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Add elements of one Array in all Subarrays of size M of other Array

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  • Difficulty Level : Expert
  • Last Updated : 27 Jan, 2023
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Given two arrays arr1[] and arr2[] of size N and M (M < N) add all elements of arr2[] in all possible subarrays of arr1[] of size M exactly once. The task is to return the final array arr1[] after performing the above operations.

Examples: 

Input: arr1[] = {1, 1, 1, 1, 1}, arr2[] = {1, 1, 1}
Output:  2 3 4 3 2
Explanation: There are exactly 3 subarrays of size M in arr1[] 
adding corresponding elements of arr2[] in first subarray from element 1 to 3. arr1[] becomes {2, 2, 2, 1, 1}
adding corresponding elements of arr2[] in second subarray from element 2 to 4. arr1[] becomes {2, 3, 3, 2, 1}
adding corresponding elements of arr2[] in the third subarray from elements 3 to 5. arr1[] becomes {2, 3, 4, 3, 2}

Input: arr1[] = {1, 2, 3, 4, 5}, arr2[] = {10}
Output: 11 12 13 14 15

Naive Approach: The problem can be solved using linear iteration based on the following idea:

Keep adding all elements of arr2[] in all possible subarrays of size M of arr1[]. There will be exactly N – M + 1 subarrays.

Follow the steps mentioned below to implement the idea:

  • Iterate from i = 0 to N-M+1:
    • Iterate from j = 0 to M:
      • Add arr2[j] with arr[i+j.
  • Return the final state of arr1[] as the required answer.

Below is the implementation of the above approach.

C++




// C++ code to implement the approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the final state of arr1[]
void addArr2ToArr1(int arr1[], int arr2[], int N, int M)
{
    // Iterating through all possible subarrays
    // of size M in arr1[] there will be
    // exactly N - M + 1 subarrays
    for (int i = 0; i < N - M + 1; i++) {
 
        // Iterating through M elements of arr2[]
        // and adding in arr1[]'s 'i'th subarray's
        // 'i + j' th element
        for (int j = 0; j < M; j++) {
            arr1[i + j] = arr1[i + j] + arr2[j];
        }
    }
 
    // Printing finally array
    for (int i = 0; i < N; i++) {
        cout << arr1[i] << " ";
    }
    cout << endl;
}
 
// Driver program
int main()
{
    int arr1[] = { 1, 1, 1, 1, 1 }, arr2[] = { 1, 1, 1 };
    int N = sizeof(arr1) / sizeof(arr1[0]);
    int M = sizeof(arr2) / sizeof(arr2[0]);
 
    // Function call for testcaase 1
    addArr2ToArr1(arr1, arr2, N, M);
 
    int arr3[] = { 10, 11, 12, 13, 14 }, arr4[] = { 10 };
    int N2 = sizeof(arr3) / sizeof(arr3[0]);
    int M2 = sizeof(arr4) / sizeof(arr4[0]);
 
    // Function call for testcaase 1
    addArr2ToArr1(arr3, arr4, N2, M2);
 
    int arr5[] = { 12, 11, 10, 9 },
        arr6[] = { 1, 2, 3, 4, 5 };
    int N3 = sizeof(arr5) / sizeof(arr5[0]);
    int M3 = sizeof(arr6) / sizeof(arr6[0]);
 
    // Function call for testcaase 1
    addArr2ToArr1(arr5, arr6, N3, M3);
 
    return 0;
}

Java




// Java code to implement the approach
import java.io.*;
 
class GFG {
 
  // Function to find the final state of arr1[]
  static void addArr2ToArr1(int[] arr1, int[] arr2, int N,
                            int M)
  {
    // Iterating through all possible subarrays
    // of size M in arr1[] there will be
    // exactly N - M + 1 subarrays
    for (int i = 0; i < N - M + 1; i++) {
 
