Как найти несколько максимальных элементов в массиве

Is it possible to find the second maximum number from an array of integers by traversing the array only once?

As an example, I have a array of five integers from which I want to find second maximum number. Here is an attempt I gave in the interview:

#define MIN -1
int main()
{
    int max=MIN,second_max=MIN;
    int arr[6]={0,1,2,3,4,5};
    for(int i=0;i<5;i++){
        cout<<"::"<<arr[i];
    }
    for(int i=0;i<5;i++){
        if(arr[i]>max){
            second_max=max;
            max=arr[i];          
        }
    }
    cout<<endl<<"Second Max:"<<second_max;
    int i;
    cin>>i;
    return 0;
}

The interviewer, however, came up with the test case int arr[6]={5,4,3,2,1,0};, which prevents it from going to the if condition the second time.
I said to the interviewer that the only way would be to parse the array two times (two for loops). Does anybody have a better solution?

answered Mar 6, 2010 at 14:34

Quickselect is the way to go with this one. Pseudo code is available at that link so I shall just explain the overall algorithm:

QuickSelect for kth largest number:
    Select a pivot element
    Split array around pivot
    If (k < new pivot index)
       perform quickselect on left hand sub array
     else if (k > new pivot index)
       perform quickselect on right hand sub array (make sure to offset k by size of lefthand array + 1)
     else
       return pivot

This is quite obviously based on the good old quicksort algorithm.

Following this algorithm through, always selecting element zero as the pivot every time:

select 4th largest number:
1) array = {1, 3, 2, 7, 11, 0, -4}
partition with 1 as pivot
{0, -4, _1_, 3, 2, 7, 11}
4 > 2 (new pivot index) so...

2) Select 1st (4 - 3) largest number from right sub array
array = {3, 2, 7, 11}
partition with 3 as pivot
{2, _3_, 7, 11}
1 < 2 (new pivot index) so...

3) select 1st largest number from left sub array
array = {2}

4) Done, 4th largest number is 2

This will leave your array in an undefined order afterwards, it’s up to you if that’s a problem.

answered Mar 6, 2010 at 18:09

Step 1. Decide on first two numbers.
Step 2. Loop through remaining numbers.
Step 3. Maintain latest maximum and second maximum.
Step 4. When updating second maximum, be aware that you are not making maximum and second maximum equal.

Tested for sorted input (ascending and descending), random input, input having duplicates, works fine.

#include <iostream>
#define MAX 50
int GetSecondMaximum(int* data, unsigned int size)
{
    int max, secmax;
    // Decide on first two numbers
    if (data[0] > data[1])
    {
        max = data[0];
        secmax = data[1];
    }
    else
    {
        secmax = data[0];
        max = data[1];
    }
    // Loop through remaining numbers
    for (unsigned int i = 2; i < size; ++i)
    {
        if (data[i] > max)
        {
            secmax = max;
            max = data[i];
        }
        else if (data[i] > secmax && data[i] != max/*removes duplicate problem*/)
            secmax = data[i];
    }
    return secmax;
}
int main()
{
    int data[MAX];
    // Fill with random integers
    for (unsigned int i = 0; i < MAX; ++i)
    {
        data[i] = rand() % MAX;
        std::cout << "[" << data[i] << "] "; // Display input
    }
    std::cout << std::endl << std::endl;
    // Find second maximum
    int nSecondMax = GetSecondMaximum(data, MAX);
    // Display output
    std::cout << "Second Maximum = " << nSecondMax << std::endl;
    // Wait for user input
    std::cin.get();
    return 0;
}

answered Mar 6, 2010 at 18:39

Here is something which may work ,

public static int secondLargest(int[] a){
    int max=0;
    int secondMax=0;

    for(int i=0;i<a.length;i++){
        if(a[i]<max){
            if(a[i]>secondMax){
                secondMax=a[i];
            }
            continue;
        }

        if(a[i]>max){
            secondMax=max;
            max=a[i];
        }

    }
    return secondMax;
}

The upper bound should have be n+log2⁡n−2, but it bigger than O(n) in case of random selection algorithm, but in worst case it much smaller. The solution might be

1. build a tree like to find the MAX element with n – 1 comparisons

   max(N)
   /
   max(N/2) max(N/2)

2. remove the MAX and find the MAX again log2n – 1 comparison

PS. It uses additional memory, but it faster than random selection algorithm in worst case.

answered Apr 5, 2012 at 11:47

answered Oct 5, 2012 at 0:16

How about the following below.
make_heap is O(n) so this is efficient and this is 1-pass
We find the second max by taking advantage that it must be one of the heap children of the parent, which had the maximum.

#include <algorithm>
#include <iostream>

int main()
{
    int arr[6]={0,1,2,3,4,5};

    std::make_heap(arr, arr+6);
    std::cout << "First Max: " << arr[0] << 'n';
    std::cout << "Second Max: " << std::max(arr[1], arr[2]) << 'n';
    return 0;
}

answered Jan 7, 2013 at 17:39

int max,secondMax;
max=secondMax=array[0];
                                                for(int i=0;i<array.length;i++)
    {                                                   if(array[i]>max)                                                    {                                           max=array[i];                                                   }
                                                        if(array[i]>secondMax && array[i]<max)                                                  {
    secondMax=array[i];                                                 }
    }

answered Apr 22, 2013 at 9:48