Sequence Equation

Given a sequence of n integers, p(1),p(2),…,p(n) where each element is distinct and satisfies 1 <= p(x) <= n. For each x where 1 <= x <= n, find any integer y such that p(p(y)) = x and print the value of y on a new line.

For example, assume the sequence p = [5, 2, 1, 3, 4]. Each value of x between 1 and 5, the length of the sequence, is analyzed as follows:

1. , so p[p[4]] = 1
2. , so p[p[2]] = 2
3. , so p[p[5]] = 3
4. , so p[p[1]] = 4
5. , so p[p[3]] = 5

The values for y are [4,2,5,1,3].

Function Description

Complete the permutationEquation function in the editor below. It should return an array of integers that represent the values of y.

permutationEquation has the following parameter(s):

• p: an array of integers

Input Format

The first line contains an integer n, the number of elements in the sequence.
The second line contains n space-separated integers p[i] where a <= i <= n.

Constraints

• 1 <= n <= 50
• 1 <= p[i] <= 50, where 1 <= i <= n.
• Each element in the sequence is distinct.

Output Format

For each x from 1 to n, print an integer denoting any valid y satisfying the equation on a new line.

Sample Input 0

1
2

3
2 3 1

Sample Output 0

1
2
3

2
3
1

Explanation 0

Given the values of p(1) = 2, p(2) = 3, and p(3) = 1, we calculate and print the following values for each x from 1 to n:

1. , so we print the value of y = 2 on a new line.
2. , so we print the value of y = 3 on a new line.
3. , so we print the value of y = 1 on a new line.

Sample Input 1

1
2

5
4 3 5 1 2

Sample Output 1

1
2
3
4
5

1
3
5
4
2

Solution

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// Complete the permutationEquation function below.
function permutationEquation(p) {
    let values = (p || []).reduce((target, value, index) => {
        target[value] = index + 1;

        return target;
    }, []);

    return (p || []).reduce((target, value, index) => {
        target.push(values[values[index + 1]])

        return target;
    }, []);
}