      // Iterating through M elements of arr2[]
      // and adding in arr1[]'s 'i'th subarray's
      // 'i + j' th element
      for (int j = 0; j < M; j++) {
        arr1[i + j] = arr1[i + j] + arr2[j];
      }
    }
 
    // Printing finally array
    for (int i = 0; i < N; i++) {
      System.out.print(arr1[i] + " ");
    }
    System.out.println();
  }
 
  public static void main(String[] args)
  {
    int[] arr1 = { 1, 1, 1, 1, 1 };
    int[] arr2 = { 1, 1, 1 };
    int N = arr1.length;
    int M = arr2.length;
 
    // Function call for testcaase 1
    addArr2ToArr1(arr1, arr2, N, M);
 
    int[] arr3 = { 10, 11, 12, 13, 14 };
    int[] arr4 = { 10 };
    int N2 = arr3.length;
    int M2 = arr4.length;
 
    // Function call for testcaase 1
    addArr2ToArr1(arr3, arr4, N2, M2);
 
    int[] arr5 = { 12, 11, 10, 9 };
    int[] arr6 = { 1, 2, 3, 4, 5 };
    int N3 = arr5.length;
    int M3 = arr6.length;
 
    // Function call for testcaase 1
    addArr2ToArr1(arr5, arr6, N3, M3);
  }
}
 
// This code is contributed by lokesh.

C#




// C# code to implement the approach
using System;
 
class GFG {
 
    // Function to find the final state of arr1[]
    static void addArr2ToArr1(int[] arr1, int[] arr2, int N,
                              int M)
    {
        // Iterating through all possible subarrays
        // of size M in arr1[] there will be
        // exactly N - M + 1 subarrays
        for (int i = 0; i < N - M + 1; i++) {
 
            // Iterating through M elements of arr2[]
            // and adding in arr1[]'s 'i'th subarray's
            // 'i + j' th element
            for (int j = 0; j < M; j++) {
                arr1[i + j] = arr1[i + j] + arr2[j];
            }
        }
 
        // Printing finally array
        for (int i = 0; i < N; i++) {
            Console.Write(arr1[i] + " ");
        }
        Console.WriteLine();
    }
 
    // Driver program
    public static void Main()
    {
        int[] arr1 = { 1, 1, 1, 1, 1 };
        int[] arr2 = { 1, 1, 1 };
        int N = arr1.Length;
        int M = arr2.Length;
 
        // Function call for testcaase 1
        addArr2ToArr1(arr1, arr2, N, M);
 
        int[] arr3 = { 10, 11, 12, 13, 14 };
        int[] arr4 = { 10 };
        int N2 = arr3.Length;
        int M2 = arr4.Length;
 
        // Function call for testcaase 1
        addArr2ToArr1(arr3, arr4, N2, M2);
 
        int[] arr5 = { 12, 11, 10, 9 };
        int[] arr6 = { 1, 2, 3, 4, 5 };
        int N3 = arr5.Length;
        int M3 = arr6.Length;
 
        // Function call for testcaase 1
        addArr2ToArr1(arr5, arr6, N3, M3);
    }
}
 
// This code is contributed by Samim Hossain Mondal.

Python3




# python code
 
# Function to find the final state of arr1[]
def addArr2ToArr1(arr1, arr2, N, M):
   
    # Iterating through all possible subarrays
    # of size M in arr1[] there will be
    # exactly N - M + 1 subarrays
    for i in range(0, N - M + 1):
       
        # Iterating through M elements of arr2[]
        # and adding in arr1[]'s 'i'th subarray's
        # 'i + j' th element
        for j in range(0, M):
            arr1[i + j] = arr1[i + j] + arr2[j]
 
    # Printing finally array
    for i in range(0, N):
        print(arr1[i], end=" ")
    print()
 
# Driver program
arr1 = [1, 1, 1, 1, 1]
arr2 = [1, 1, 1]
N = len(arr1)
M = len(arr2)
 
# Function call for testcase 1
addArr2ToArr1(arr1, arr2, N, M)
 
arr3 = [10, 11, 12, 13, 14]
arr4 = [10]
N2 = len(arr3)
M2 = len(arr4)
 
