Count frequencies of array elements in range 1 to n

Given an array of length n having integers 1 to n with some elements being repeated. Count frequencies of all elements from 1 to n.

Example:
Input Array: {2, 3, 3, 2, 5}
Output:
1 0
2 2
3 2
4 0
5 1

Algorithm 1:
Find frequency of elements 1 – n one by one using 2 loops:
1. Outer loop runs from i = 1 to n.
2. Inner loop calculates the count of i in the input array.
3. Print the count of i when inner loop ends.
Time Complexity: O(n^2)
Space Complexity: O(1)

Algorithm 2:
1. Create a count array of size n with all elements from index i = 0 to n-1 initialized to 0.Here, count[i] is count of i+1.
2. Traverse the array once. For i = 0 to n-1, increment count[input[i]-1] by 1.
3. Traverse count array and print count array.
Time Complexity: O(n)
Space Complexity: O(n)

Algorithm 3(Optimized):
1. Reduce all elements by 1 so that the elements are converted in the range 0 to n-1.
2. Traverse the input array. For i = 0 to n-1, add n to element at index (input[i]%n). After all the elements are completed, element at index i will be incremented by n*k where k is the number of times i occurs in the array.
3. Finally, print counts of elements and simultaneously convert the array back to original array.
a: Print count of i+1 as input[i]/n.
b: Set input[i] = input[i]%n+1.
Time Complexity: O(n)
Space Complexity: O(1)

Code and Algorithm Visualization:

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