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Problem · Math

Minimum Number of Permutation Operations 👑

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● MediumGeneva TradingOA

Problem statement

A permutation of n numbers is a sequence where each number from 1 to n appears exactly once. For a given permutation p and any arbitrary array arr, a permutation operation is defined as

For each index i (1 ≤ i ≤ n) temp_arr[i] = arr[p[i]]

arr = temp_arr

Given a permutation p of n numbers, start with any arbitrary array arr of n distinct elements and find out the minimum number of permutation operations (at least 1) needed in order to reach the original array. Since the answer can be quite large, return the answer modulo (109 + 7)

Function

minNumberOfPermutationOperations(p: int[]) → int

Examples

Example 1

p = [1, 3, 2]return = 2
In the above example, n = 3. Taking any arbitrary array arr = [7, 8, 9] In each operation:
  • the element at index 1 stays at index 1
  • the element at index 2 gets mapped to index 3
  • the element at index 3 gets mapped to index 2
    • After applying operation for the first time on arr, the resulting array is [7, 9, 8]. After applying operation for the second time the resulting array is [7, 8, 9]. After 2 operations we get back to the original array, hence we return 2 as the answer.

    Constraints

  • 1 ≤ n ≤ 105
  • 1 ≤ p[i] ≤ n
  • p contains all distinct elements, the integers 1 through n
    • drafts saved locally
    public int minNumberOfPermutationOperations(int[] p) {
    // write your code here
}
    p[1, 3, 2]
    expected2
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