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Maximize the maximum among minimum of K consecutive sub-arrays in C++
Given the task is to divide an array arr[] into K consecutive sub-arrays and find the maximum possible value of maximum among the minimum of the K consecutive sub-srrays.
Input
arr[]={2,8,4,3,9,1,5}, K=3Output
9
Explanation − The 3 consecutive sub arrays that can made are: {2, 8, 4, 3}, {9}, and {1, 5}
The minimum values out of all these arrays are: (2, 9, 1)
The maximum value out of these three is 9.
Input
arr[] = { 8, 4, 1, 9, 11}, K=1Output
11
Approach used in the below program as follows
If we look at the task, it can be divided into 3 cases − when K=1, k=2 and k>=3.
Case 1 − K=1
When k=1 the sub-array is equal to the array itself and so the minimum value in the array will be the output.
Case 2 − K=2
This is a tough case. In this case we will have to make two arrays that will contain the prefix and suffix minimums as the array can only be divided into 2 parts. Then for every element of the array we will have to do so −
MaxValue = max(MaxValue, max(prefix minimum value at i, suffix maximum value at i+1))
Example
#include <bits/stdc++.h>
using namespace std;
/* Function to find the maximum possible value
of the maximum of minimum of K sub-arrays*/
int Max(const int* arr, int size, int K){
dint Max;
int Min;
//Obtain maximum and minimum
for (int i = 0; i < size; i++){
Min = min(Min, arr[i]);
Max = max(Max, arr[i]);
}
//When K=1, return minimum value
if (K == 1){
return Min;
}
//When K>=3, return maximum value
else if (K >= 3){
return Max;
}
/*When K=2 then make prefix and suffix minimums*/
else{
// Arrays to store prefix and suffix minimums
int Left[size], Right[size];
Left[0] = arr[0];
Right[size - 1] = arr[size - 1];
// Prefix minimum
for (int i = 1; i < size; i++){
Left[i] = min(Left[i - 1], arr[i]);
}
// Suffix minimum
for (int i = size - 2; i >= 0; i--){
Right[i] = min(Right[i + 1], arr[i]);
}
int MaxValue=INT_MIN;
// Get the maximum possible value
for (int i = 0; i < size - 1; i++){
MaxValue = max(MaxValue, max(Left[i], Right[i + 1]));
}
return MaxValue;
}
}
int main(){
int arr[] = {9,4,12,5,6,11};
int size = sizeof(arr) / sizeof(arr[0]);
int K = 2;
cout<<"Maximize the maximum among minimum of K consecutive sub-arrays is: "<<Max(arr, size, K);
return 0;
}Output
If we run the above code we will get the following output −
Maximize the maximum among minimum of K consecutive sub-arrays is: 11
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