Minimum peak elements from an array by their repeated removal at every iteration of the array

Difficulty Level : Hard
Last Updated : 12 May, 2021

Given an array arr[] consisting of N distinct positive integers, the task is to repeatedly find the minimum peak element from the given array and remove that element until all the array elements are removed.

Peak Element: Any element in the array is know as the peak element based on the following conditions:
If arr[i – 1] < arr[i] > arr[i + 1], where 1 < i < N – 1, then arr[i] is the peak element.
If arr[0] > arr[1], then arr[0] is the peak element, where N is the size of the array.
If arr[N – 2] < arr[N – 1], then arr[N – 1] is the peak element, where N is the size of the array.
If more than one peak element exists in the array, then the minimum value among them needs to be printed.

Examples:

Input: arr[] = {1, 9, 7, 8, 2, 6}
Output: [6, 8, 9, 7, 2, 1]
Explanation:
First min peak = 6, as 2 < 6.
The array after removing min peak will be [1, 9, 7, 8, 2].
Second min peak = 8, as 7 < 8 > 2.
The array after removing min peak will be [1, 9, 7, 2]
Third min peak = 9, as 1 < 9 > 7.
The array after removing min peak will be [1, 7, 2]
Fourth min peak = 7, as 1 < 7 > 2.
The array after removing min peak will be [1, 2]
Fifth min peak = 2, as 1 < 2.
The array after removing min peak will be [1]
Sixth min peak = 1.
Therefore, the list of minimum peak is [6, 8, 9, 7, 2, 1].

Input: arr []= {1, 5, 3, 7, 2}
Output: [5, 7, 3, 2, 1]
Explanation:
First min peak = 5, as 1 < 5 > 3.
The array after removing min peak will be [1, 3, 7, 2]
Second min peak = 7, as 3 < 7 > 2.
The array after removing min peak will be [1, 3, 2]
Third min peak = 3, as 1 < 3 > 2.
The array after removing min peak will be [1, 2]
Fourth min peak = 2, as 1 < 2.
The array after removing min peak will be [1]
Fifth min peak = 1.
Therefore, the list of minimum peak is [5, 7, 3, 2, 1]

Approach: The idea is to find the minimum peak element of the array by iterating over the array using two nested loops, where the outer loop points to the current element and the inner loop execute to find the index of min peak element, remove that peak element from the array and store the current peak element in the resultant list. After completing the above steps, print all the minimum peak elements stored in the list.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include<bits/stdc++.h>
using namespace std;
 
// Function to return the list of
// minimum peak elements
void minPeaks(vector<int>list)
{
     
    // Length of original list
    int n = list.size();
     
    // Initialize resultant list
    vector<int>result;
 
    // Traverse each element of list
    for(int i = 0; i < n; i++)
    {
        int min = INT_MAX;
        int index = -1;
 
        // Length of original list after
        // removing the peak element
        int size = list.size();
 
        // Traverse new list after removal
        // of previous min peak element
        for(int j = 0; j < size; j++)
        {
             
            // Update min and index,
            // if first element of
            // list > next element
            if (j == 0 && j + 1 < size)
            {
                if (list[j] > list[j + 1] &&
                        min > list[j])
                {
                    min = list[j];
                    index = j;
                }
            }
 
            else if (j == size - 1 &&
                     j - 1 >= 0)
            {
                 
                // Update min and index,
                // if last element of
                // list > previous one
                if (list[j] > list[j - 1] &&
                        min > list[j])
                {
                    min = list[j];
                    index = j;
                }
            }
 
            // Update min and index, if
            // list has single element
            else if (size == 1)
            {
                min = list[j];
                index = j;
            }
 
            // Update min and index,
            // if current element >
            // adjacent elements
            else if (list[j] > list[j - 1] &&
                     list[j] > list[j + 1] &&
                         min > list[j])
            {
                min = list[j];
                index = j;
            }
        }
 
        // Remove current min peak
        // element from list
        list.erase(list.begin() + index);
 
        // Insert min peak into
        // resultant list
        result.push_back(min);
    }
     
    // Print resultant list
    cout << "[";
    for(int i = 0; i < result.size(); i++)
    {
        cout << result[i] << ", ";
    }
    cout << "]";
}
 
// Driver Code
int main()
{
     
    // Given array arr[]
    vector<int> arr = { 1, 9, 7, 8, 2, 6 };
 
    // Function call
    minPeaks(arr);
}
 
// This code is contributed by bikram2001jha

Java

// Java program for the above approach
 
import java.util.*;
import java.lang.*;
 
class GFG {
 
    // Function to return the list of
    // minimum peak elements
    static void
    minPeaks(ArrayList<Integer> list)
    {
 
        // Length of original list
        int n = list.size();
 
        // Initialize resultant list
        ArrayList<Integer> result
            = new ArrayList<>();
 
        // Traverse each element of list
        for (int i = 0; i < n; i++) {
 
            int min = Integer.MAX_VALUE;
            int index = -1;
 
            // Length of original list after
            // removing the peak element
            int size = list.size();
 
            // Traverse new list after removal
            // of previous min peak element
            for (int j = 0; j < size; j++) {
 
