Cyclic Sort (Place 1..n in Correct Positions)

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Cyclic Sort (Place 1..n in Correct Positions)

Edge cases:

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IDE

def cyclic_sort(arr: list) -> list:public int[] cyclicSort(int[] arr)vector<int> cyclicSort(vector<int> &arr)function cyclicSort(arr)

def cyclic_sort(arr):
    # Write your solution here
    pass

class Solution {
    public int[] cyclicSort(int[] arr) {
        // Write your solution here
        return arr;
    }
}

#include <vector>
using namespace std;

vector<int> cyclicSort(vector<int> &arr) {
    // Write your solution here
    return arr;
}

function cyclicSort(arr) {
    // Write your solution here
}

Common Bugs to Avoid

Wrong: Array not fully sorted or partially sortedSwapping only once per element instead of looping until correct position✅ Use a while loop to swap arr[i] with arr[arr[i]-1] until arr[i] == i+1 or duplicates prevent swap

Wrong: Infinite loop or timeout on arrays with duplicatesSwapping duplicates endlessly without checking if arr[i] == arr[arr[i]-1]✅ Add condition to skip swap if arr[i] == arr[arr[i]-1]

Wrong: Index out of range error or crash on empty or single element arraysNo base case checks for empty or very small arrays✅ Return input immediately if array length is 0 or 1

Wrong: Unnecessary swaps on already sorted arrays causing incorrect outputSwapping elements even if arr[i] == i+1✅ Swap only if arr[i] != i+1

Wrong: Timeout on large inputsUsing sorting or nested loops instead of O(n) cyclic sort✅ Implement index-based cyclic sort with O(n) time complexity

✓

Test Cases

Focus on handling base cases like empty and single-element arrays.

Watch out for duplicates causing infinite loops and greedy swap traps.

Optimize your solution to linear time complexity for large inputs.

t1_01basic

Input{"arr":[3,1,5,4,2]}

Expected[1,2,3,4,5]

⏱ Performance - must finish in 2000ms

Each number is placed at its correct index: 1 at index 0, 2 at index 1, etc.

💡 Try placing each number at its correct index by swapping.

💡 Use cyclic sort technique: swap arr[i] with arr[arr[i]-1] until correct.

💡 Repeat swaps until all elements are at their correct indices.

Why it failed: Output incorrect - likely missing the swap loop or incorrect swap condition. Fix by swapping arr[i] with arr[arr[i]-1] while arr[i] != i+1.

✓ Core cyclic sort logic correctly places all elements.

t1_02basic

Input{"arr":[2,3,1,5,4]}

Expected[1,2,3,4,5]

⏱ Performance - must finish in 2000ms

Numbers rearranged so that each i is at index i-1.

💡 Focus on swapping elements to their correct indices.

💡 Check if arr[i] != i+1 and swap with arr[arr[i]-1].

💡 Continue until no swaps needed for any index.

Why it failed: Incorrect output due to missing repeated swaps for some elements. Fix by looping swaps until arr[i] == i+1 or duplicates prevent swap.

✓ Correctly handles standard input with shuffled elements.

t2_01edge

Input{"arr":[]}

Expected[]

⏱ Performance - must finish in 2000ms

Empty array input returns empty array.

💡 Consider what happens when input array is empty.

💡 Check if your code handles n=0 without errors.

💡 Return empty array immediately if input is empty.

Why it failed: Fails on empty input due to no base case check. Fix by returning input if length is zero.

✓ Handles empty input gracefully.

t2_02edge

Input{"arr":[1]}

Expected[1]

⏱ Performance - must finish in 2000ms

Single element array remains unchanged.

💡 Check behavior when array size is 1.

💡 No swaps needed if arr[0] == 1.

💡 Return array as is if single element is correct.

Why it failed: Fails single element case by unnecessary swaps or index errors. Fix by ensuring swap condition checks bounds and equality.

✓ Correctly returns single element array unchanged.

t2_03edge

Input{"arr":[1,2,3,4,5]}

Expected[1,2,3,4,5]

⏱ Performance - must finish in 2000ms

Already sorted array remains unchanged.

💡 Test if your code avoids unnecessary swaps on sorted input.

💡 Check if swap condition correctly skips elements already in place.

💡 Return input unchanged if all elements are at correct indices.

Why it failed: Incorrect output due to swapping elements already in correct position. Fix by swapping only if arr[i] != i+1.

✓ Efficiently handles already sorted input without changes.

t2_04edge

Input{"arr":[1,1,1,1]}

Expected[1,1,1,1]

⏱ Performance - must finish in 2000ms

All elements identical; duplicates remain unchanged.

