2, 2, 3, 3, 4, 8.

3. Final Answer:

   [1, 2, 2, 3, 3, 4, 8] -> Option A

4. Quick Check:

   Sorted array matches counting sort output [OK]

Hint: Counting sort output is sorted array with duplicates in order [OK]

Common Mistakes:

• Returning original array instead of sorted
• Reversing order by mistake
• Missing duplicates in output

4. Identify the bug in this Counting Sort implementation and select the fix:

function countingSort(arr) {
  const maxVal = Math.max(...arr);
  const count = new Array(maxVal).fill(0);
  for (const num of arr) {
    count[num]++;
  }
  let sorted = [];
  for (let i = 0; i < maxVal; i++) {
    while (count[i] > 0) {
      sorted.push(i);
      count[i]--;
    }
  }
  return sorted;
}

medium

A. Change count array size to maxVal + 1 and loop to i <= maxVal

B. Initialize count array with zeros using fill(1)

C. Use for loop from i = 1 to maxVal instead of 0

D. Remove the while loop and use if condition instead

Solution

1. Step 1: Check count array size and loop range

   Count array size is maxVal but should be maxVal + 1 to include maxVal index.

2. Step 2: Fix loop to include maxVal index

   Loop should run from 0 to maxVal inclusive (i <= maxVal) to cover all counts.

3. Final Answer:

   Change count array size to maxVal + 1 and loop to i <= maxVal -> Option A

4. Quick Check:

   Count array size and loop range must match maxVal + 1 [OK]

Hint: Count array size = maxVal + 1; loop to i <= maxVal [OK]

Common Mistakes:

• Using wrong count array size causing index errors
• Looping less than needed, missing maxVal counts
• Changing fill value incorrectly

5. Given an array arr = [5, 3, 0, 2, 3, 5, 1], how would you modify Counting Sort to sort only the elements between 1 and 4 inclusive, ignoring others?

hard

A. Use counting sort on full range but skip pushing elements outside 1 to 4

B. Count only elements between 1 and 4, then output sorted elements in that range

C. Sort entire array normally and then remove elements outside 1 to 4

D. Filter array first, then apply counting sort on filtered array

Solution

1. Step 1: Count only elements in range 1 to 4

   Ignore elements outside 1 to 4 while counting to focus sorting on this range.

2. Step 2: Output sorted elements only in that range

   Build sorted array using counts only for values 1 to 4, ignoring others.

3. Final Answer:

   Count only elements between 1 and 4, then output sorted elements in that range -> Option B

4. Quick Check:

   Counting and output limited to range [1,4] [OK]

Hint: Count and output only target range elements [OK]

Common Mistakes:

• Sorting full array then filtering, wasting effort
• Counting full range but skipping output incorrectly
• Filtering after sorting instead of before