Max Heap Binary Tree data structure is the best choice to find the maximum value as it takes the least amount of time and can only return the maximum value of the data.
Takeaways
Max Heap is the best data structure to find the maximum value.
Which Data Structure is Considered Best to Find Maximum Value ?
- Sorted Array
- Max Heap
- Min Heap
- Unordered Set
Correct Answer
Max Heap is considered the best data structure to find the maximum value in a given set of data.
Explanation
Among the options, the Max Heap Binary Tree data structure is the best choice to find the maximum value as it takes the least amount of time and can only return the maximum value of the data.
A Sorted Array would be a good option but sorting the array is a time-heavy process and very inefficient just for finding the maximum value.
Min Heap is the worst option among all of these as we would need to empty the data structure to access the last element (maximum value).
An Unordered Set is an unordered data structure, finding the maximum element in this would require a linear search.
Examples for Data Structures to Find the Maximum Value
Let us see how to retrieve the maximum value using different data structures (C++) :
Using a Sorted Array
An array is a sequence of elements in an ordered form. Sorting an array takes O(nlogn) time and therefore is not an efficient method for getting the maximum value among the data.
Code :
// Finding the maximum value using a Sorted Array
#include <bits/stdc++.h>
using namespace std;
int main() {
// Initializing a dynamic array
vector<int> input;
string buff;
int data;
// Inputting the values into the vector (dynamic array)
cout<<"Enter the array: ";
getline(cin, buff);
// Using an input string stream
istringstream iss(buff);
while (iss >> data)
input.push_back(data);
// Sorting the array
sort(input.begin(), input.end());
// Returning the maximum value
cout<<"The maximum value among the data is "<<input.back();
return 0;
}
// Which data structure is considered best to find maximum value?
Output :
Enter the array: 5 3 2 6 4 2
The maximum value among the data is 6
In the above example, we are finding the maximum value in a sorted array by printing the last element of the array (as the array is sorted in ascending order).
Time Complexity : O(nlogn)
In this method, we are sorting an array, that has a time complexity of O(nlogn) .
Space Complexity : O(1)
No auxiliary space is used except for some variables.
Using Max Heap
A Max Heap data structure returns the maximum value first when retrieving the data, therefore, it is the best data structure to get the maximum value.
Code :
// Finding the maximum value using a Max Heap Data structure
#include <bits/stdc++.h>
using namespace std;
int main() {
// Initializing a max-heap data structure
priority_queue<int> input;
string buff;
int data;
// Inputting the values into the queue
cout<<"Enter the array: ";
getline(cin, buff);
// Using an input string stream
istringstream iss(buff);
while (iss >> data)
input.push(data);
// Returning the maximum value
cout<<"The maximum value among the data is "<<input.top();
return 0;
}
// Which data structure is considered best to find maximum value?
Output :
Enter the array: 64 7 4 3 2
The maximum value among the data is 64
In the above example, we are finding the maximum value in a Max Heap by returning the top of the data structure.
Time Complexity : O(1)
The lookup time in a Max Heap data structure is O(1).
Space Complexity : O(1)
No auxiliary space is used except for some variables.
Using Min Heap
A Min Heap data structure returns the minimum value first when retrieving the data, therefore, we will need to empty the Min Heap to be able to access the last value (maximum value) of the data.
Code :
// Finding the maximum value using a Min Heap Data structure
#include <bits/stdc++.h>
using namespace std;
int main() {
// Initializing a min-heap data structure
priority_queue<int, vector<int>, greater<>> input;
string buff;
int data;
// Inputting the values
cout<<"Enter the array: ";
getline(cin, buff);
// Using an input string stream
istringstream iss(buff);
while (iss >> data)
input.push(data);
int last;
// Emptying the queue and extracting the last element (maximum value)
while(!input.empty()){
last = input.top();
input.pop(); // Removing the top element from the Min Heap data structure
}
// Returning the maximum value
cout<<"The maximum value among the data is "<<last;
return 0;
}
// Which data structure is considered best to find maximum value?
Output :
Enter the array: 54 264 3 2
The maximum value among the data is 264
In the above example, we are finding the maximum value in a min-heap by emptying it till the last element. The last element of a min-heap is the maximum.
Time Complexity : O(n)
In this method, we will empty the Min Heap data structure which will require n iterations, therefore, the time complexity will be O(n).
Space Complexity : O(1)
No auxiliary space is used except for some variables.
Using an Unordered Set
We can use an unordered set in C++ using STL. We will need to traverse the whole set to find the maximum number.
Code :
// Finding the maximum value using an Unordered Set data structure
#include <bits/stdc++.h>
using namespace std;
int main() {
// Initializing an unordered set
unordered_set<int> input;
string buff;
int data;
// Inputting the values
cout<<"Enter the array: ";
getline(cin, buff);
// Using an input string stream
istringstream iss(buff);
while (iss >> data)
input.insert(data);
int maximum {0};
// Finding the maximum value in the unordered set
for(auto x: input){
maximum = max(maximum, x); // Using inbuilt max() function
}
// Returning the maximum value
cout<<"The maximum value among the data is "<<maximum;
return 0;
}
// Which data structure is considered best to find maximum value?
Output :
Enter the array: 4 3 73 2
The maximum value among the data is 73
In the above example, we are finding the maximum value in an unordered set by iterating over it and storing the greatest number in the variable maximum.
Time Complexity : O(n)
As the set is unordered, we will need to traverse the whole set and search for the biggest element, the worst-case time complexity can be O(n)O(n).
Space Complexity : O(1)
No auxiliary space is used except for some variables.
So Which Data Structure is Considered Best to Find Maximum Value you Ask ?
The answer is right in front of your eyes, the Max-Heap data structure, it is the only data structure to have O(1) lookup time (i.e., the least time complexity) to find the maximum value, others have a time complexity of O(n) or O(nlogn) for the same task.
Learn About Needs & Applications Of Data Structures
Different data structures are used for different purposes to store data efficiently to save time as well as space.
Data structures are needed in almost all scenarios where data is mentioned, whether it be problem-solving, data storage in companies, or some real-world problems. Using appropriate data structures in different cases is very important otherwise the data storage can be very inefficient and cluttered.
Like in this article, we have used a Max Heap data structure to find the maximum value.
To learn about data structures, their needs, and applications, click here.
Conclusion
- A Max Heap is the best data structure to find the maximum value.
- We can find the maximum using a Sorted Array, Min Heap, or an Unordered Set, but they are not as efficient as a Max Heap data structure.
- Using a Min Heap to find the maximum value is the worst solution as for that we will need to empty the data structure (loss of information) or store those values in another data structure (wastage of space).
- Using appropriate data structures in different scenarios is very important, otherwise, the data storage will be very inefficient and cluttered.