💡 Duplicates can cause infinite loops if not handled.

💡 Check if your code avoids swapping when target index already has correct value.

💡 Add condition to skip swap if arr[i] == arr[arr[i]-1].

Why it failed: Infinite loop or incorrect output due to swapping duplicates endlessly. Fix by adding check to skip swap if arr[i] == arr[arr[i]-1].

✓ Correctly handles identical duplicates without infinite loops.

t3_01corner

Input{"arr":[2,2,2,2,2]}

Expected[2,2,2,2,2]

⏱ Performance - must finish in 2000ms

All duplicates remain; no infinite swaps occur.

💡 Duplicates can cause infinite swap loops if not handled.

💡 Check if your code avoids swapping when target index already has correct value.

💡 Add condition to skip swap if arr[i] == arr[arr[i]-1].

Why it failed: Infinite loop or incorrect output due to swapping duplicates endlessly. Fix by adding check to skip swap if arr[i] == arr[arr[i]-1]. This is the duplicates handling test.

✓ Correctly handles duplicates without infinite loops.

t3_02corner

Input{"arr":[4,3,2,7,8,2,3,1]}

Expected[1,2,2,3,3,4,7,8]

⏱ Performance - must finish in 2000ms

Array with duplicates and missing numbers placed as correctly as possible.

💡 Handle missing numbers by leaving their positions as is.

💡 Duplicates should be placed at their correct indices if possible.

💡 Ensure swap only if arr[i] != arr[arr[i]-1] to avoid infinite loops.

Why it failed: Incorrect output due to ignoring duplicates or missing numbers. Fix by swapping only when arr[i] != arr[arr[i]-1]. This is the duplicates and missing numbers test.

✓ Handles duplicates and missing numbers correctly.

t3_03corner

Input{"arr":[5,4,3,2,1]}

Expected[1,2,3,4,5]

⏱ Performance - must finish in 2000ms

Reverse sorted array correctly sorted by cyclic sort.

💡 Greedy approach of swapping only once per element fails here.

💡 Repeated swaps needed until all elements are in place.

💡 Use while loop to swap until arr[i] == i+1 or duplicates prevent swap.

Why it failed: Fails due to single swap per element approach. Fix by using while loop to swap until correct position reached. This is the greedy trap test.

✓ Correctly sorts reverse sorted input with repeated swaps.

t4_01performance

Input{"arr":[100000,99999,99998,99997,99996,99995,99994,99993,99992,99991,99990,99989,99988,99987,99986,99985,99984,99983,99982,99981,99980,99979,99978,99977,99976,99975,99974,99973,99972,99971,99970,99969,99968,99967,99966,99965,99964,99963,99962,99961,99960,99959,99958,99957,99956,99955,99954,99953,99952,99951,99950,99949,99948,99947,99946,99945,99944,99943,99942,99941,99940,99939,99938,99937,99936,99935,99934,99933,99932,99931,99930,99929,99928,99927,99926,99925,99924,99923,99922,99921,99920,99919,99918,99917,99916,99915,99914,99913,99912,99911,99910,99909,99908,99907,99906,99905,99904,99903,99902,99901]}

Expectednull

⏱ Performance - must finish in 2000ms

n=100000, O(n) cyclic sort must complete within 2 seconds.

💡 Use O(n) cyclic sort with index-based swapping.

💡 Avoid nested loops or sorting algorithms with O(n log n) or worse.

💡 Ensure swaps happen only when arr[i] != arr[arr[i]-1].

Why it failed: TLE due to using O(n log n) or O(n^2) approach like sorting or nested loops. Fix by implementing O(n) cyclic sort with index swaps.

✓ Algorithm runs in O(n) time confirming efficiency.

Practice

1. You are given an unsorted array of integers that may contain duplicates and negative numbers. Your task is to find the first k positive integers missing from the array. Which algorithmic approach guarantees an optimal time complexity while handling duplicates and negatives correctly?

easy

A. Sort the array and then scan sequentially to find missing positive numbers.

B. Use dynamic programming to build a table of present and missing numbers.

C. Use cyclic sort to place numbers in their correct indices, then identify missing positives and track extras with a boolean array.

D. Use a max-heap to extract the smallest missing positive numbers one by one.

Solution

1. Step 1: Understand problem constraints

   The array may contain duplicates and negative numbers, so naive sorting or heap approaches may be inefficient or incorrect.

