Queries to update array by adding or multiplying array elements and print the element present at specified index

Given an array arr[] consisting of N integers and an array Q[] of M pairs representing a query of type {X, Y}, the task is to perform queries of the following type:

• Query(0, X): Add integer X to every array elements.
• Query(1, Y): Multiply each array element by Y.
• Query(2, i): Print the value at index i.

Examples:

Input: arr[] = {5, 1, 2, 3, 9}, Q[][] = {{0, 5}, {2, 4}, {1, 4}, {0, 2}, {2, 3}}
Output: 14 34
Explanation:
Below are the results after performing each query:

1. Query(0, 5): Adding 5 to every array elements, modifies the array as arr[] = {10, 6, 7, 8, 14}.
2. Query(2, 4): Print the array element at index 4, i.e., arr[4] = 14.
3. Query(1, 4): Multiplying every array elements with 4, modifies the array as arr[] = {40, 24, 28, 32, 56}
4. Query(0, 2): Adding 2 to every array elements, modifies the array as arr[] = {42, 26, 30, 34, 58}
5. Query(2, 3): Print the element at index 4, i.e., arr[3] = 34.

Input: arr[] = {3, 1, 23, 45, 100}, Q[][] = {{1, 2}, {0, 10}, {2, 3}, {1, 5}, {2, 4}}
Output: 100 1050

Naive Approach: The simplest approach is to solve the given problem is to perform each query by traversing the given array and print the result accordingly for each query.

Time Complexity: O(N * M)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized based on the following observations:

• Suppose A is an element and the following operation is performed:
  • Adding a1 to A, then the value of A becomes A = A + a1.
  • Multiply A by b1, then the value of A becomes A = b1 * A + b1 * a1.
  • Add a2 to A, then the value of A becomes A = b1 * A + b1 * a1 + a2.
  • Multiply A by b2, then the value of A becomes, A = b1 * b2 * A + b1 * b2 * a1 + a2 * b2
• Suppose Mul is the multiplication of all the integers of the query of type 1 and Add stores the value of all the query of type 0, and type 1 performed in the given order starting as 0. Then it can be observed from above that any array element arr[i] modifies to (arr[i] * Mul + Add).

Follow the steps below to solve the problem:

• Initialize two variables, say Mul as 1 and Add as 0, stores the multiplication of all the integers in the query of type 2 and stores the value got after performing the query of type 1 and 2 in the given order on a number 0.
• Traverse the given array of queries Q[][2] and perform the following steps:
  • If Q[i][0] is 0, then increment the value of Add by Q[i][1].
  • Otherwise, if the value of Q[i][0] is 1 then multiply Mul and Add by Q[i][1].
  • Otherwise, print the value (arr[Q[i][1]] * Mul + Add) as the result for the query of type 2.

Below is the implementation of the above approach:

// C++ program for the above approach

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

// Function to modify the array
// by performing given queries
void Query(int arr[], int N,
           vector<vector<int> > Q)
{
    // Stores the multiplication
    // of all integers of type 1
    int mul = 1;

    // Stores the value obtained after
    // performing queries of type 1 & 2
    int add = 0;

    // Iterate over the queries
    for (int i = 0; i < Q.size(); i++) {

        // Query of type 0
        if (Q[i][0] == 0) {

            // Update the value of add
            add = add + Q[i][1];
        }

        // Query of type 1
        else if (Q[i][0] == 1) {

            // Update the value of mul
            mul = mul * Q[i][1];

            // Update the value of add
            add = add * Q[i][1];
        }

        // Otherwise
        else {

            // Store the element at index Q[i][1]
            int ans = arr[Q[i][1]] * mul + add;

            // Print the result for
            // the current query
            cout << ans << " ";
        }
    }
}

// Driver Code
int main()
{
    int arr[] = { 3, 1, 23, 45, 100 };
    int N = sizeof(arr) / sizeof(arr[0]);

    vector<vector<int> > Q = {
        { 1, 2 }, { 0, 10 }, 
        { 2, 3 }, { 1, 5 }, { 2, 4 }
    };
    Query(arr, N, Q);

    return 0;
}

// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

public class GFG
{

    // Function to modify the array
    // by performing given queries
    static void Query(int arr[], int N, int Q[][])
    {
      
        // Stores the multiplication
        // of all integers of type 1
        int mul = 1;

        // Stores the value obtained after
        // performing queries of type 1 & 2
        int add = 0;

        // Iterate over the queries
        for (int i = 0; i < Q.length; i++) {

            // Query of type 0
            if (Q[i][0] == 0) {

                // Update the value of add
                add = add + Q[i][1];
            }

            // Query of type 1
            else if (Q[i][0] == 1) {

                // Update the value of mul
                mul = mul * Q[i][1];

