! Missing Number

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• Problem Statement
• Uncomplicated Approach
• C Implementation
• Java Implementation
• Python Implementation
• XoR Approach
• Dry Run of XoR Approach
• C Implementation of XoR Approach
• Java Implementation of XoR Approach
• Python Implementation of XoR Arroyo
• Do Questions
• Frequently Asked Questions

Problem Statement

You are given an array of integers of size N – i ranging from 1 to N. There are no duplicates in the list. I of the integers is missing in the assortment. The task is to observe the missing number in the series.

Examples:

Input: list[] = {ane, 2, 4, 6, iii, vii, 8,10,5}
Output: 9
Explanation: The missing number from 1 to 10 is 9.

Input: list[] = {3, 2, 4, 5}
Output: 3
Caption: The missing number from 1 to 5 is ane.

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Simple Arroyo

This method uses the formula of summation.

The size of the array is N – 1. So the sum of northward elements, that is the sum of numbers from 1 to N can be calculated by using the formula N * (Northward + 1) / 2. At present find the summation of all elements in the array and subtract it from the summation of first N natural numbers, the value obtained will be the value of the missing element.

Algorithm:

• Calculate the summation of beginning N natural numbers as Total = Northward * (N + one) / 2
• Create a variable sum to shop the summation of elements of the array.
• Iterate the array from showtime to end.
• Updating the value of sum every bit sum = sum + array[i]
• Impress the missing number as the Full – sum

C Implementation

int MissingNo(int a[], int n) {   int i, full;   total = (north + 1) * (n + 2) / 2;   for (i = 0; i < due north; i++)     total -= a[i];   return total; }

Coffee Implementation

MissingNumbers(int[] arr) {   for (int i = 0; i < arr.length; i++) {     int index = Math.abs(arr[i]);     if (arr[index - ane] > 0) {       arr[index - 1] *= -1;     }   }   List < Integer > ans = new ArrayList < > ();   for (int i = 0; i < arr.length; i++) {     if (arr[i] > 0) {       ans.add together(i + 1);     }   }   return ans;  }

Python Implementation

def MissingNo(arr):     north = len(arr)     total = (northward + 1)*(n + two)/2     arr_sum = sum(arr)     return full - arr_sum

Time Complexity: O(Northward) where N is the size of the assortment.
Space Complexity: O(1) because no extra infinite is needed.

XoR Arroyo

This method uses the technique of XOR to solve the problem.

Approach: XOR has certain properties Assume
a1 ^ a2 ^ a3 ^ …^ an = A1 and a1 ^ a2 ^ a3 ^ …^ an-1 = A2, And then A1 ^ A2 = an

Algorithm:

• Create two variables a1= 0 and a2 = 0
• Iterate from 1 to north with i as the counter.
• For every index i update a1 as a1 = a1 ^ i
• At present iterate over the array from starting time to end.
• For every index i update a2 equally a2 = a2 ^ arr[i]
• Print the missing number as a1 ^ a2.

Dry Run of XoR Arroyo

Dry Run of XoR Arroyo

C Implementation of XoR Approach

int MissingNo(int arr[], int northward) {   int x1 = arr[0];   int x2 = 1;    for (int i = i; i < n; i++)     x1 = x1 ^ arr[i];    for (int i = 2; i <= n + 1; i++)     x2 = x2 ^ i;    return (x1 ^ x2); }

Coffee Implementation of XoR Approach

static int MissingNo(int arr[], int northward) {   int x1 = arr[0];   int x2 = 1;    for (int i = ane; i < north; i++)     x1 = x1 ^ arr[i];    for (int i = 2; i <= n + i; i++)     x2 = x2 ^ i;    return (x1 ^ x2); }

Python Implementation of XoR Arroyo

def MissingNo(arr, due north):     x1 = arr[0]     x2 = 1           for i in range(1, due north):         x1 = x1 ^ arr[i]               for i in range(two, n + ii):         x2 = x2 ^ i           render x1 ^ x2

Time Complexity: O(N) where N is the size of the assortment because only 1 traversal is needed.
Space Complexity: O(1) because no extra infinite is needed.

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Practice Questions

First Missing Integer
Repeat and Missing Number Array

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Frequently Asked Questions

What are the constraints of this problem?
All the numbers in the array should be betwixt one to N, where N -1 is the size of the array.

Will these approaches piece of work for larger numbers?
No, it will merely work for numbers less than 10^6 because we tin non make an array of greater size.

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Source: https://www.interviewbit.com/blog/find-the-missing-number/

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