### Find Missing Element

January 16, 2020

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)].

Use **trapezoid area** (calculated with height=A.length+1) **minus** existing array's summation to get the missing element.

```
function missingElement(A) {
console.log(A)
var length = A.length;
const height = length + 1
const sum = (1+ height) * height /2 // trapezoid area
var sumMinusMissing = 0;
for (i = 0; i < length; i++) {
sumMinusMissing += A[i];
}
return sum - sumMinusMissing;
}
A1 = [2, 3, 1, 5]
console.log("missingElement : ", missingElement(A1))
```