# C Programming Exercises, Practice, Solution : Searching and Sorting

## C Searching and Sorting Algorithm [31 exercises with solution]

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## Searching: [5 exercises with solution]

**1.** Write a C program to find the position of a target value within a sorted array using binary search.

Binary Search : In computer science, a binary search or half-interval search algorithm finds the position of a target value within a sorted array. The binary search algorithm can be classified as a dichotomies divide-and-conquer search algorithm and executes in logarithmic time.

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**2.** Write a C program to find the position of a target value within an array using interpolation search.

From Wikipedia:

Interpolation search is an algorithm for searching for a key in an array that has been ordered by numerical values assigned to the keys (key values). It was first described by W. W. Peterson in 1957. Interpolation search resembles the method by which people search a telephone directory for a name (the key value by which the book's entries are ordered): in each step the algorithm calculates where in the remaining search space the sought item might be, based on the key values at the bounds of the search space and the value of the sought key, usually via a linear interpolation. The key value actually found at this estimated position is then compared to the key value being sought. If it is not equal, then depending on the comparison, the remaining search space is reduced to the part before or after the estimated position. This method will only work if calculations on the size of differences between key values are sensible.

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**3.** Write a C program to find the position of a target value within a sorted array using Jump search. >

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**4.** Write a C program to find the position of a target value within an array using linear search. >

In computer science, a Linear search or sequential search is a method for finding an element within a list. It sequentially checks each element of the list until a match is found or the whole list has been searched

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**5.** Write a C program to find the position of a target value within an array using ternary search. >

From Wikipedia

A ternary search algorithm is a technique in computer science for finding the minimum or maximum of a unimodal function. A ternary search determines either that the minimum or maximum cannot be in the first third of the domain or that it cannot be in the last third of the domain, then repeats on the remaining two thirds. A ternary search is an example of a divide and conquer algorithm.

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## Sorting: [26 exercises with solution]

**1.** Write a C program to sort a list of elements using the selection sort algorithm. >

*According to Wikipedia "In computer science, selection sort is a sorting algorithm, specifically an in-place comparison sort. It has O(n2) time complexity, making it inefficient on large lists, and generally performs worse than the similar insertion sort".
*Note :

a) To find maximum of elements

b) To swap two elements

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**2.** Write a C program to sort a list of elements using the bubble sort algorithm. >

Bubble Sort works by swapping adjacent elements if they are in the wrong order.

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**3.** Write a C program to sort a list of elements using the insertion sort algorithm. >

Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than other algorithms such as quicksort, heapsort, or merge sort.

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**4.** Write a C program to sort a list of elements using the merge sort algorithm. >

Merge sort is an O(n log n) comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output.

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**5.** Write a C program to sort numbers using the MAX heap algorithm. >

A sorting algorithm that works by first organizing the data to be sorted into a special type of binary tree called a heap.

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**6.** Write a C program to sort a list of elements using the quick sort algorithm. >

Quick sort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined.

Note:
Read n values into array and Sort using Quick Sort

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**7.** Write a C program to sort a list of elements using the radix sort algorithm. >

Radix sort is a non-comparative integer sorting algorithm that sorts data with integer keys by grouping keys by the individual digits which share the same significant position and value.

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**8.** Write a C program for counting sort. >

According to Wikipedia “In computer science, counting sort is an algorithm for sorting a collection of objects according to keys that are small integers; that is, it is an integer sorting algorithm. It operates by counting the number of objects that have each distinct key value, and using arithmetic on those counts to determine the positions of each key value in the output sequence. Its running time is linear in the number of items and the difference between the maximum and minimum key values, so it is only suitable for direct use in situations where the variation in keys is not significantly greater than the number of items. However, it is often used as a subroutine in another sorting algorithm, radix sort, that can handle larger keys more efficiently”.

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**9.** Write a C program to display a sorted list using Gnome sort. >

Gnome sort is a sorting algorithm originally proposed by Dr. Hamid Sarbazi-Azad (Professor of Computer Engineering at Sharif University of Technology) in 2000 and called "stupid sort" (not to be confused with bogosort), and then later on described by Dick Grune and named "gnome sort".
The algorithm always finds the first place where two adjacent elements are in the wrong order, and swaps them. It takes advantage of the fact that performing a swap can introduce a new out-of-order adjacent pair only next to the two swapped elements.

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**10.** Write a C program that sorts numbers using the shell sorting method. >

According to Wikipedia "Shell sort or Shell's method, is an in-place comparison sort. It can be seen as either a generalization of sorting by exchange (bubble sort) or sorting by insertion (insertion sort). The method starts by sorting pairs of elements far apart from each other, then progressively reducing the gap between elements to be compared. Starting with far apart elements can move some out-of-place elements into position faster than a simple nearest neighbor exchange."

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**11.** Write a C program that sorts numbers using the QuickSort method. >

Note: According to Wikipedia "Quicksort is a comparison sort, meaning that it can sort items of any type for which a "less-than" relation (formally, a total order) is defined. Inefficient implementations it is not a stable sort, meaning that the relative order of equal sort items is not preserved. Quicksort can operate in-place on an array, requiring small additional amounts of memory to perform the sorting."

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**12.** Write a C program that sorts numbers using the Bead Sort method. >

According to Wikipedia "Bead sort, also called gravity sort, is a natural sorting algorithm, developed by Joshua J. Arulanandham, Cristian S. Calude and Michael J. Dinneen in 2002, and published in The Bulletin of the European Association for Theoretical Computer Science. Both digital and analog hardware implementations of bead sort can achieve a sorting time of O(n); however, the implementation of this algorithm tends to be significantly slower in software and can only be used to sort lists of positive integers. Also, it would seem that even in the best case, the algorithm requires O(n2) space".

