# counting sort complexity

Counting sort algorithm is based on keys in a specific range. In this article, we will be going through a specific sorting algorithm – Counting Sort. After applying the counting sort algorithm, sortedA[] will be {2,2,3,5,5,5,9} Complexity. Counting sort utilizes the knowledge of the smallest and the largest element in the array (structure). Facing Issues On IT. The complexity of counting Sort Technique. It is not that counting sort is a comparison sort algorithm and gives O ( n ) complexity for sorting. share. Output − Array after Sorting: 2 2 3 3 5 6 6 7 8 10. It counts the number of items for distinct key value, use these keys to determine position or indexing on the array and store respective counts for each key. Aux[] is traversed in O(K) time. Share a … Counting Sort is stable sort as relative order of elements with equal values is maintained. The task of arranging numbers or things in a specific order has really put mankind in deep thoughts. It is an integer-based sorting algorithm unlike others which are usually comparison-based. Therefore, the overall time complexity of counting sort algorithm is O(N+K). Counting Sort is an sorting algorithm, which sorts the integers( or Objects) given in a specific range. The array A is traversed in O(N) time and the resulting sorted array is also computed in O(N) time. Worst case time complexity:Θ(N+K) Count[] will store the counts of each integer in the given array. Counting sort is a distribution sort that achieves linear time complexity given some trade-offs and provided some requirements are met. It will not work if we have 5 elements to sort in the range of 0 to 10,000. This algorithm works wonders when the range of numbers involved in sorting is restricted. Time Complexity: O(n+r) Space Complexity: O(n+r) Input − A list of unsorted data: 2 5 6 2 3 10 3 6 7 8. Counting Sort Time Complexity. In Counting sort it is assumed that all array elements are in the range between m to k where m and k are integers. This sorting technique is efficient when difference between different keys are not so big, otherwise it can increase the space complexity. Update the Count[] so that each index will store the sum till previous step. Counting sort (ultra sort, math sort) is an efficient sorting algorithm with asymptotic complexity, which was devised by Harold Seward in 1954.As opposed to bubble sort and quicksort, counting sort is not comparison based, since it enumerates occurrences of contained values.. Then doing some arithmetic to calculate the position of each object in the output sequence … More on Counting Sort It is not an in-place sorting algorithm as it requires extra additional space O (k). Counting sort works by creating an auxiliary array the size of the range of values, the unsorted values are then placed into the new array using the value as the index . It works by counting the number of objects having distinct key values (kind of hashing). So, the time complexity of sorting is linear i.e. In Computer Science, sorting algorithms form the basis of many complex concepts and techniques. Algorithm: Time Complexity O(n) Take two arrays, Count[] and Result[] and given array is input[]. Counting sort is a sorting technique based on keys between a specific range. O ( n + k ) {\displaystyle O (n+k)} 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. Counting Sort is a linear sorting algorithm. Finally, sort values based on keys and make…. 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 … O ( k-m ). Counting Sort algorithm is efficient if the range of input data (k) is not much greater than the number of elements in the input array (n). Furthermore, we can make stronger statements: when k=O (n 2) or O (n 3 ), we can say that the complexity of the counting sort is Θ (n 2) or Θ (n 3 ). Worst-case space complexity. Time complexity of Counting Sort is O (n+k), where n is the size of the sorted array and k is the range of key values. Description. 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