Find the missing value from Array B formed by adding some value X to Array A
Last Updated :
28 Oct, 2021
Given two arrays arr1[] and arr2[] of size N and N - 1 respectively. Each value in arr2[] is obtained by adding a hidden value say X to any arr1[i] for N-1 times, which means for any i, arr1[i]+X is not included in arr2[] that is the missing value in arr2[]. The task is to find both the hidden value X and the missing value which is not picked from arr1[].
Examples:
Input: arr1[] = {3, 6, 5, 10}, arr2[] = {17, 10, 13}
Output: Hidden = 7, Missing = 5
Explanation: The elements of the second array are obtained in the following way:
First element: (10 + 7) = 17, 10 is the element at index 4 of arr1[]
Second element: (3 + 7) = 10, 3 is the element at index 0 of arr1[]
Third element: (6 + 7) = 13, 6 is the element at index 1 of arr1[]
So, 7 is the hidden value and 5 is the missing value.
Input: arr1[] = {4, 1, 7}, arr2[] = {4, 10}
Output: Hidden = 3, Missing = 4
Approach: This problem can be solved by using
- Sort both the given arrays in non-decreasing order.
- Create an unordered map to store differences.
- Traverse the arrays till N - 1 and check for the values by storing the differences of elements of both the arrays.
- Let a = arr2[i] - arr1[i] and b = arr2[i] - arr1[i+1].
- If a!=b then check if
- a > 0, then store it in map.
- b > 0, then store it in map.
- else check if a > 0, then store it in map.
- Iterate over the map and find the hidden value and print it.
- Traverse arr1[] by adding the hidden value and check if it is present in arr2[], else print the missing value.
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the hidden
// and missing values
void findHiddenMissing(int arr1[], int arr2[], int N)
{
// Sorting both the arrays
sort(arr1, arr1 + N);
sort(arr2, arr2 + N - 1);
// Create a map
unordered_map<int, int> mp;
// Traversing the arrays and
// checking for the values
for (int i = 0; i < N - 1; i++) {
// Variable to store the difference
// between the elements of arr2
// and arr1 in same indices
int a = arr2[i] - arr1[i];
// Variable to store the difference
// between the elements of arr2
// and arr1 next index
int b = arr2[i] - arr1[i + 1];
// If a is not equals to b
if (a != b) {
// If a is greater than 0
if (a > 0)
mp[a] += 1;
// If b is greater than 0
if (b > 0)
mp[b] += 1;
}
// If a is equal to b
else {
// If a is greater than 0
if (a > 0)
mp[a] += 1;
}
}
// To store the hidden value
int hidden;
// Iterate over the map and searching
// for the hidden value
for (auto it : mp) {
if (it.second == N - 1) {
hidden = it.first;
cout << "Hidden: " << it.first;
break;
}
}
cout << endl;
// Find the missing value
for (int i = 0; i < N; i++) {
if (arr1[i] + hidden != arr2[i]) {
cout << "Missing: " << arr1[i];
break;
}
}
}
// Driver Code
int main()
{
int arr1[] = { 3, 6, 5, 10 };
int arr2[] = { 17, 10, 13 };
int N = sizeof(arr1) / sizeof(arr1[0]);
findHiddenMissing(arr1, arr2, N);
return 0;
}
// Java program for the above approach
import java.util.Arrays;
import java.util.HashMap;
class GFG {
// Function to find the hidden
// and missing values
public static void findHiddenMissing(int arr1[], int arr2[], int N)
{
// Sorting both the arrays
Arrays.sort(arr1);
Arrays.sort(arr2);
// Create a map
HashMap<Integer, Integer> mp = new HashMap<Integer, Integer>();
// Traversing the arrays and
// checking for the values
for (int i = 0; i < N - 1; i++)
{
// Variable to store the difference
// between the elements of arr2
// and arr1 in same indices
int a = arr2[i] - arr1[i];
// Variable to store the difference
// between the elements of arr2
// and arr1 next index
int b = arr2[i] - arr1[i + 1];
// If a is not equals to b
if (a != b) {
// If a is greater than 0
if (a > 0) {
if (mp.containsKey(a))
mp.put(a, mp.get(a) + 1);
else
mp.put(a, 1);
}
// If b is greater than 0
if (b > 0)
if (mp.containsKey(b))
mp.put(b, mp.get(b) + 1);
else
mp.put(b, 1);
}
// If a is equal to b
else {
// If a is greater than 0
if (a > 0)
if (mp.containsKey(a))
mp.put(a, mp.get(a) + 1);
else
mp.put(a, 1);
}
}
// To store the hidden value
int hidden = 0;
// Iterate over the map and searching
// for the hidden value
for (int it : mp.keySet()) {
if (mp.get(it) == N - 1) {
hidden = it;
System.out.println("Hidden: " + it);
break;
}
}
// Find the missing value
for (int i = 0; i < N; i++) {
if (arr1[i] + hidden != arr2[i]) {
System.out.println("Missing: " + arr1[i]);
break;
}
}
}
// Driver Code
public static void main(String args[]) {
int arr1[] = { 3, 6, 5, 10 };
int arr2[] = { 17, 10, 13 };
int N = arr1.length;
findHiddenMissing(arr1, arr2, N);
}
}
// This code is contributed by saurabh_jaiswal.
