5kyu_OperationsOnSequences.js

// 5kyu - Operations on Sequences 

// Let an array or a list

// arr = [x(1), x(2), x(3), x(4), ..., x(i), x(i+1), ..., x(m), x(m+1)]

// where all x(i) are positive integers. The length lg of this array will be a positive multiple of 4.

// Let

// P = (x(1) ** 2 + x(2) ** 2) * (x(3) ** 2 + x(4) ** 2) * ... * (x(m) ** 2 + x(m+1) ** 2),

// x ** y means x raised to the power y.

// Task
// Given an array or list arr the task is to find:

// two nonnegative integers A and B such as P = A ** 2 + B ** 2 (1).
// The function solve(arr) should return an array or a list [A, B] where A and B verify (1).

// Examples:
// solve([2, 1, 3, 4]) returns [2, 11] :
// (2*2 + 1*1) * (3*3 + 4*4) = 5 * 25 = 125 and 2 * 2 + 11 * 11 = 125

// solve([2, 1, 3, 4, 2, 2, 1, 5, 2, 3, 4, 5]) returns [2344, 2892] :
// (2*2 + 1*1) * (3*3 + 4*4) * (2*2 + 2*2) * (1*1 + 5*5) * (2*2 + 3*3) * (4*4 + 5*5) = 13858000
// and 2344 * 2344 + 2892 * 2892 = 13858000
// Notes
// The decomposition into A ** 2 + B ** 2 is not unique: the testing function checks if (1) is verified.
// Lengths of lists are less than 100 and elements of lists less than 30
// solve([21, 24, 15, 22, 1, 2]) can return [639, 1788] or [1431, 1248]; both return are correct.
// P is     3605265
// A*A+B*B  3605265
// Please ask before translating

const BN = require('bignumber.js');

function solve(arr) {
  arr = arr.map(n => BN(n));
  while (arr.length > 2) {
    arr.splice(0, 4,
      arr[0].times(arr[2]).minus(arr[1].times(arr[3])).abs(),
      arr[0].times(arr[3]).plus(arr[1].times(arr[2]))
    );
  }
  return arr;
}