Quick Sort Partition Lomuto and Hoare in DSA Javascript - Execution Trace

Concept Flow - Quick Sort Partition Lomuto and Hoare

Choose pivot = last element

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Initialize i = low - 1

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For j from low to high-1

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If arr[j

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i++, swap arr[i

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After loop, swap arr[i+1

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Return i+1 as pivot index

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Choose pivot = arr[low

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i = low, j = high + 1

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Repeat forever

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j-- while arr[j

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i++ while arr[i

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If i >= j return j

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Else swap arr[i

↩Back to Repeat

Lomuto picks last element as pivot and partitions by moving smaller elements left. Hoare picks first element as pivot and partitions by moving pointers inward and swapping.

Execution Sample

DSA Javascript

function lomutoPartition(arr, low, high) {
  let pivot = arr[high];
  let i = low - 1;
  for (let j = low; j < high; j++) {
    if (arr[j] <= pivot) {
      i++;
      [arr[i], arr[j]] = [arr[j], arr[i]];
    }
  }
  [arr[i + 1], arr[high]] = [arr[high], arr[i + 1]];
  return i + 1;
}

This code partitions the array using Lomuto scheme, placing elements smaller or equal to pivot on left and returns pivot index.

Execution Table

Step	Operation	i	j	Pivot	Array State	Pointer Changes	Visual State
1	Initialize i = low - 1	-1	-	5	[3, 8, 2, 5, 1, 4]	i = -1	3 -> 8 -> 2 -> 5 -> 1 -> 4
2	j = 0, arr[j] = 3 <= 5?	-1	0	5	[3, 8, 2, 5, 1, 4]	No change	3 -> 8 -> 2 -> 5 -> 1 -> 4
3	arr[j] <= pivot, i++ and swap arr[i], arr[j]	0	0	5	[3, 8, 2, 5, 1, 4]	i=0, swap arr[0], arr[0]	3 -> 8 -> 2 -> 5 -> 1 -> 4
4	j = 1, arr[j] = 8 <= 5?	0	1	5	[3, 8, 2, 5, 1, 4]	No change	3 -> 8 -> 2 -> 5 -> 1 -> 4
5	j = 2, arr[j] = 2 <= 5?	0	2	5	[3, 8, 2, 5, 1, 4]	No change	3 -> 8 -> 2 -> 5 -> 1 -> 4
6	arr[j] <= pivot, i++ and swap arr[i], arr[j]	1	2	5	[3, 2, 8, 5, 1, 4]	i=1, swap arr[1], arr[2]	3 -> 2 -> 8 -> 5 -> 1 -> 4
7	j = 3, arr[j] = 5 <= 5?	1	3	5	[3, 2, 8, 5, 1, 4]	No change	3 -> 2 -> 8 -> 5 -> 1 -> 4
8	arr[j] <= pivot, i++ and swap arr[i], arr[j]	2	3	5	[3, 2, 5, 8, 1, 4]	i=2, swap arr[2], arr[3]	3 -> 2 -> 5 -> 8 -> 1 -> 4
9	j = 4, arr[j] = 1 <= 5?	2	4	5	[3, 2, 5, 8, 1, 4]	No change	3 -> 2 -> 5 -> 8 -> 1 -> 4
10	arr[j] <= pivot, i++ and swap arr[i], arr[j]	3	4	5	[3, 2, 5, 1, 8, 4]	i=3, swap arr[3], arr[4]	3 -> 2 -> 5 -> 1 -> 8 -> 4
11	j = 5, arr[j] = 4 <= 5?	3	5	5	[3, 2, 5, 1, 8, 4]	No change	3 -> 2 -> 5 -> 1 -> 8 -> 4
12	arr[j] <= pivot, i++ and swap arr[i], arr[j]	4	5	5	[3, 2, 5, 1, 4, 8]	i=4, swap arr[4], arr[5]	3 -> 2 -> 5 -> 1 -> 4 -> 8
13	After loop, swap arr[i+1], pivot	4	-	5	[3, 2, 5, 1, 4, 8]	swap arr[5], arr[5] (pivot stays)	3 -> 2 -> 5 -> 1 -> 4 -> 8
14	Return pivot index i+1 = 5	4	-	5	[3, 2, 5, 1, 4, 8]	-	3 -> 2 -> 5 -> 1 -> 4 -> 8
15	Hoare Partition start: i = low = 0, j = high + 1 = 6	0	6	3	[3, 2, 5, 1, 4, 8]	i=0, j=6	3 -> 2 -> 5 -> 1 -> 4 -> 8
16	Decrement j while arr[j] > pivot (arr[5]=8>3), j=5->4->3->2	0	2	3	[3, 2, 5, 1, 4, 8]	j moves to 2	3 -> 2 -> 5 -> 1 -> 4 -> 8
17	Increment i while arr[i] < pivot (arr[0]=3<3? No), i=0	0	2	3	[3, 2, 5, 1, 4, 8]	i stays 0	3 -> 2 -> 5 -> 1 -> 4 -> 8
18	i < j? 0 < 2 yes, swap arr[i], arr[j]	0	2	3	[5, 2, 3, 1, 4, 8]	swap arr[0], arr[2]	5 -> 2 -> 3 -> 1 -> 4 -> 8
19	Decrement j while arr[j] > pivot (arr[2]=3>3? No), j=2	0	2	3	[5, 2, 3, 1, 4, 8]	j stays 2	5 -> 2 -> 3 -> 1 -> 4 -> 8
20	Increment i while arr[i] < pivot (arr[1]=2<3 yes), i=1->2	2	2	3	[5, 2, 3, 1, 4, 8]	i moves to 2	5 -> 2 -> 3 -> 1 -> 4 -> 8
21	i >= j? 2 >= 2 yes, return j=2	2	2	3	[5, 2, 3, 1, 4, 8]	partition index = 2	5 -> 2 -> 3 -> 1 -> 4 -> 8