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**13.** Write a C program that sorts numbers using the Bogo Sort method. >

In computer science, Bogo Sort is a particularly ineffective sorting algorithm based on the generate and test paradigm. The algorithm successively generates permutations of its input until it finds one that is sorted. It is not useful for sorting but may be used for educational purposes, to contrast it with other more realistic algorithms.

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**14.** Write a C program that sorts numbers using the Cocktail Sort method. >

Cocktail shaker sort (also known as bidirectional bubble sort, cocktail sort, shaker sort, ripple sort, shuffle sort, or shuttle sort ) is a variation of bubble sort that is both a stable sorting algorithm and a comparison sort. The algorithm differs from a bubble sort in that it sorts in both directions on each pass through the list. This sorting algorithm is only marginally more difficult to implement than a bubble sort and solves the problem of turtles in bubble sorts. It provides only marginal performance improvements, and does not improve asymptotic performance; like the bubble sort, it is not of practical interest, though it finds some use in education.

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**15.** Write a C program that sorts numbers using the Cycle sort method. >

Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm. It is based on the idea that the permutation to be sorted can be factored into cycles, which can individually be rotated to give a sorted result.

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**16.** Write a C program that sorts numbers using the Permutation Sort method. >

Permutation sort, proceeds by generating the possible permutations of the input array/list until discovering the sorted one.

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**17.** Write a C program to sort a list of elements using the insertion-sort algorithm. >

Input numbers you want to input: Input 5 values to sort The ascending order of the values: 11 13 15 20 25Click me to see the solution

**18.** Write a C program that sorts numbers using the Stooge Sort method. >

Stooge sort is a recursive sorting algorithm with a time complexity of O(nlog 3 / log 1.5 ) = O(n2.7095...). The running time of the algorithm is thus slower compared to efficient sorting algorithms, such as Merge sort, and is even slower than Bubble sort.

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**19.** Write a C program that sorts numbers using the Randomised quick sort method. >

From Wikipedia:

A simple example is randomized QuickSort, where the pivot is chosen randomly, and divides the elements into three partitions: elements less than pivot, elements equal to pivot, and elements greater than pivot. The randomized QuickSort require a lot of resources but always generate the sorted array as an output.

It is obvious that QuickSort always generates the solution which in this case the sorted array. Unfortunately, the time complexity is not that obvious. It turns out that the running time depends on which element we pick as a pivot.

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**20.** Write a C program that sorts numbers using the Pigeonhole sort method. >

From Wikipedia:

Pigeonhole sorting is a sorting algorithm that is suitable for sorting lists of elements where the number of elements (n) and the length of the range of possible key values (N) are approximately the same. It requires O(n + N) time. It is similar to counting sort, but differs in that it "moves items twice: once to the bucket array and again to the final destination [whereas] counting sort builds an auxiliary array then uses the array to compute each item's final destination and move the item there.

The pigeonhole algorithm works as follows:

Given an array of values to be sorted, set up an auxiliary array of initially empty "pigeonholes", one pigeonhole for each key in the range of the keys in the original array.

Going over the original array, put each value into the pigeonhole corresponding to its key, such that each pigeonhole eventually contains a list of all values with that key.

Iterate over the pigeonhole array in increasing order of keys, and for each pigeonhole, put its elements into the original array in increasing order.

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**21.** Write a C program that sorts numbers using the partition sort method. >

Partition-exchange sort is an efficient sorting algorithm. Developed by British computer scientist Tony Hoare in 1959 and published in 1961, it is still a commonly used algorithm for sorting. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort.

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**22.** Write a C program that sorts numbers using the Pancake sort method. >

From Wikipedia,

Pancake sorting is the colloquial term for the mathematical problem of sorting a disordered stack of pancakes in order of size when a spatula can be inserted at any point in the stack and used to flip all pancakes above it. A pancake number is the minimum number of flips required for a given number of pancakes. In this form, the problem was first discussed by American geometer Jacob E. Goodman. A variant of the problem is concerned with burnt pancakes, where each pancake has a burnt side and all pancakes must, in addition, end up with the burnt side on bottom.

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**23.** Write a C program that sorts numbers using the Multi-key quicksort method. >

Multi-key quicksort, also known as three-way radix quicksort, is an algorithm for sorting strings. This hybrid of quicksort and radix sort was originally suggested by P. Shackleton, as reported in one of C.A.R. Hoare's seminal papers on quicksort, its modern incarnation was developed by Jon Bentley and Robert Sedgewick in the mid-1990s. The algorithm is designed to exploit the property that in many problems, strings tend to have shared prefixes.

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**24.** Write a C program that sorts numbers using the Comb sort method. >

From Wikipedia,

Comb sort is a relatively simple sorting algorithm originally designed by Włodzimierz Dobosiewicz and Artur Borowy in 1980, later rediscovered by Stephen Lacey and Richard Box in 1991. Comb sort improves on bubble sort.

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**25.** Write a C program that sorts numbers using the Bucket sort method. >

From Wikipedia,

Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, a generalization of pigeonhole sort, and is a cousin of radix sort in the most-to-least significant digit flavor. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm.

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**26.** Write a C program that sorts numbers using the Binary insertion sort method. >

Binary insertion sort employs a binary search to determine the correct location to insert new elements, and therefore performs ⌈log2 n⌉ comparisons in the worst case, which is O(n log n).

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