Given an unsorted array. The task is to calculate the cumulative frequency of each element of the array using count array.
Input : arr = [1, 2, 2, 1, 3, 4] Output :1->2 2->4 3->5 4->6 Input : arr = [1, 1, 1, 2, 2, 2] Output :1->3 2->6
A simple solution is to use two nested loops, the outer loops picks an element from left to right that are not visited. The inner loop counts its occurrences and mark occurrences as visited. Time complexity of this solution is O(n*n) and auxiliary space required is O(n).
A better solution is to use sorting. We sort the array so that same elements come together. After sorting, we linearly traverse elements and count their frequencies.
An efficient solution is to use hashing. Insert the element and its frequency in a set of pairs. As the set stores unique values in a sorted order, it will store all the elements with their frequencies in a sorted order. Iterate in the set and print the frequencies by adding the previous ones at every step.
Below is the implementation of the above approach.
1 2 2 4 3 5 4 6
Time complexity of the solution is O(n log n).
What if we need frequencies of elements according to the order of the first occurrence?
For example, an array [2, 4, 1, 2, 1, 3, 4], the frequency of 2 should be printed first, then of 4, then 1 and finally 3.
Approach: Hash the count of occurrences of an element. Traverse in the array and print the cumulative frequency. Once the element and its cumulative frequency has been printed, hash the occurrence of that element as 0 so that it not printed again if it appears in the latter half of array while traversal.
Below is the implementation of the above approach:
1->2 3->3 2->5 4->6
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- Replace each element by the difference of the total size of the array and frequency of that element
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- K'th Smallest/Largest Element in Unsorted Array | Set 1
- Kth smallest or largest element in unsorted Array | Set 4
- Search an element in an unsorted array using minimum number of comparisons
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- K'th Smallest/Largest Element in Unsorted Array | Set 2 (Expected Linear Time)
- K'th Smallest/Largest Element in Unsorted Array | Set 3 (Worst Case Linear Time)
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- Sorting element of an array by frequency in decreasing order
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- Find frequency of each element in a limited range array in less than O(n) time
- Count pairs in an array such that frequency of one is at least value of other
- Count number of occurrences (or frequency) in a sorted array
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