Missing Number In Arithmetic Progression using C++

Suppose we have an array that represents elements of arithmetic progression in order. One element is missing. We have to find the missing element. So if arr = [2, 4, 8, 10, 12, 14], output is 6, as 6 is missing.

Using binary search, we can solve this problem. We will go to the middle element, then check whether the difference between the middle and next to the middle is the same as diff or not. If not, then the missing element is present between indices mid and mid + 1. If the middle element is the n/2th element in the AP, then the missing element lies in the right half, otherwise to the left half.

Example (C++)

 Live Demo

#include <iostream>
using namespace std;
#define INT_MAX 999999
class Progression {
   public:
   int missingUtil(int arr[], int left, int right, int diff) {
      if (right <= left)
         return INT_MAX;
      int mid = left + (right - left) / 2;
      if (arr[mid + 1] - arr[mid] != diff)
         return (arr[mid] + diff);
      if (mid > 0 && arr[mid] - arr[mid - 1] != diff)
         return (arr[mid - 1] + diff);
      if (arr[mid] == arr[0] + mid * diff)
         return missingUtil(arr, mid + 1, right, diff);
      return missingUtil(arr, left, mid - 1, diff);
   }
   int missingElement(int arr[], int n) {
      int diff = (arr[n - 1] - arr[0]) / n;
      return missingUtil(arr, 0, n - 1, diff);
   }
};
int main() {
   Progression pg;
   int arr[] = {2, 4, 8, 10, 12, 14};
   int n = sizeof(arr) / sizeof(arr[0]);
   cout << "The missing element is: " << pg.missingElement(arr, n)<<endl;
}

Input

[2,4,8,10,12,14]

Output

The missing element is: 6

Arnab Chakraborty

Published on 09-Jan-2020 09:59:40

• Related Questions & Answers
• Find the missing number in Arithmetic Progression in C++
• Finding the missing number in an arithmetic progression sequence in JavaScript
• Find the missing number in Geometric Progression in C++
• Count of AP (Arithmetic Progression) Subsequences in an array in C++
• C Program for N-th term of Arithmetic Progression series
• C program to find the sum of arithmetic progression series
• Arithmetic Number in C++
• Convert given array to Arithmetic Progression by adding an element in C++
• Find the one missing number in range using C++
• Program to check we can make arithmetic progression from sequence in Python
• JavaScript code to find nth term of a series - Arithmetic Progression (AP)
• Find the only missing number in a sorted array using C++
• Missing Number in Python
• Arithmetic of Number Systems
• Binary Number System - Overflow in Arithmetic Addition in C/C++?