Find K such that array A can be converted into array B by adding K to a selected range [L, R]

Given two arrays a[] and b[] of length N consisting of unique elements, the task is to find a number K (K > 0) such that the first array can be converted into second array by adding K to a selected range [L, R] in the array. If no such number K exists, print NA

Examples:

Input: a[] = {3, 7, 1, 4, 0, 2, 2}, b[] = {3, 7, 3, 6, 2, 2, 2}
Output: 2
Explanation:
Array a[] can be converted into Array b[] by adding K = 2 to range [2, 4]



Input: a[] = {3, 7, 1, 4, 0, 1, 2}, b[] = {3, 7, 3, 6, 2, 2}
Output: NA

Approach:

  • Create a temporary array c[] which contains the difference of the array elements, i.e.,
    ci = bi - ai
    
  • Then create a vector pair for all non zero elements of array c[n] with there index. Therefore the vector pair will be as:
    vector<c[i], o>
    
    where c[i] is a non zero value in c[]
    and     i  is the index of c[i]
    
  • If the index value differs by 1 and the difference value is same, then K = difference value and [L, R] = the index range.
  • Hence the array a[n] can be converted into b[n] by adding K to [a[L], a[R]].

For Example:

  • Given
    a[n] = [3, 7, 1, 4, 0, 2, 2]
    b[n] = [3, 7, 3, 6, 2, 2, 2]
    
  • So, upon creating temporary array c[] and vector pair:
    c[n] = [0, 0, 2, 2, 2, 0, 0]
    vector pair = {{2, 2}, {2, 3}, {2, 4}}
    
  • As all the index values (2, 3, 4) in the vector pair differ by 1, so they are consecutive.
  • And the value of the difference is the same (2).
  • Hence, we can simply add that difference value in the first array a[n] in the given indexes [2, 4] to convert it into second array b[n].
  • Hence the required K value will be 2

Below is the implementation of the above approach:

C++

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// C++ implementation of above approach
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to Check if it is possible to
// convert a given array to another array
// by adding elements to first array
bool checkconv(int a[], int b[], int n)
{
    int c[n], flag = 0;
  
    // Create a temporary array c[]
    // which contains the difference
    // of the array elements
    for (int i = 0; i < n; i++) {
  
        c[i] = b[i] - a[i];
    }
  
    // Create a vector pair for all non zero
    // elements of array c[n] with there index
    vector<pair<int, int> > idxs;
    for (int i = 0; i < n; i++) {
        if (c[i] != 0)
            idxs.push_back(make_pair(i, c[i]));
    }
  
    // Check If the index value differs by 1
    // and the difference value is same
    for (int i = 0; i < idxs.size() - 1; i++) {
        if (idxs[i + 1].first - idxs[i].first != 1
            || idxs[i + 1].second != idxs[i].second) {
            flag = 1;
            break;
        }
    }
  
    return !flag;
}
  
// Function to calculate the value of K
int diffofarrays(int a[], int b[], int n)
{
    int c[n], ans = 0;
    for (int i = 0; i < n; i++) {
        c[i] = b[i] - a[i];
    }
    for (int i = 0; i < n; i++) {
        if (c[i] != 0) {
            ans = c[i];
            break;
        }
    }
  
    return ans;
}
  
// Driver code
int main()
{
    int A[] = { 3, 7, 1, 4, 0, 2, 2 };
    int B[] = { 3, 7, 3, 6, 2, 2, 2 };
    int arr_size = sizeof(A) / sizeof(A[0]);
  
    if (checkconv(A, B, arr_size)) {
        cout << diffofarrays(A, B, arr_size) << endl;
    }
    else
        cout << "NA" << endl;
    return 0;
}

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Java

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// Java implementation of above approach
import java.util.*;
  
class GFG
{
    static class pair
    
        int first, second; 
        public pair(int first, int second) 
        
            this.first = first; 
            this.second = second; 
        
    }
      
// Function to Check if it is possible to
// convert a given array to another array
// by adding elements to first array
static boolean checkconv(int a[], int b[], int n)
{
    int []c = new int[n];
    int flag = 0;
  
    // Create a temporary array c[]
    // which contains the difference
    // of the array elements
    for (int i = 0; i < n; i++)
    {
  
        c[i] = b[i] - a[i];
    }
  
    // Create a vector pair for all non zero
    // elements of array c[n] with there index
    Vector<pair > idxs = new Vector<pair>();
    for (int i = 0; i < n; i++)
    {
        if (c[i] != 0)
            idxs.add(new pair(i, c[i]));
    }
  
