JavaScript Program to Find Missing Number in Matrix

You are presented with a two-dimensional matrix, matrix[][]where each row contains an ordered sequence of positive integers. The task is to find the missing number in the matrix.

NOTE: Each row is a sequence of unique positive integers, arranged in ascending order.

Approach 1: Using Summation of First N Natural Numbers

• Flatten the Matrix: Convert the 2D matrix into a 1D array to work with the numbers more easily.
• Calculate Expected Total: Determine the total sum of the first N natural numbers (1 to N), where N is the length of the flattened array plus one.
• Calculate Actual Sum: Iterate through the flattened array and compute the sum of its elements.
• Find the Missing Number: Subtract the actual sum from the expected total to find the missing number.
• Display the Result: Print the missing number to the console.

We know,

Sum of first n natural numbers is (n * (n + 1)) / 2;

Example: In this example, the code efficiently calculates and finds the missing number in a 2D matrix by comparing the expected and actual sums of the numerical sequence using JavaScript.

Javascript

const matrix = [
    [1, 2],
    [4, 5],
    [6, 8],
    [7, 9]
];

const flattenedArray = matrix.flat();
const n = flattenedArray.length + 1;
const sumOfFirstN = (n * (n + 1)) / 2;

let sumOfArray = 0;
for (let i = 0; i < n - 1; i++) {
    sumOfArray += flattenedArray[i];
}

const missingNumber = sumOfFirstN - sumOfArray;

console.log("Missing Number: ", missingNumber);

Output

Missing Number:  3

Approach 2: Using Hashing

• Flatten the Matrix: Convert the 2D matrix into a 1D array to work with individual elements more easily.
• Create a Temporary Array: Create a temporary array temp of size n + 1, where n is the length of the flattened array. Initialize all elements of temp to 0.
• Mark Existing Numbers: Iterate through the flattened array. For each element, set the corresponding index in the temp array to 1, indicating that the number exists in the sequence.
• Find the Missing Number: Iterate through the temp array. The first index with a value of 0 corresponds to the missing number. Add 1 to the index to get the missing number itself.
• Display the Result: Print the missing number to the console.

Example: In this example, the code efficiently finds the missing number in a 2D matrix by marking existing numbers and identifying the missing one using JavaScript.

Javascript

const matrix = [
    [1, 2],
    [3, 4],
    [6, 7]
];
const flattenedArray = matrix.flat();
let n = flattenedArray.length;

let temp = new Array(n + 1).fill(0);

// If array element exists then set the frequency to 1
for (let i = 0; i < n; i++) {
    temp[flattenedArray[i] - 1] = 1;
}

let missingNumber = 0;
for (let i = 0; i <= n; i++) {
    if (temp[i] === 0) {
        missingNumber = i + 1;
        break;
         // Exit loop once missing number is found
    }
}

console.log("Missing Number:", missingNumber);

Output

Missing Number: 5