                // Update min and index,
                // if first element of
                // list > next element
                if (j == 0 && j + 1 < size) {
 
                    if (list.get(j) > list.get(j + 1)
                        && min > list.get(j)) {
                        min = list.get(j);
                        index = j;
                    }
                }
 
                else if (j == size - 1
                         && j - 1 >= 0) {
 
                    // Update min and index,
                    // if last element of
                    // list > previous one
                    if (list.get(j)
                            > list.get(j - 1)
                        && min
                               > list.get(j)) {
                        min = list.get(j);
                        index = j;
                    }
                }
 
                // Update min and index, if
                // list has single element
                else if (size == 1) {
 
                    min = list.get(j);
                    index = j;
                }
 
                // Update min and index,
                // if current element >
                // adjacent elements
                else if (list.get(j)
                             > list.get(j - 1)
                         && list.get(j)
                                > list.get(j + 1)
                         && min
                                > list.get(j)) {
 
                    min = list.get(j);
                    index = j;
                }
            }
 
            // Remove current min peak
            // element from list
            list.remove(index);
 
            // Insert min peak into
            // resultant list
            result.add(min);
        }
 
        // Print resultant list
        System.out.println(result);
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        // Given array arr[]
        ArrayList<Integer> arr = new ArrayList<>(
            Arrays.asList(1, 9, 7, 8, 2, 6));
 
        // Function Call
        minPeaks(arr);
    }
}

Python3

# Python3 program for
# the above approach
import sys
 
# Function to return the list of
# minimum peak elements
def minPeaks(list1):
 
    # Length of original list
    n = len(list1)
     
    # Initialize resultant list
    result = []
 
    # Traverse each element of list
    for i in range (n):
        min = sys.maxsize
        index = -1
 
        # Length of original list
        # after removing the peak
        # element
        size = len(list1)
 
        # Traverse new list after removal
        # of previous min peak element
        for j in range (size):
             
            # Update min and index,
            # if first element of
            # list > next element
            if (j == 0 and j + 1 < size):
       
                if (list1[j] > list1[j + 1] and
                    min > list1[j]):
                    min = list1[j];
                    index = j;
                
            elif (j == size - 1 and
                  j - 1 >= 0):
             
                # Update min and index,
                # if last element of
                # list > previous one
                if (list1[j] > list1[j - 1] and
                    min > list1[j]):
                    min = list1[j]
                    index = j
               
            # Update min and index, if
            # list has single element
            elif (size == 1):
                min = list1[j]
                index = j
        
            # Update min and index,
            # if current element >
            # adjacent elements
            elif (list1[j] > list1[j - 1] and
                  list1[j] > list1[j + 1] and
                  min > list1[j]):
                min = list1[j]
                index = j
      
        # Remove current min peak
        # element from list
        list1.pop(index)
 
        # Insert min peak into
        # resultant list
        result.append(min)
    
    # Print resultant list
    print (result)
 
# Driver Code
if __name__ == "__main__":
     
    # Given array arr[]
    arr = [1, 9, 7, 8, 2, 6]
 
    # Function call
    minPeaks(arr)
   
# This code is contributed by Chitranayal

C#

// C# program for
// the above approach
using System;
using System.Collections.Generic;
class GFG{
 
// Function to return the list of
// minimum peak elements
static void minPeaks(List<int> list)
{
  // Length of original list
  int n = list.Count;
 
  // Initialize resultant list
  List<int> result = new List<int>();
 
  // Traverse each element of list
  for (int i = 0; i < n; i++)
  {
    int min = int.MaxValue;
    int index = -1;
 
    // Length of original list after
    // removing the peak element
    int size = list.Count;
 
    // Traverse new list after removal
    // of previous min peak element
    for (int j = 0; j < size; j++)
    {
      // Update min and index,
      // if first element of
      // list > next element
      if (j == 0 && j + 1 < size)
      {
        if (list[j] > list[j + 1] &&
            min > list[j])
        {
          min = list[j];
          index = j;
        }
      }
 
      else if (j == size - 1 && j - 1 >= 0)
      {
        // Update min and index,
        // if last element of
        // list > previous one
        if (list[j] > list[j - 1] &&
            min > list[j])
        {
          min = list[j];
          index = j;
        }
      }
 
      // Update min and index, if
      // list has single element
      else if (size == 1)
      {
        min = list[j];
        index = j;
      }
 
      // Update min and index,
      // if current element >
      // adjacent elements
      else if (list[j] > list[j - 1] &&
               list[j] > list[j + 1] &&
               min > list[j])
      {
        min = list[j];
        index = j;
      }
    }
 
    // Remove current min peak
    // element from list
    list.RemoveAt(index);
 
    // Insert min peak into
    // resultant list
    result.Add(min);
  }
 
  // Print resultant list
  for (int i = 0; i < result.Count; i++)
    Console.Write(result[i] +", ");
}
 
// Driver Code
public static void Main(String[] args)
{
  // Given array []arr
  List<int> arr = new List<int>{1, 9, 7,
                                8, 2, 6};
 
  // Function Call
  minPeaks(arr);
}
}
 
// This code is contributed by 29AjayKumar

Output:

[6, 8, 9, 7, 2, 1]

Time Complexity: O(N²)
Auxiliary Space: O(N)

My Personal Notes

Related Articles

C++

Java

Python3

C#