C++ program to find maximum of each k sized contiguous subarray

Suppose we have an array with n elements and a value k. We shall have to find maximum value for each of the contiguous subarray of size k.

So, if the input is like arr = [3,4,6,2,8], k = 3, then the output will be The contiguous subarrays of size 3 are [3,4,6], [4,6,2], [6,2,8], so the maximum elements are 6, 6 and 8.

To solve this, we will follow these steps −

• Define one deque Qi of size k
• for initialize i := 0, when i < k, update (increase i by 1), do:
  • while Qi is not empty and arr[i] >= arr[last element of Qi], do:
    • delete last element from Qi
  • insert i at the end of Qi
• for i < size of arr, update (increase i by 1), do:
  • display arr[first element of Qi]
  • while Qi is not empty and first element of Qi <= i - k, do:
    • delete front element from Qi
  • while Qi is not empty and arr[i] >= arr[last element of Qi], do:
    • delete last element from Qi
  • insert i at the end of Qi
• display arr[first element of Qi]

Example

Let us see the following implementation to get better understanding −

#include <iostream>
#include <vector>
#include <deque>
using namespace std;
int main(){
   vector<int> arr = {3,4,6,2,8};
   int k = 3;
   deque<int> Qi(k);
   int i;
   for (i = 0; i < k; ++i){
      while ( (!Qi.empty()) && arr[i] >= arr[Qi.back()])
         Qi.pop_back();

         Qi.push_back(i);
     }
     for ( ; i < arr.size(); ++i){
        cout << arr[Qi.front()] << " ";
        while ( (!Qi.empty()) && Qi.front() <= i - k)
            Qi.pop_front();
        while ( (!Qi.empty()) && arr[i] >= arr[Qi.back()])
            Qi.pop_back();
        Qi.push_back(i);
    }
    cout << arr[Qi.front()] << endl;
}

Input

{3,4,6,2,8}, 3

Output

6 6 8