GeeksforGeeks » Algorithms
kth largest element
(12 posts)-
Find kth largest element in an array of n elements where k > 0 and k < n
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All the methods discussed at http://geeksforgeeks.org/?p=2392 for k largest elements can also be used to get the kth largest element.
Method 1 (use temp array)
1) Create a temp array temp[0..k-1] of size k.
2) Traverse the array arr[k..n-1]. While traversing, keep updating the smallest element of temp[]
3) Return the smallest of temp[]
Time Complexity: O((n-k)*k).Method 2 (Use a O(nlogn) Sorting)
1) Sort the elements in ascending order.
2) Return the element at indeax k-1.
Time complexity: O(nlogn)Method 3 (Use partition method of quicksort)
1) Randomly pick an element and partition the array around it.
2) If partition method places the mid element at kth position from the start then we have got the kth largest element, stop further processing and return.
Time complexity: O(n^n)Method 4 (Use Max Heap)
1) Build a Max Heap tree in O(n)
2) Use Extract Max k times to get kth maximum element. O(klogn)
Time complexity: O(n + klogn)Method 5 (Use Oder Statistics)
Use order statistic algorithm to find the kth largest element. Please see http://net.pku.edu.cn/~course/cs101/resource/Intro2Algorithm/book6/chap10.htm for details
Time complexity: O(n) -
Here is another method. This method is mainly an optimization of method 1.
Instead of using temp[] array, use Min Heap.
1) Build a Min Heap of first k elements in the given array. O(k) 2) For each element after the kth element (in given array), compare it with root of Min Heap a) If the element is greater than the root then insert it to the tree. b) Else ignore it. O((n-k)*logk) 3) Finally, root of the Min Heap has kth largest element, return it. O(1)Time Complexity O(k + (n-k)Logk)
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The method 3 can be optimized. Based on the result of partition, you can reduce the set for next processing. If returned index is smaller than k then call select for left part else for the right part.
Randomized-Select(A[p..r],i) looking for ith o.s. if p = r return A[p] q <- Randomized-Partition(A,p,r) k <- q-p+1 the size of the left partition if i=k then the pivot value is the answer return A[q] else if i < k then the answer is in the front return Randomized-Select(A,p,q-1,i) else then the answer is in the back half return Randomized-Select(A,q+1,r,i-k)
This optimized version is called randomized selection. You can refer to this ppt http://jonah.cs.elon.edu/sduvall2/courses/csc331/2006spring/Lectures/Order_statistics.ppt
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Is there any way of finding the nth largest element in a stream of numbers,with the condition that the list should not be storted??
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@komal
You can use method 2 or method 6 of http://geeksforgeeks.org/?p=2392 because these methods do not require all the elements to be present in memory.Among these two methods, method 6 is a better choice.
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dharmendra hans
guest
Posted 11 months ago #
there is another method to find the kth largest element. make tree(balanced ,if elements are sorted choose middle element) such that leaves points the elements.
every non-leaf contains the number of elements in its left . e-g-- suppose non-leaf node contains k= 5 and you are searching for r= 4th element then you compare r with k .
since r<k move to left .now again on next left node compare r with k if r>k move right and make r=r-k again keep on searching in right tree in the same way.
this method will require extra space to build the tree. you can use this method to search kth element in linear linked list also. since tree will be having max depth log(n).so it will require max (log n)+1 number of access. -
there's a condition that the list should not be sorted directly or indirectly...
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Can i have a simple program to display all the subsets of a set...like..
for {1,2,3} the answer would be ..
1
2
3
1,2
1,3
2,3
1,2,3 -
It is published
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time complexity of partitioning method (quick select ) is now O(n-square) but O(n).
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we can find the kth largest in an array in O(n) time also
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