# Find The Missing Number From The Array — JavaScript

Discovering the absent number within an array presents multiple strategies in JavaScript. Below, I outline a couple of distinctive approaches for this task.

# Approach 1:

# Using Arithmetic Progression Formula

`function findMissingNumber(arr) {`

const n = arr.length + 1;

const expectedSum = (n * (n + 1)) / 2;

const actualSum = arr.reduce((sum, num) => sum + num, 0);

return expectedSum - actualSum;

}

const array = [1, 2, 4, 6, 3, 7, 8];

const uniqueArray = [...new Set(array)];

const missingNumber = findMissingNumber(uniqueArray);

console.log(`Missing number: ${missingNumber}`);

**Output:**

**Explanation:**

The `findMissingNumber`

function efficiently identifies the missing element in an array. By leveraging the arithmetic sum formula, it calculates the expected sum for a complete sequence of numbers up to the array's length. The actual sum of the array is then computed using the `reduce`

method. The missing number is obtained by subtracting the actual sum from the expected sum. In the provided example with `array1`

, the missing number is determined and displayed using `console.log`

. This concise and effective approach simplifies the process of identifying missing numbers in arrays.

# Approach 2:

# Using Summation Formula

`function findMissingNumber(inputArray, length) {`

let result = Math.floor((length + 1) * (length + 2) / 2);

for (let i = 0; i < length; i++) result -= inputArray[i];

return result;

}

let myArray = [1, 2, 3, 5];

let missingNumber = findMissingNumber(myArray, myArray.length);

document.write(missingNumber);

**Output**

**Explanation:**

The approach employed in the given JavaScript code utilizes the Gauss formula, also known as the arithmetic sum formula. This formula calculates the expected sum of a sequence of consecutive numbers up to a certain value. By subtracting the actual sum of the array elements from this expected sum, the code efficiently identifies and returns the missing number in the array.

# Approach 3:

# Using XOR

`function findMissingNumberWithXOR(sequence) {`

const length = sequence.length + 1; // Including the missing number

let xorOfAllNumbers = 0;

for (let i = 1; i <= length; i++) {

xorOfAllNumbers ^= i;

}

let xorOfArrayElements = sequence.reduce((acc, num) => acc ^ num, 0);

return xorOfAllNumbers ^ xorOfArrayElements;

}

const inputSequence = [2, 4, 6, 8, 10, 12, 14];

const result = findMissingNumberWithXOR(inputSequence);

console.log(`Missing number in the sequence ${inputSequence}: ${result}`);

**Output:**

**Explanation:**

The modified JavaScript code utilizes XOR operations to find the missing number in an array. The function, now named `findMissingNumberWithXOR`

, XORs the expected and actual XOR values of the sequence and array elements, respectively. The result effectively identifies the missing number. The example usage with `myArray`

demonstrates this XOR-based approach, highlighting the missing number in the array.

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