Codility302-Time Complexity-PermMissingElem.js

// https://app.codility.com/demo/results/training4NY26W-G3D/
// Task description
// An array A consisting of N different integers is given. The array contains integers in the range [1..(N + 1)], which means that exactly one element is missing.

// Your goal is to find that missing element.

// Write a function:

// function solution(A);

// that, given an array A, returns the value of the missing element.

// For example, given array A such that:

//   A[0] = 2
//   A[1] = 3
//   A[2] = 1
//   A[3] = 5
// the function should return 4, as it is the missing element.

// Write an efficient algorithm for the following assumptions:

// N is an integer within the range [0..100,000];
// the elements of A are all distinct;
// each element of array A is an integer within the range [1..(N + 1)].

function solution(A) {
  // write your code in JavaScript (Node.js 8.9.4)
  if (A.length === 0) return 1
  // find max number
  let Along = A.length + 1
  // total value use trapezoid formula
  let total = ( (1 + Along)*Along/2)
  // total value - all A[i] 
  for ( i = 0 ; i < A.length ; i++ )
  {
      total = total - A [i]
  }
  return total
}