💡 Lomuto ends after placing pivot at correct index; Hoare ends when pointers cross (i >= j)

Variable Tracker

Variable	Start	After Step 3	After Step 6	After Step 8	After Step 10	After Step 12	Final
i (Lomuto)	-1	0	1	2	3	4	4
j (Lomuto)	-	0	2	3	4	5	-
Pivot (Lomuto)	5	5	5	5	5	5	5
Array (Lomuto)	[3,8,2,5,1,4]	[3,8,2,5,1,4]	[3,2,8,5,1,4]	[3,2,5,8,1,4]	[3,2,5,1,8,4]	[3,2,5,1,4,8]	[3,2,5,1,4,8]
i (Hoare)	0	-	-	-	-	-	2
j (Hoare)	6	-	-	-	-	-	2
Pivot (Hoare)	3	-	-	-	-	-	3
Array (Hoare)	[3,2,5,1,4,8]	[5,2,3,1,4,8]	[5,2,3,1,4,8]	[5,2,3,1,4,8]	[5,2,3,1,4,8]	[5,2,3,1,4,8]	[5,2,3,1,4,8]

Key Moments - 3 Insights

Why does Lomuto partition use i = low - 1 initially?

Because i tracks the last position where a smaller or equal element was placed. Starting at low - 1 means no elements placed yet. See execution_table step 1 and 3 where i increments before swapping.

In Hoare partition, why do we decrement j and increment i before swapping?

We move j left until we find element <= pivot and i right until element >= pivot. This ensures elements less than pivot go left, greater go right. See execution_table steps 16-18 for pointer moves and swap.

Why does Hoare partition return j, not i?

Because j is the last index where left side elements are <= pivot. When i >= j, pointers crossed and partitioning is done. Returning j splits array correctly. See execution_table step 21.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of i after step 6 in Lomuto partition?

A 0

B 2

C 1

D -1

💡 Hint

Check the 'i' column in execution_table row with step 6.

At which step does Hoare partition swap elements for the first time?

A Step 18

B Step 16

C Step 20

D Step 21

💡 Hint

Look for 'swap' in the Operation column for Hoare partition steps.

If in Lomuto partition the pivot was chosen as the first element instead of last, how would the pointer i initialization change?

A i would start at low - 1

B i would start at low

C i would start at high

D i would start at 0

💡 Hint

Recall that i tracks last smaller element index; changing pivot position affects i start.

Concept Snapshot

Quick Sort Partition Schemes:
- Lomuto: pivot = last element
  i starts at low-1
  j scans low to high-1
  swap if arr[j] <= pivot
  finally swap pivot to i+1
- Hoare: pivot = first element
  i = low, j = high+1
  move i right while arr[i]<pivot
  move j left while arr[j]>pivot
  swap arr[i], arr[j] if i<j
  else return j
Both partition arrays around pivot for recursive quicksort.

Full Transcript

This visual execution traces two popular quick sort partition methods: Lomuto and Hoare. Lomuto picks the last element as pivot and uses a pointer i starting before low to track smaller elements. It scans with j and swaps elements smaller or equal to pivot to the left. After scanning, it places the pivot after the last smaller element. Hoare picks the first element as pivot and uses two pointers i and j starting inside and outside the array bounds respectively. It moves i right until it finds an element not less than pivot, and j left until it finds an element not greater than pivot, then swaps them. When pointers cross, partitioning ends. The execution table shows step-by-step pointer movements, swaps, and array states for both methods on the example array [3,8,2,5,1,4]. Variable tracker summarizes pointer and array changes. Key moments clarify common confusions about pointer initialization and return values. Visual quiz tests understanding of pointer values and swap steps. The snapshot summarizes the key steps and differences between Lomuto and Hoare partitions.