Question: Write an efficient program for printing k largest elements in an array. Elements in array can be in any order.
For example, if given array is [1, 23, 12, 9, 30, 2, 50] and you are asked for the largest 3 elements i.e., k = 3 then your program should print 50, 30 and 23.
Method 1 (Use Bubble k times)
Thanks to Shailendra for suggesting this approach.
1) Modify Bubble Sort to run the outer loop at most k times.
2) Print the last k elements of the array obtained in step 1.
Time Complexity: O(nk)
Like Bubble sort, other sorting algorithms like Selection Sort can also be modified to get the k largest elements.
Method 2 (Use temporary array)
K largest elements from arr[0..n-1]
1) Store the first k elements in a temporary array temp[0..k-1].
2) Find the smallest element in temp, let the smallest element be min.
3-a) For each element x in arr[k] to arr[n-1]. O(n-k)
If x is greater than the min then remove min from temp and insert x.
3-b)Then, determine the new min from temp. O(k)
4) Print final k elements of temp
Time Complexity: O((n-k)*k). If we want the output sorted then O((n-k)*k + klogk)
Thanks to nesamani1822 for suggesting this method.
Method 3(Use Sorting)
1) Sort the elements in descending order in O(nLogn)
2) Print the first k numbers of the sorted array O(k).
Following is the implementation of above.
50 30 23
Time complexity: O(nlogn)
Method 4 (Use Max Heap)
1) Build a Max Heap tree in O(n)
2) Use Extract Max k times to get k maximum elements from the Max Heap O(klogn)
Time complexity: O(n + klogn)
Method 5(Use Oder Statistics)
1) Use order statistic algorithm to find the kth largest element. Please see the topic selection in worst-case linear time O(n)
2) Use QuickSort Partition algorithm to partition around the kth largest number O(n).
3) Sort the k-1 elements (elements greater than the kth largest element) O(kLogk). This step is needed only if sorted output is required.
Time complexity: O(n) if we don’t need the sorted output, otherwise O(n+kLogk)
Thanks to Shilpi for suggesting the first two approaches.
Method 6 (Use Min Heap)
This method is mainly an optimization of method 1. Instead of using temp array, use Min Heap.
1) Build a Min Heap MH of the first k elements (arr to arr[k-1]) of the given array. O(k)
2) For each element, after the kth element (arr[k] to arr[n-1]), compare it with root of MH.
……a) If the element is greater than the root then make it root and call heapify for MH
……b) Else ignore it.
// The step 2 is O((n-k)*logk)
3) Finally, MH has k largest elements and root of the MH is the kth largest element.
Time Complexity: O(k + (n-k)Logk) without sorted output. If sorted output is needed then O(k + (n-k)Logk + kLogk)
All of the above methods can also be used to find the kth largest (or smallest) element.
Please write comments if you find any of the above explanations/algorithms incorrect, or find better ways to solve the same problem.
- Check if array elements are consecutive | Added Method 3
- Elements to be added so that all elements of a range are present in array
- Find the smallest and second smallest elements in an array
- Find whether an array is subset of another array | Added Method 3
- Average of remaining elements after removing K largest and K smallest elements from array
- Smallest greater elements in whole array
- k-th smallest absolute difference of two elements in an array
- Smallest perfect square divisible by all elements of an array
- Print n smallest elements from given array in their original order
- Smallest perfect Cube divisible by all elements of an array
- Smallest power of 2 which is greater than or equal to sum of array elements
- Smallest number that never becomes negative when processed against array elements
- Find the lexicographically smallest sequence which can be formed by re-arranging elements of second array
- Print elements that can be added to form a given sum
- Find the minimum value to be added so that array becomes balanced