# Function call for testcase 2
addArr2ToArr1(arr3, arr4, N2, M2)
 
arr5 = [12, 11, 10, 9]
arr6 = [1, 2, 3, 4, 5]
N3 = len(arr5)
M3 = len(arr6)
 
# Function call for testcase 3
addArr2ToArr1(arr5, arr6, N3, M3)
 
# This code is contributed by ksam24000

Output

2 3 4 3 2 
20 21 22 23 24 
12 11 10 9 

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

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

This can be observed every element i of arr1[] will have some range of elements from arr2[] that gets added.
For example.
in case of arr1[] = {0, 0, 0, 0, 0}, arr2[] = {1, 2, 3}
element 1 will have 1 in its sum. Range of elements that got added from arr2[] is [0, 0].
element 2 will have 1 and 2 in its sum. Range of elements that got added from arr2[] is [0, 1].
element 3 will have 1, 2, and 3 in its sum. Range of elements that got added from arr2[] is [0, 2].
element 4 will have 2 and 3 in its sum. Range of elements that got added of arr2[] is  [1, 2].
element 5 will have 3 in its sum. Range of elements that got added of arr2[] is  [2, 2].

Observation: every element ‘i’ will have sum of elements of arr2[] from max(0, M – N + i) to min(i, M-1).
Sum from max(1, M – N + i) to min(i, M-1) can be calculated using prefix sum in constant time. 

Follow the steps below to solve the problem:

  • Initializing prefix[] array which will be used to store the sum of all ranges of arr2[].
  • Initializing L = max(1, M – N + i) and R = min(i, M).
  • Traverse  from 1 to N, Adding prefix[R] – prefix[L  – 1] in arr[i – 1] . 
  • print the final array

Below is the implementation of the above approach.

C++




// C++ code to implement the approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to add corresponding
// elements of arr2[] in all possible
// subarrays of size M of arr1[]
void addArr2ToArr1(int arr1[], int arr2[], int N, int M)
{
    // Prefix sum array will be used
    // to store sum of all ranges of arr2[]
    int prefix[M + 1] = { 0 };
 
    // Taking prefix sum
    for (int i = 1; i <= M; i++) {
        prefix[i] = prefix[i - 1] + arr2[i - 1];
    }
 
    for (int i = 1; i <= N; i++) {
 
        // Add element i of arr1[] with range of
        // elements of arr2[] from l to r
        int r = min(i, M), l = max(1, M - N + i);
 
        // Every element 'i' of arr1[] will
        // have sum of elements of arr2[] from
        // max(1, M - N + i) to min(i, M-1) which
        // can be calculate using prefix
        // sum in constant time
        arr1[i - 1]
            = arr1[i - 1] + prefix[r] - prefix[l - 1];
    }
 
    for (int i = 0; i < N; i++) {
        cout << arr1[i] << " ";
    }
}
 
// Driver program
int main()
{
    int arr1[] = { 1, 1, 1, 1, 1 }, arr2[] = { 1, 1, 1 };
    int N = sizeof(arr1) / sizeof(arr1[0]);
    int M = sizeof(arr2) / sizeof(arr2[0]);
 
    // Function call
    addArr2ToArr1(arr1, arr2, N, M);
 
    return 0;
}

Java




// Java code to implement the approach
import java.util.*;
 
public class GFG {
 
  // Function to add corresponding
  // elements of arr2[] in all possible
  // subarrays of size M of arr1[]
  static void addArr2ToArr1(int arr1[], int arr2[], int N,
                            int M)
  {
    // Prefix sum array will be used
    // to store sum of all ranges of arr2[]
    int prefix[] = new int[M + 1];
    for (int i = 0; i < M + 1; i++) {
      prefix[i] = 0;
    }
 
