Peak element in an array in c

Question

I am given an array of integers. I have to find a peak element in it. An array element is peak if it is NOT smaller than its neighbors. For corner elements,consider only one neighbor.

For example:

For input array {10, 20, 15, 2, 23, 90, 67} there are two peak elements: 20 and 90. I need to return any one peak element.

The solution i tried is a linear scan of array and i found a peak element. The worst case time complexity of this method would be O(n).

Can we find the peak element in worst time complexity better than O(n)?

IMHO, You have to check all elements of this array, so O(n) is minimum. — Jayan, Jun 05 '13 at 07:09

Daniel Martín · Accepted Answer · 2013-06-05T07:27:03.500

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Yes, you can do it in O(log n) using an idea similar to binary search. Point to the middle of the vector and check its neighbours. If it is greater than both of its neighbours, then return the element, it is a peak. If the right element is greater, then find the peak recursively in the right side of the array. If the left element is greater, then find the peak recursively in the left side of the array.

edited Jun 05 '13 at 07:27

answered Jun 05 '13 at 07:13

Daniel Martín

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@Navnath: this search does not require sorted data. – Jonathan Leffler Jun 05 '13 at 07:20
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No, it is O(log n). Say your right element is greater than the current . Then you can be certain that the sequence to the right contains a peak. Thus, you have halved the number of elemnts to look at, resulting in O(log n). Good example for a divide and conquer algorithm. – Thilo Jun 05 '13 at 07:22
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@Navnath In this problem we don't because given an element and given (for example) its right neighbour, we can guarantee that there is a peak in the right side if the neighbour is greater than the central point: If all the elements continue to be increasing, a peak is the right extreme of the array; if the next element is smaller than the neighbour, then the neighbour is a peak. For any other case, recurse. – Daniel Martín Jun 05 '13 at 07:26
@JonathanLeffler Suppose you would look at the right side, thus the element one to the right is greater than the current. Now we only have to options: The element to the right is a peak or the element next to it still is greater. Repeat that until you either found a peak or reach the end of the sequence, which then is a peak by definition. Thus, you will certainly find a peak once you go to the right. – Thilo Jun 05 '13 at 07:28
No: worst case is O(log N). Read the PDF in [rahul-deshmukhpatil](http://stackoverflow.com/users/1423320/rahul-deshmukhpatil)'s answer to see why. – Jonathan Leffler Jun 05 '13 at 07:40
http://stackoverflow.com/questions/16887279/divide-and-conquer-algorithm-applied-in-finding-a-peak-in-an-array/16887717#16887717 – SomeWittyUsername Jun 05 '13 at 07:48
@PreetKukreti The question explicitly stated "For corner elements,consider only one neighbor". Thus, in the situation at hand the corner case is no problem. The plateau neither is a problem, considering the definition "it is NOT smaller than". Agreed, you could quickly loose O(log n) if you change the question slightly. – Thilo Jun 05 '13 at 08:07
This should be "greater than or equal to both its neighbors", as OP phrased the question. – l0b0 Jun 05 '13 at 08:09
@Thilo after reviewing the question, I agree with you. An oversight on my part. Apologies for the confusion – Preet Kukreti Jun 05 '13 at 08:24
@Dariusz Nope, it's O(log n). You will never in the worst-case traverse all elements. Best case is O(1), average and worst case is O(log n). – Shashank Nov 06 '13 at 20:44

score 10 · Answer 2 · answered Jun 05 '13 at 07:16

10

Yes, it is possible to find it in better time complexity. Using devide and conquer method

Following link will help you. http://courses.csail.mit.edu/6.006/spring11/lectures/lec02.pdf

answered Jun 05 '13 at 07:16

rahul.deshmukhpatil

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Soumik Das · Answer 3 · 2013-06-05T07:30:32.113

As per other's peoples answers (below mine) some code (with O(log n) ):

// A divide and conquer solution to find a peak element element
#include <stdio.h>

// A binary search based function that returns index of a peak element
int findPeakUtil(int arr[], int low, int high, int n)
{
    // Fin index of middle element
    int mid = low + (high - low)/2;  /* (low + high)/2 */

    // Compare middle element with its neighbours (if neighbours exist)
    if ((mid == 0 || arr[mid-1] <= arr[mid]) &&
            (mid == n-1 || arr[mid+1] <= arr[mid]))
        return mid;

    // If middle element is not peak and its left neighbor is greater than it
    // then left half must have a peak element
    else if (mid > 0 && arr[mid-1] > arr[mid])
        return findPeakUtil(arr, low, (mid -1), n);

    // If middle element is not peak and its right neighbor is greater than it
    // then right half must have a peak element
    else return findPeakUtil(arr, (mid + 1), high, n);
}

// A wrapper over recursive function findPeakUtil()
int findPeak(int arr[], int n)
{
    return findPeakUtil(arr, 0, n-1, n);
}

/* Driver program to check above functions */
int main()
{
    int arr[] = {1, 3, 20, 4, 1, 0};
    int n = sizeof(arr)/sizeof(arr[0]);
    printf("Index of a peak point is %d", findPeak(arr, n));
    return 0;
}

Used this for MIT 6.006 OCW course may be check that out as well

http://courses.csail.mit.edu/6.006/spring11/rec/rec02.pdf

@mobbarley,how to search for just the big peaks ( not every peaks e.g. bigger than the neighbor with 100 ) ? — josef, Aug 29 '14 at 21:52
This code doesn't find the peak but the index of the peak..u can then use the index to get your peak element..also refer live example.https://repl.it/DgBs/1 — Soumik Das, Sep 23 '16 at 10:36

Peak element in an array in c

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