sequence-equation.js

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

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

//solution 1
function permutationEquation(p) {
  let arr = [];
  for (let i = 0; i < p.length; i++) {
    let j = p.indexOf(i + 1) + 1;
    arr.push(p.indexOf(j) + 1);
  }
  return arr;
}

//solution 2
function permutationEquation(p) {
  let arr = [...p];
  let finalArr = [];
  p.sort((a, b) => a - b);
  for (let i = 0; i < p.length; i++) {
    let j = arr.indexOf(p[i]) + 1;
    finalArr.push(arr.indexOf(j) + 1);
  }
  return finalArr;
}