# python program for the above approach
# Function to find the hidden
# and missing values
def findHiddenMissing(arr1, arr2, N):
# Sorting both the arrays
arr1.sort()
arr2.sort()
# Create a map
mp = {}
# Traversing the arrays and
# checking for the values
for i in range(0, N - 1):
# Variable to store the difference
# between the elements of arr2
# and arr1 in same indices
a = arr2[i] - arr1[i]
# Variable to store the difference
# between the elements of arr2
# and arr1 next index
b = arr2[i] - arr1[i + 1]
# If a is not equals to b
if (a != b):
# If a is greater than 0
if (a > 0):
if not a in mp:
mp[a] = 1
else:
mp[a] += 1
# If b is greater than 0
if (b > 0):
if not b in mp:
mp[b] = 1
else:
mp[b] += 1
# If a is equal to b
else:
# If a is greater than 0
if (a > 0):
if not a in mp:
mp[a] = 1
else:
mp[a] += 1
# To store the hidden value
hidden = 0
# Iterate over the map and searching
# for the hidden value
for it in mp:
if (mp[it] == N - 1):
hidden = it
print("Hidden:", end=" ")
print(it)
break
# Find the missing value
for i in range(0, N):
if (arr1[i] + hidden != arr2[i]):
print("Missing:", end=" ")
print(arr1[i])
break
# Driver Code
if __name__ == "__main__":
arr1 = [3, 6, 5, 10]
arr2 = [17, 10, 13]
N = len(arr1)
findHiddenMissing(arr1, arr2, N)
# This code is contributed by rakeshsahni
// C# program for the above approach
using System;
using System.Collections;
using System.Collections.Generic;
class GFG {
// Function to find the hidden
// and missing values
public static void findHiddenMissing(int []arr1, int []arr2, int N)
{
// Sorting both the arrays
Array.Sort(arr1);
Array.Sort(arr2);
// Create a map
Dictionary<int, int> mp = new Dictionary<int, int>();
// Traversing the arrays and
// checking for the values
for (int i = 0; i < N - 1; i++)
{
// Variable to store the difference
// between the elements of arr2
// and arr1 in same indices
int a = arr2[i] - arr1[i];
// Variable to store the difference
// between the elements of arr2
// and arr1 next index
int b = arr2[i] - arr1[i + 1];
// If a is not equals to b
if (a != b) {
// If a is greater than 0
if (a > 0) {
if (mp.ContainsKey(a))
mp[a] = mp[a] + 1;
else
mp.Add(a, 1);
}
// If b is greater than 0
if (b > 0)
if (mp.ContainsKey(b))
mp[b] = mp[b] + 1;
else
mp.Add(b, 1);
}
// If a is equal to b
else {
// If a is greater than 0
if (a > 0)
if (mp.ContainsKey(a))
mp[a] = mp[a] + 1;
else
mp.Add(a, 1);
}
}
// To store the hidden value
int hidden = 0;
// Iterate over the map and searching
// for the hidden value
foreach(int it in mp.Keys) {
if (mp[it] == N - 1) {
hidden = it;
Console.WriteLine("Hidden: " + it);
break;
}
}
// Find the missing value
for (int i = 0; i < N; i++) {
if (arr1[i] + hidden != arr2[i]) {
Console.WriteLine("Missing: " + arr1[i]);
break;
}
}
}
// Driver Code
public static void Main(string []args) {
int []arr1 = { 3, 6, 5, 10 };
int []arr2 = { 17, 10, 13 };
int N = arr1.Length;
findHiddenMissing(arr1, arr2, N);
}
}
// This code is contributed by rutvik_56.
<script>
// Javascript program for the above approach
// Function to find the hidden
// and missing values
function findHiddenMissing(arr1, arr2, N)
{
// Sorting both the arrays
arr1.sort((a, b) => a - b);
arr2.sort((a, b) => a - b);
// Create a map
let mp = new Map();
// Traversing the arrays and
// checking for the values
for (let i = 0; i < N - 1; i++)
{
// Variable to store the difference
// between the elements of arr2
// and arr1 in same indices
let a = arr2[i] - arr1[i];
// Variable to store the difference
// between the elements of arr2
// and arr1 next index
let b = arr2[i] - arr1[i + 1];
// If a is not equals to b
if (a != b) {
// If a is greater than 0
if (a > 0) {
if (mp.has(a)) {
mp.set(a, mp.get(a) + 1);
} else {
mp.set(a, 1);
}
}
// If b is greater than 0
if (b > 0)
if (mp.has(b)) {
mp.set(b, mp.get(b) + 1);
} else {
mp.set(b, 1);
}
}
// If a is equal to b
else {
// If a is greater than 0
if (a > 0) {
if (mp.has(a)) {
mp.set(a, mp.get(a) + 1);
} else {
mp.set(a, 1);
}
}
}
}
// To store the hidden value
let hidden;
// Iterate over the map and searching
// for the hidden value
for (let it of mp) {
if (it[1] == N - 1) {
hidden = it[0];
document.write("Hidden: " + it[0]);
break;
}
}
document.write("<br>");
// Find the missing value
for (let i = 0; i < N; i++) {
if (arr1[i] + hidden != arr2[i]) {
document.write("Missing: " + arr1[i]);
break;
}
}
}
// Driver Code
let arr1 = [3, 6, 5, 10];
let arr2 = [17, 10, 13];
let N = arr1.length;
findHiddenMissing(arr1, arr2, N);
// This code is contributed by saurabh_jaiswal.
</script>
OutputHidden: 7
Missing: 5
Time Complexity: O(N)
Auxiliary Space: O(N)
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