C++ Program to Find lost element from a duplicated array
Last Updated :
09 Dec, 2022
Given two arrays that are duplicates of each other except one element, that is one element from one of the array is missing, we need to find that missing element.
Examples:
Input: arr1[] = {1, 4, 5, 7, 9}
arr2[] = {4, 5, 7, 9}
Output: 1
1 is missing from second array.
Input: arr1[] = {2, 3, 4, 5}
arr2[] = {2, 3, 4, 5, 6}
Output: 6
6 is missing from first array.
One simple solution is to iterate over arrays and check element by element and flag the missing element when an unmatched element is found, but this solution requires linear time oversize of the array.
Another efficient solution is based on a binary search approach. Algorithm steps are as follows:
- Start a binary search in a bigger array and get mid as (lo + hi) / 2
- If the value from both arrays is the same then the missing element must be in the right part so set lo as mid
- Else set hi as mid because the missing element must be in the left part of the bigger array if mid-elements are not equal.
- A special case is handled separately as for single element and zero elements array, the single element itself will be the missing element.
If the first element itself is not equal then that element will be the missing element./li>
Below is the implementation of the above steps
C++
// C++ program to find missing element from same
// arrays (except one missing element)
#include <bits/stdc++.h>
using namespace std;
// Function to find missing element based on binary
// search approach. arr1[] is of larger size and
// N is size of it. arr1[] and arr2[] are assumed
// to be in same order.
int findMissingUtil(int arr1[], int arr2[], int N)
{
// special case, for only element which is
// missing in second array
if (N == 1)
return arr1[0];
// special case, for first element missing
if (arr1[0] != arr2[0])
return arr1[0];
// Initialize current corner points
int lo = 0, hi = N - 1;
// loop until lo < hi
while (lo < hi)
{
int mid = (lo + hi) / 2;
// If element at mid indices are equal
// then go to right subarray
if (arr1[mid] == arr2[mid])
lo = mid;
else
hi = mid;
// if lo, hi becomes contiguous, break
if (lo == hi - 1)
break;
}
// missing element will be at hi index of
// bigger array
return arr1[hi];
}
// This function mainly does basic error checking
// and calls findMissingUtil
void findMissing(int arr1[], int arr2[], int M, int N)
{
if (N == M-1)
cout << "Missing Element is "
<< findMissingUtil(arr1, arr2, M) << endl;
else if (M == N-1)
cout << "Missing Element is "
<< findMissingUtil(arr2, arr1, N) << endl;
else
cout << "Invalid Input";
}
// Driver Code
int main()
{
int arr1[] = {1, 4, 5, 7, 9};
int arr2[] = {4, 5, 7, 9};
int M = sizeof(arr1) / sizeof(int);
int N = sizeof(arr2) / sizeof(int);
findMissing(arr1, arr2, M, N);
return 0;
}
Output :
Missing Element is 1
Time Complexity: O(logM + logN), where M and N represents the size of the given two arrays.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
What if input arrays are not in the same order?
In this case, the missing element is simply XOR of all elements of both arrays. Thanks to Yolo Song for suggesting this.
C++
// C++ program to find missing element from one array
// such that it has all elements of other array except
// one. Elements in two arrays can be in any order.
#include <bits/stdc++.h>
using namespace std;
// This function mainly does XOR of all elements
// of arr1[] and arr2[]
void findMissing(int arr1[], int arr2[], int M,
int N)
{
if (M != N-1 && N != M-1)
{
cout << "Invalid Input";
return;
}
// Do XOR of all element
int res = 0;
for (int i=0; i<M; i++)
res = res^arr1[i];
for (int i=0; i<N; i++)
res = res^arr2[i];
cout << "Missing element is " << res;
}
// Driver Code
int main()
{
int arr1[] = {4, 1, 5, 9, 7};
int arr2[] = {7, 5, 9, 4};
int M = sizeof(arr1) / sizeof(int);
int N = sizeof(arr2) / sizeof(int);
findMissing(arr1, arr2, M, N);
return 0;
}
Output :
Missing Element is 1
Time Complexity: O(M + N), where M and N represents the size of the given two arrays.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
Please refer complete article on Find lost element from a duplicated array for more details!
Similar Reads
DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. Data structures manage how data is stored and accessed, while algorithms focus on
7 min read
C++ Programming Language C++ is a computer programming language developed by Bjarne Stroustrup as an extension of the C language. It is known for is fast speed, low level memory management and is often taught as first programming language. It provides:Hands-on application of different programming concepts.Similar syntax to
5 min read
Quick Sort QuickSort is a sorting algorithm based on the Divide and Conquer that picks an element as a pivot and partitions the given array around the picked pivot by placing the pivot in its correct position in the sorted array. It works on the principle of divide and conquer, breaking down the problem into s
12 min read
Merge Sort - Data Structure and Algorithms Tutorials Merge sort is a popular sorting algorithm known for its efficiency and stability. It follows the divide-and-conquer approach. It works by recursively dividing the input array into two halves, recursively sorting the two halves and finally merging them back together to obtain the sorted array. Merge
14 min read
Bubble Sort Algorithm Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity are quite high.We sort the array using multiple passes. After the fir
8 min read
Data Structures Tutorial Data structures are the fundamental building blocks of computer programming. They define how data is organized, stored, and manipulated within a program. Understanding data structures is very important for developing efficient and effective algorithms. What is Data Structure?A data structure is a st
2 min read
Breadth First Search or BFS for a Graph Given a undirected graph represented by an adjacency list adj, where each adj[i] represents the list of vertices connected to vertex i. Perform a Breadth First Search (BFS) traversal starting from vertex 0, visiting vertices from left to right according to the adjacency list, and return a list conta
15+ min read
Binary Search Algorithm - Iterative and Recursive Implementation Binary Search Algorithm is a searching algorithm used in a sorted array by repeatedly dividing the search interval in half. The idea of binary search is to use the information that the array is sorted and reduce the time complexity to O(log N). Binary Search AlgorithmConditions to apply Binary Searc
15 min read
Insertion Sort Algorithm Insertion sort is a simple sorting algorithm that works by iteratively inserting each element of an unsorted list into its correct position in a sorted portion of the list. It is like sorting playing cards in your hands. You split the cards into two groups: the sorted cards and the unsorted cards. T
9 min read
Dijkstra's Algorithm to find Shortest Paths from a Source to all Given a weighted undirected graph represented as an edge list and a source vertex src, find the shortest path distances from the source vertex to all other vertices in the graph. The graph contains V vertices, numbered from 0 to V - 1.Note: The given graph does not contain any negative edge. Example
12 min read