2. Step 2: Identify optimal approach

   Cyclic sort places numbers in their correct indices in O(n) time, ignoring negatives and duplicates. Then, a boolean array tracks extra numbers beyond the array length to find missing positives efficiently.

3. Final Answer:

   Option C -> Option C

4. Quick Check:

   Cyclic sort + boolean array handles duplicates and negatives optimally [OK]

Hint: Cyclic sort handles duplicates and negatives efficiently [OK]

Common Mistakes:

• Assuming sorting is always optimal
• Using heaps which add unnecessary overhead
• Confusing DP with presence tracking

2. You are given an unsorted array of integers that may contain duplicates, negatives, and zeros. Your task is to find the smallest continuous range of positive integers that are missing from the array. Which algorithmic approach guarantees an optimal O(n) time and O(1) space solution for this problem?

easy

A. Using a hash set to store all positive numbers and then checking for the missing range

B. Sorting the array and then scanning linearly to find the missing range

C. Using a dynamic programming approach to track presence of numbers

D. Using cyclic sort to place each positive integer at its correct index and then scanning for the missing range

Solution

1. Step 1: Understand problem constraints

   The problem requires finding the smallest missing positive range in O(n) time and O(1) space, which excludes sorting (O(n log n)) and hash sets (O(n) space).

2. Step 2: Identify the algorithm that achieves in-place linear time

   Cyclic sort places each positive integer at its correct index in the array, enabling a single pass to find the missing range efficiently.

3. Final Answer:

   Option D -> Option D

4. Quick Check:

   Cyclic sort is known for in-place linear time sorting of numbers in range 1 to n [OK]

Hint: Cyclic sort achieves O(n) time and O(1) space for this problem [OK]

Common Mistakes:

• Assuming sorting is optimal
• Confusing hash set space with time complexity

3. You are given an unsorted integer array and need to find the smallest positive integer missing from it in O(n) time and O(1) extra space. Which algorithmic approach best guarantees this optimal solution?

easy

A. Sorting the array and then scanning for the first missing positive

B. Applying a greedy approach to pick the smallest missing positive at each step

C. Using a hash set to track presence of numbers and then scanning from 1 upwards

D. Placing each number in its correct index position using cyclic sort and then scanning

Solution

1. Step 1: Understand the problem constraints

   The problem requires O(n) time and O(1) space, which rules out sorting (O(n log n)) and hash sets (O(n) space).

2. Step 2: Identify the approach that rearranges elements in-place

   Cyclic sort places each number in its correct index (number k at index k-1), enabling a linear scan to find the first missing positive efficiently.

3. Final Answer:

   Option D -> Option D

4. Quick Check:

   Cyclic sort achieves O(n) time and O(1) space [OK]

Hint: Optimal solution uses in-place cyclic sort [OK]

Common Mistakes:

• Choosing sorting which is O(n log n)
• Using hash sets which use extra space
• Greedy approaches that don't guarantee correctness

4. Identify the bug in the following cyclic sort implementation for finding the corrupt pair:

medium

A. Line 6: Missing increment of i after else condition

B. Line 3: Incorrect initialization of n

C. Line 7: Swap logic is incorrect

D. Line 10: Return statement does not handle all cases

Solution

1. Step 1: Analyze the while loop behavior

   Without incrementing i in the else branch, the loop can get stuck when nums[i] == nums[correct_index], causing infinite loop.

2. Step 2: Identify fix

   Adding i += 1 in the else branch ensures progress and termination.

3. Final Answer:

   Option A -> Option A

4. Quick Check:

   Infinite loop caused by missing index increment [OK]

Hint: Always increment index if no swap to avoid infinite loops [OK]

Common Mistakes:

• Forgetting to increment index after no swap
• Swapping incorrectly
• Misplaced return statements

5. Consider this buggy code snippet for finding the duplicate and missing numbers. Which line contains the subtle bug that can cause an infinite loop or incorrect result?

medium

A. Line 5: missing check before swapping

B. Line 3: initialization of i

C. Line 8: incrementing i

D. Line 10: returning the result

Solution

1. Step 1: Analyze the swapping condition

   Without checking if nums[i] == nums[correct], swapping duplicates causes infinite loops or incorrect swaps.

2. Step 2: Confirm other lines are correct

   Initialization, increment, and return lines are standard and not buggy here.

3. Final Answer:

   Option A -> Option A

4. Quick Check:

   Missing conditional check before swap causes infinite loop [OK]

Hint: Always check if swap is needed to avoid infinite loops [OK]

Common Mistakes:

• Forgetting to check for duplicates before swapping
• Misplacing increment of index i
• Returning wrong values after loop