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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 −
#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
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