Number of Subarrays with Bounded Maximum in C++

Suppose we have an array A of positive integers, and two positive integers L and R are also given. We have to find the number of (contiguous, non-empty) subarrays such that the value of the maximum array element in that subarray is at least L and at most R. So if A = [2,1,4,3] and L = 2 and R = 3, then output will be 3 as there are three sub arrays that meet the requirements. So these are [2], [2,1], [3].

To solve this, we will follow these steps −

• ret := 0, dp := 0, prev := -1

• for i in range 0 to size of A – 1

  • if A[i] < L and i > 0, then ret := ret + dp

  • if A[i] > R, then prev := i and dp := 0

  • otherwise when A[i] >= L and A[i] <= R, then dp := i – prev and ret := ret + dp

• return ret

Example (C++)

Let us see the following implementation to get better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
   public:
   int numSubarrayBoundedMax(vector<int>& A, int L, int R) {
      int ret = 0;
      int dp = 0;
      int prev = -1;
      for(int i = 0; i < A.size(); i++){
         if(A[i] < L && i > 0){
            ret += dp;
         }
         if(A[i] > R){
            prev = i;
            dp = 0;
         }
         else if(A[i] >= L && A[i] <= R){
            dp = i - prev;
            ret += dp;
         }
      }
      return ret;
   }
};
main(){
   vector<int> v = {2,1,4,3};
   Solution ob;
   cout << (ob.numSubarrayBoundedMax(v, 2, 3));
}

Input

[2,1,4,3]
2
3

Output

3