                // Update the value of add
                add = add * Q[i][1];
            }

            // Otherwise
            else {

                // Store the element at index Q[i][1]
                int ans = arr[Q[i][1]] * mul + add;

                // Print the result for
                // the current query
                System.out.print(ans + " ");
            }
        }
    }

    // Driver Code
    public static void main(String[] args)
    {

        int arr[] = { 3, 1, 23, 45, 100 };
        int N = arr.length;

        int Q[][] = { { 1, 2 },
                      { 0, 10 },
                      { 2, 3 },
                      { 1, 5 },
                      { 2, 4 } };
        Query(arr, N, Q);
    }
}

// This code is contributed by Kingash.

# Python3 program for the above approach

# Function to modify the array
# by performing given queries
def Query(arr, N, Q):
  
    # Stores the multiplication
    # of all integers of type 1
    mul = 1

    # Stores the value obtained after
    # performing queries of type 1 & 2
    add = 0

    # Iterate over the queries
    for i in range(len(Q)):
      
        # Query of type 0
        if (Q[i][0] == 0):
          
            # Update the value of add
            add = add + Q[i][1]
            
        # Query of type 1
        elif (Q[i][0] == 1):

            # Update the value of mul
            mul = mul * Q[i][1]

            # Update the value of add
            add = add * Q[i][1]
        # Otherwise
        else:

            # Store the element at index Q[i][1]
            ans = arr[Q[i][1]] * mul + add

            # Print result for
            # the current query
            print(ans,end=" ")

# Driver Code
if __name__ == '__main__':

    arr = [3, 1, 23, 45, 100]
    N = len(arr)
    Q = [
        [ 1, 2 ], [ 0, 10 ],
        [ 2, 3 ], [ 1, 5 ], [ 2, 4 ]
    ]
    Query(arr, N, Q)

# This code is contributed by mohit kumar 29.

// C# program for the above approach
using System;
class GFG {

  // Function to modify the array
  // by performing given queries
  static void Query(int[] arr, int N, int[, ] Q)
  {
    // Stores the multiplication
    // of all integers of type 1
    int mul = 1;

    // Stores the value obtained after
    // performing queries of type 1 & 2
    int add = 0;

    // Iterate over the queries
    for (int i = 0; i < Q.GetLength(0); i++) {

      // Query of type 0
      if (Q[i, 0] == 0) {

        // Update the value of add
        add = add + Q[i, 1];
      }

      // Query of type 1
      else if (Q[i, 0] == 1) {

        // Update the value of mul
        mul = mul * Q[i, 1];

        // Update the value of add
        add = add * Q[i, 1];
      }

      // Otherwise
      else {

        // Store the element at index Q[i][1]
        int ans = arr[Q[i, 1]] * mul + add;

        // Print the result for
        // the current query
        Console.Write(ans + " ");
      }
    }
  }

  // Driver Code
  public static void Main()
  {
    int[] arr = { 3, 1, 23, 45, 100 };
    int N = arr.Length;

    int[, ] Q = { { 1, 2 },
                 { 0, 10 },
                 { 2, 3 },
                 { 1, 5 },
                 { 2, 4 } };
    Query(arr, N, Q);
  }
}

// This code is contributed by ukasp.

<script>
// Javascript implementation of the above approach

    // Function to modify the array
    // by performing given queries
    function Query(arr, N, Q)
    {
      
        // Stores the multiplication
        // of all integers of type 1
        let mul = 1;

        // Stores the value obtained after
        // performing queries of type 1 & 2
        let add = 0;

        // Iterate over the queries
        for (let i = 0; i < Q.length; i++) {

            // Query of type 0
            if (Q[i][0] == 0) {

                // Update the value of add
                add = add + Q[i][1];
            }

            // Query of type 1
            else if (Q[i][0] == 1) {

                // Update the value of mul
                mul = mul * Q[i][1];

                // Update the value of add
                add = add * Q[i][1];
            }

            // Otherwise
            else {

                // Store the element at index Q[i][1]
                let ans = arr[Q[i][1]] * mul + add;

                // Print the result for
                // the current query
                document.write(ans + " ");
            }
        }
    }

  // Driver Code
    
     let arr = [ 3, 1, 23, 45, 100 ];
        let N = arr.length;

        let Q = [[ 1, 2 ],
                      [ 0, 10 ],
                      [ 2, 3 ],
                      [ 1, 5 ],
                      [ 2, 4 ]];
        Query(arr, N, Q);
      
</script>


    

100 1050

Time Complexity: O(M)
Auxiliary Space: O(1),  since no extra space has been taken.