Why is My Quicksort Algorithm Failing to Assign the Pivot Correctly?

What are common reasons for incorrect pivot assignment in a quicksort algorithm implementation?

function quicksort(arr) {
  if (arr.length <= 1) return arr;
  const pivot = arr[arr.length - 1]; // Common pivot assignment
  const left = [];
  const right = [];
  for (let i = 0; i < arr.length - 1; i++) {
    if (arr[i] < pivot) {
      left.push(arr[i]);
    } else {
      right.push(arr[i]);
    }
  }
  return [...quicksort(left), pivot, ...quicksort(right)];
}

The quicksort algorithm is a commonly used sorting technique that relies on the correct assignment of a pivot element. When the pivot is not assigned correctly, it can lead to incorrect sorting results or inefficient performance. Understanding the common pitfalls in pivot assignment is crucial for implementing an effective quicksort.

// Example of improved pivot selection using median-of-three
function improvedQuicksort(arr) {
  if (arr.length <= 1) return arr;

  const midIndex = Math.floor(arr.length / 2);
  const pivotCandidates = [arr[0], arr[midIndex], arr[arr.length - 1]];
  const pivot = pivotCandidates.sort((a, b) => a - b)[1]; // Median of three

  const left = [];
  const right = [];
  for (const element of arr) {
    if (element < pivot) left.push(element);
    else if (element > pivot) right.push(element);
  }
  return [...improvedQuicksort(left), pivot, ...improvedQuicksort(right)];
}

Causes

• Using incorrect indices for the pivot assignment, such as always using the last element instead of selecting a random pivot.
• Not handling edge cases, such as arrays with all identical elements, leading to poor performance.
• Failing to properly partition the array around the pivot, which can lead to an infinite loop or incorrect recursions.

Solutions

• Ensure the pivot is chosen appropriately, possibly by selecting a random element or using the median-of-three method to improve efficiency.
• Handle edge cases explicitly, checking if the array has one or zero elements before proceeding to sort.
• Review your partitioning logic to guarantee that all elements less than the pivot are correctly placed in the left subtree and all elements greater in the right subtree.

Mistake: Using the same pivot index repeatedly without changing it during recursive calls.

Solution: Ensure that each recursive call uses the updated partitioned indices.

Mistake: Not checking if the array is already sorted before attempting to sort.

Solution: Implement a check to exit if the array length is 0 or 1 to avoid unnecessary processing.

Mistake: Misplacing comparisons in partition logic, which can lead to infinite loops or incorrect results.

Solution: Double-check that all comparisons and assignments in your partition function are correctly implemented.