Minimum number of operations to convert array A to array B by adding an integer into a subarray

Given two arrays A[] and B[] of length N, the task is to find the minimum number of operations in which the array A can be converted into array B where each operation consists of adding an integer K into a subarray from L to R.

Examples:

Input: A[] = {3, 7, 1, 4, 1, 2}, B[] = {3, 7, 3, 6, 3, 2} 
Output: 1 
Explanation:
In the above given example only one operation is required to convert from A to B: L = 3, R = 5 and K = 2 
Array after the following operation: 
Index 0: A[0] = 3, B[0] = 3 
Index 1: A[1] = 7, B[1] = 7 
Index 2: A[2] = 1 + 2 = 3, B[2] = 3 
Index 3: A[3] = 4 + 2 = 6, B[3] = 6 
Index 4: A[4] = 1 + 2 = 3, B[4] = 3 
Index 5: A[5] = 2, B[5] = 2

Input: A[] = {1, 1, 1, 1, 1}, B[] = {1, 2, 1, 3, 1} 
Output: 2 
Explanation:
In the above given example only one operation is required to convert from A to B - 
Operation 1: Add 1 to L = 2 to R = 2 
Operation 2: Add 2 to L = 4 to R = 4 

Approach: The idea is to count the consecutive elements, in array A, having an equal difference with the corresponding element in array B.

• Find the difference of the corresponding element from the array A and B:

Difference = A[i] - B[i]

• If the difference of the corresponding elements is equal to 0, then continue checking for the next index.
• Otherwise, Increase the index until the difference between consecutive elements is not equal to the previous difference of the consecutive elements
• Increment the count by 1, until all the indexes are iterated having the same difference.
• In the end, return the count as the minimum number of operations.

Below is the implementation of the above approach: 

C++

// C++ implementation to find the
// minimum number of operations in
// which the array A can be converted
// to another array B

#include <bits/stdc++.h>
using namespace std;

// Function to find the minimum
// number of operations in which
// array A can be converted to array B
void checkArray(int a[], int b[], int n)
{
    int operations = 0;
    int i = 0;
    
    // Loop to iterate over the array
    while (i < n) {
        
        // if both elements are equal
        // then move to next element
        if (a[i] - b[i] == 0) {
            i++;
            continue;
        }

        // Calculate the difference
        // between two elements
        int diff = a[i] - b[i];
        i++;

        // loop while the next pair of
        // elements have same difference
        while (i < n &&
           a[i] - b[i] == diff) {
            i++;
        }

        // Increase the number of
        // operations by 1
        operations++;
    }

    // Print the number of
    // operations required
    cout << operations << "\n";
}

// Driver Code
int main()
{
    int a[] = { 3, 7, 1, 4, 1, 2 };
    int b[] = { 3, 7, 3, 6, 3, 2 };
    int size = sizeof(a) / sizeof(a[0]);

    checkArray(a, b, size);

    return 0;
}

Java

// Java implementation to find the
// minimum number of operations in
// which the array A can be converted
// to another array B
class GFG {

    // Function to find the minimum
    // number of operations in which
    // array A can be converted to array B
    static void checkArray(int a[], int b[], int n)
    {
        int operations = 0;
        int i = 0;
        
        // Loop to iterate over the array
        while (i < n) {
            
            // if both elements are equal
            // then move to next element
            if (a[i] - b[i] == 0) {
                i++;
                continue;
            }
    
            // Calculate the difference
            // between two elements
            int diff = a[i] - b[i];
            i++;
    
            // loop while the next pair of
            // elements have same difference
            while (i < n &&
               a[i] - b[i] == diff) {
                i++;
            }
    
            // Increase the number of
            // operations by 1
            operations++;
        }
    
        // Print the number of
        // operations required
        System.out.println(operations);
    }
    
    // Driver Code
    public static void main (String[] args)
    {
        int a[] = { 3, 7, 1, 4, 1, 2 };
        int b[] = { 3, 7, 3, 6, 3, 2 };
        int size = a.length;
    
        checkArray(a, b, size);
    }
}

// This code is contributed by AnkitRai01

C#

// C# implementation to find the
// minimum number of operations in
// which the array A can be converted
// to another array B
using System;

class GFG {

    // Function to find the minimum
    // number of operations in which
    // array A can be converted to array B
    static void checkArray(int []a, int []b, int n)
    {
        int operations = 0;
        int i = 0;
        
        // Loop to iterate over the array
        while (i < n) {
            
            // if both elements are equal
            // then move to next element
            if (a[i] - b[i] == 0) {
                i++;
                continue;
            }
    
            // Calculate the difference
            // between two elements
            int diff = a[i] - b[i];
            i++;
    
            // loop while the next pair of
            // elements have same difference
            while (i < n &&
               a[i] - b[i] == diff) {
                i++;
            }
    
            // Increase the number of
            // operations by 1
            operations++;
        }
    
        // Print the number of
        // operations required
        Console.WriteLine(operations);
    }
    
    // Driver Code
    public static void Main (string[] args)
    {
        int []a = { 3, 7, 1, 4, 1, 2 };
        int []b = { 3, 7, 3, 6, 3, 2 };
        int size = a.Length;
    
        checkArray(a, b, size);
    }
}

// This code is contributed by AnkitRai01

Python3

# Python3 implementation to find the
# minimum number of operations in
# which the array A can be converted
# to another array B

# Function to find the minimum
# number of operations in which
# array A can be converted to array B
def checkArray(a, b, n) :

    operations = 0;
    i = 0;
    
    # Loop to iterate over the array
    while (i < n) :
        
        # if both elements are equal
        # then move to next element
        if (a[i] - b[i] == 0) :
            i += 1;
            continue;

        # Calculate the difference
        # between two elements
        diff = a[i] - b[i];
        i += 1;

        # loop while the next pair of
        # elements have same difference
        while (i < n and a[i] - b[i] == diff) :
            i += 1;

        # Increase the number of
        # operations by 1
        operations += 1;
    
    # Print the number of
    # operations required
    print(operations);

# Driver Code
if __name__ == "__main__" :

    a = [ 3, 7, 1, 4, 1, 2 ];
    b = [ 3, 7, 3, 6, 3, 2 ];
    size = len(a);

    checkArray(a, b, size);

# This code is contributed by AnkitRai01

JavaScript

<script>
// javascript implementation to find the
// minimum number of operations in
// which the array A can be converted
// to another array B    
// Function to find the minimum
    // number of operations in which
    // array A can be converted to array B
    function checkArray(a , b , n) {
        var operations = 0;
        var i = 0;

        // Loop to iterate over the array
        while (i < n) {

            // if both elements are equal
            // then move to next element
            if (a[i] - b[i] == 0) {
                i++;
                continue;
            }

            // Calculate the difference
            // between two elements
            var diff = a[i] - b[i];
            i++;

            // loop while the next pair of
            // elements have same difference
            while (i < n && a[i] - b[i] == diff) {
                i++;
            }

            // Increase the number of
            // operations by 1
            operations++;
        }

        // Print the number of
        // operations required
        document.write(operations);
    }

    // Driver Code
    
        var a = [ 3, 7, 1, 4, 1, 2 ];
        var b = [ 3, 7, 3, 6, 3, 2 ];
        var size = a.length;

        checkArray(a, b, size);

// This code contributed by Rajput-Ji 
</script>

Output

1

Performance Analysis:

• Time Complexity: As in the above approach, there is only one loop that takes O(N) time in the worst case. Hence, the Time Complexity will be O(N).
• Auxiliary Space Complexity: As in the above approach, there is no extra space used. Hence, the auxiliary space complexity will be O(1).

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