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The number of cycles in a given array of integers.
Objective: Given an array of size N which contains integers from range 0 to N1. (No duplicates). Write a program to find the number of cycles in the array.
Cycles in Array: Since the array is of size N and elements are from 0 to N1 without any duplicates means all the elements appear exactly once. Create a graph with n vertices. Create an edge from vertex Vi to Vj if the element at position i should be in position j in the sorted ordering, With the logic above find the number of cycles in the given array. See the image below for better understanding.
Example:
Given Array : [3, 2, 1, 0] Number of cycles: 2 Given Array : [2, 0, 1] Number of cycles: 1 Given Array : [1, 3, 4, 0, 2, 6, 5] Number of cycles: 3
Approach: Use DFS
 Given array input [].
 Create a visited[] to check if the array element is already visited.
 Initialize NoOfCycles = 0.
 Now iterate through input[] created in step 1, for each index i.
 If input[i] != i
 If i is not already visited then mark i as visited and jump to the next index which is at the index = input[i]. For example (1, 0) and i = 0 then jump to index=1. Repeat this process until you find an index which is already visited.
 NoOfCycles++.
 If input[i] != i
 Return NoOfCycles.
Walkthrough:
Input[] = [3, 2, 1, 0] visited = [false, false, false, false] NoOfCycles = 0 Index = 0, element = 3 0!=3 and 3 is not visited. Mark 3 visited. Jump to index = 3, element = 0 element 0 is not visited Mark 0 visited. Jump to index = 0, element = 3 3 is already visited. NoOfCycles = 1 visited = [true, false, false, true] Index = 1, process element = 2 1!=2 and 2 is not visited. Mark 2 visited. Jump to index = 2, element = 1 element 1 is not visited Mark 1 visited. Jump to index = 1, element = 2 2 is already visited. NoOfCycles = 2 visited = [true, true, true, true] NoOfCycles = 2
Complete Code:
Output:
Given Array : [3, 2, 1, 0] No of cycles: 2 Given Array : [2, 0, 1] No of cycles: 1 Given Array : [1, 3, 4, 0, 2, 6, 5] No of cycles: 3
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