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Find missing element in a sorted array of consecutive numbers in C++
Concept
With respect of a given array array[] of n distinct integers, elements are placed sequentially in ascending order with one missing element. Our task is to determine the missing element.
Input
array[] = {1, 2, 3, 4, 5, 6, 7, 9}Output
8
Input
array[] = {-4, -2, -1, 0, 1, 2}Output
-3
Input
array[] = {1, 2, 3, 4}Output
-1
No element is missing.
Method
Principles
Look for inconsistency: According to this principle, the difference between any element and its index must be array[0] for every element.
Example,
A[] = {1, 2, 3, 4, 5} -> Consistent
B[] = {201, 202, 203, 204} -> Consistent
C[] = {1, 2, 3, 5, 6} -> Inconsistent as C[3] – 3 != C[0] i.e. 5 – 3 != 1
Determining inconsistency helps to scan only half of the array each time in O(logN).
Algorithm
Determine middle element and verify if it’s consistent.
If middle element is consistent, then verify if the difference between middle element and its next element is higher than 1 i.e. verify if array[mid + 1] – array[mid] > 1
If yes, then array[mid] + 1 is the missing element.
Else, we have to scan the right half array from the middle element and jump to step-1.
If middle element is inconsistent, then verify if the difference between middle element and its previous element is higher than 1 i.e. verify if array[mid] – array[mid – 1] > 1
If yes, then array[mid] – 1 is the missing element.
Else, we have to scan the left half array from the middle element and jump to step-1.
Example
// CPP implementation of the approach
#include<bits/stdc++.h>
using namespace std;
// Shows function to return the missing element
int findMissing(int array[], int n1){
int low = 0, high = n1 - 1;
int mid1;
while (high > low){
mid1 = low + (high - low) / 2;
// Verify if middle element is consistent
if (array[mid1] - mid1 == array[0]){
// Here, no inconsistency till middle elements
// When missing element is just after
// the middle element
if (array[mid1 + 1] - array[mid1] > 1)
return array[mid1] + 1;
else{
// Go right
low = mid1 + 1;
}
}
else{
// Here inconsistency found
// When missing element is just before
// the middle element
if (array[mid1] - array[mid1 - 1] > 1)
return array[mid1] - 1;
else{
// Go left
high = mid1 - 1;
}
}
}
// Here, no missing element found
return -1;
}
// Driver code
int main(){
int array[] = { -9, -8, -6, -5, -4, -3, -2, -1, 0 };
int n1 = sizeof(array)/sizeof(array[0]);
cout <<"The Missing Element:" <<(findMissing(array, n1));
}Output
The Missing Element:-7
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