Introduction to Cyclic Sort
Explore how cyclic sort works by placing each integer in its correct index through swaps, effectively sorting arrays with numbers in a limited range. Understand its in-place, linear-time approach, typical use cases, limitations, and how to handle edge cases like duplicates or missing values. This lesson equips you to identify problems suited for cyclic sort, such as detecting missing or repeated numbers, while recognizing when alternatives are needed.
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About the pattern
Imagine we have a classroom with numbered seats, and each student is given a card with a number corresponding to their seat number. To maintain classroom decorum and order, students are required to sit in their assigned seats. However, students have randomly taken seats, so the seating arrangement is all jumbled up. If we have to fix this, we start with the first seat, seat 1, and check if the student sitting here has the right card, i.e., the number 1. If not, we move the student to the seat corresponding to their card number. We repeat this process for each seat until every student is in their proper seat according to the number on their card. After completing this process for all seats, the students will be sitting in ascending order according to their seat numbers.
The repeated swapping of students until they find their correct positions is nothing but the cyclic sort. It can be seen as the cycling of elements through the array until they settle into their proper places.
Cyclic sort is a simple and efficient in-place sorting algorithm used for sorting arrays with integers in a specific range, most of the time
But how do we know the correct position of any element? This is where the algorithm makes things even easier: the correct place of any element is simply the value of element - 1. For example, if we have the array