    // Taking prefix sum
    for (int i = 1; i <= M; i++) {
      prefix[i] = prefix[i - 1] + arr2[i - 1];
    }
 
    for (int i = 1; i <= N; i++) {
 
      // Add element i of arr1[] with range of
      // elements of arr2[] from l to r
      int r = Math.min(i, M);
      int l = Math.max(1, M - N + i);
 
      // Every element 'i' of arr1[] will
      // have sum of elements of arr2[] from
      // max(1, M - N + i) to min(i, M-1) which
      // can be calculate using prefix
      // sum in constant time
      arr1[i - 1]
        = arr1[i - 1] + prefix[r] - prefix[l - 1];
    }
 
    for (int i = 0; i < N; i++) {
      System.out.print(arr1[i] + " ");
    }
  }
 
  // Driver program
  public static void main(String args[])
  {
    int arr1[] = { 1, 1, 1, 1, 1 };
    int arr2[] = { 1, 1, 1 };
    int N = arr1.length;
    int M = arr2.length;
 
    // Function call
    addArr2ToArr1(arr1, arr2, N, M);
  }
}
 
// This code is contributed by Samim Hossain Mondal.

Python3




# Python code to implement the approach
def addArr2toArr1(arr1, arr2, n, m):
   
    # Prefix sum array will be used
    # to store sum for all ranges of arr2[]
    prefix = []
    for i in range(m+1):
        prefix.append(0)
 
    # Taking prefix sum
    for i in range(1, m+1):
        prefix[i] = prefix[i-1] + arr2[i-1]
 
    for i in range(1, n+1):
        # Add elements i of arr1 with range of
        # elements of arr2 from 1 to r
        r = int(min(i, m))
        l = int(max(1, m-n+i))
 
        # Every element 'i' of arr1 will
        # have sum of elements of arr2 from
        # max(1, m-n+1) to min(1, m-1) which
        # can be calculated using prefix
        # sum in constant time
        arr1[i-1] = arr1[i-1] + prefix[r] - prefix[l-1]
 
    for i in range(n):
        print(arr1[i], end=" ")
 
 
arr1 = [1, 1, 1, 1, 1]
arr2 = [1, 1, 1]
 
# function call
addArr2toArr1(arr1, arr2, len(arr1), len(arr2))

C#




// C# code to implement the approach
using System;
 
public class GFG {
 
  // Function to add corresponding
  // elements of arr2[] in all possible
  // subarrays of size M of arr1[]
  static void addArr2ToArr1(int[] arr1, int[] arr2, int N,
                            int M)
  {
    // Prefix sum array will be used
    // to store sum of all ranges of arr2[]
    int[] prefix = new int[M + 1];
    for (int i = 0; i < M + 1; i++) {
      prefix[i] = 0;
    }
 
    // Taking prefix sum
    for (int i = 1; i <= M; i++) {
      prefix[i] = prefix[i - 1] + arr2[i - 1];
    }
 
    for (int i = 1; i <= N; i++) {
 
      // Add element i of arr1[] with range of
      // elements of arr2[] from l to r
      int r = Math.Min(i, M);
      int l = Math.Max(1, M - N + i);
 
      // Every element 'i' of arr1[] will
      // have sum of elements of arr2[] from
      // max(1, M - N + i) to min(i, M-1) which
      // can be calculate using prefix
      // sum in constant time
      arr1[i - 1]
        = arr1[i - 1] + prefix[r] - prefix[l - 1];
    }
 
    for (int i = 0; i < N; i++) {
      Console.Write(arr1[i] + " ");
    }
  }
 
  static public void Main()
  {
 
    // Code
    int[] arr1 = { 1, 1, 1, 1, 1 };
    int[] arr2 = { 1, 1, 1 };
    int N = arr1.Length;
    int M = arr2.Length;
 
    // Function call
    addArr2ToArr1(arr1, arr2, N, M);
  }
}
 
// This code is contributed by lokeshmvs21.

Output

2 3 4 3 2 

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

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