    // Check If the index value differs by 1
    // and the difference value is same
    for (int i = 0; i < idxs.size() - 1; i++)
    {
        if (idxs.get(i + 1).first - idxs.get(i).first != 1
            || idxs.get(i + 1).second != idxs.get(i).second) 
        {
            flag = 1;
            break;
        }
    }
  
    return flag == 1 ? false:true;
}
  
// Function to calculate the value of K
static int diffofarrays(int a[], int b[], int n)
{
    int []c = new int[n];
    int ans = 0;
    for (int i = 0; i < n; i++) 
    {
        c[i] = b[i] - a[i];
    }
    for (int i = 0; i < n; i++)
    {
        if (c[i] != 0)
        {
            ans = c[i];
            break;
        }
    }
    return ans;
}
  
// Driver code
public static void main(String[] args)
{
    int A[] = { 3, 7, 1, 4, 0, 2, 2 };
    int B[] = { 3, 7, 3, 6, 2, 2, 2 };
    int arr_size = A.length;
  
    if (checkconv(A, B, arr_size))
    {
        System.out.print(diffofarrays(A, B, arr_size) +"\n");
    }
    else
        System.out.print("NA" +"\n");
}
}
  
// This code is contributed by 29AjayKumar

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Python3

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# Python3 implementation of above approach 
  
# Function to Check if it is possible to 
# convert a given array to another array 
# by adding elements to first array 
def checkconv(a, b, n) : 
  
    c = [0]*n; flag = 0
  
    # Create a temporary array c[] 
    # which contains the difference 
    # of the array elements 
    for i in range(n) :
        c[i] = b[i] - a[i]; 
  
    # Create a vector pair for all non zero 
    # elements of array c[n] with there index 
    idxs = []; 
    for i in range(n) :
        if (c[i] != 0) :
            idxs.append((i, c[i])); 
  
    # Check If the index value differs by 1 
    # and the difference value is same 
    for i in range(len(idxs) - 1) :
        if (idxs[i + 1][0] - idxs[i][0] != 1
            or idxs[i + 1][1] != idxs[i][1]) :
            flag = 1
            break
  
    return not flag; 
  
# Function to calculate the value of K 
def diffofarrays(a, b, n) : 
    c = [0] * n; 
    ans = 0;
      
    for i in range(n) :
        c[i] = b[i] - a[i];
          
    for i in range(n) :
        if (c[i] != 0) :
            ans = c[i];
            break;
      
    return ans; 
  
# Driver code 
if __name__ == "__main__"
  
    A = [ 3, 7, 1, 4, 0, 2, 2 ];
    B = [ 3, 7, 3, 6, 2, 2, 2 ];
    arr_size = len(A);
      
    if (checkconv(A, B, arr_size)) :
        print(diffofarrays(A, B, arr_size));
          
    else :
        print("NA"); 
  
# This code is contributed by AnkitRai01

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C#

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// C# implementation of above approach
using System;
using System.Collections.Generic;
  
class GFG
{
    class pair
    
        public int first, second; 
        public pair(int first, int second) 
        
            this.first = first; 
            this.second = second; 
        
    }
      
// Function to Check if it is possible to
// convert a given array to another array
// by adding elements to first array
static bool checkconv(int []a, int []b, int n)
{
    int []c = new int[n];
    int flag = 0;
  
    // Create a temporary array c[]
    // which contains the difference
    // of the array elements
    for (int i = 0; i < n; i++)
    {
  
        c[i] = b[i] - a[i];
    }
  
    // Create a vector pair for all non zero
    // elements of array c[n] with there index
    List<pair > idxs = new List<pair>();
    for (int i = 0; i < n; i++)
    {
        if (c[i] != 0)
            idxs.Add(new pair(i, c[i]));
    }
  
    // Check If the index value differs by 1
    // and the difference value is same
    for (int i = 0; i < idxs.Count - 1; i++)
    {
        if (idxs[i + 1].first - idxs[i].first != 1
            || idxs[i + 1].second != idxs[i].second) 
        {
            flag = 1;
            break;
        }
    }
  
    return flag == 1 ? false:true;
}
  
// Function to calculate the value of K
static int diffofarrays(int []a, int []b, int n)
{
    int []c = new int[n];
    int ans = 0;
    for (int i = 0; i < n; i++) 
    {
        c[i] = b[i] - a[i];
    }
    for (int i = 0; i < n; i++)
    {
        if (c[i] != 0)
        {
            ans = c[i];
            break;
        }
    }
    return ans;
}
  
// Driver code
public static void Main(String[] args)
{
    int []A = { 3, 7, 1, 4, 0, 2, 2 };
    int []B = { 3, 7, 3, 6, 2, 2, 2 };
    int arr_size = A.Length;
  
    if (checkconv(A, B, arr_size))
    {
        Console.Write(diffofarrays(A, B, arr_size) +"\n");
    }
    else
        Console.Write("NA" +"\n");
}
}
  
// This code is contributed by 29AjayKumar

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Output:

2



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