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Generate Bitonic Sequence of length N from integers in a given range

  • Difficulty Level : Medium
  • Last Updated : 18 May, 2021

Given integers N, L and R, the task is to generate a Bitonic Sequence of length N from the integers in the range [L, R] such that the first element is the maximum. If it is not possible to create such a sequence, then print “-1”.

A Bitonic Sequence is a sequence that must be strictly increasing at first and then strictly decreasing.

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Examples:

Input: N = 5, L = 3, R = 10
Output: 9, 10, 9, 8, 7
Explanation: The sequence {9, 10, 9, 8, 7} is first strictly increasing and then strictly decreasing.



Input: N = 5, L = 2, R = 5
Output: 4, 5, 4, 3, 2
Explanation:
[ The sequence {4, 5, 4, 3, 2} is first strictly increasing and then strictly decreasing.

Approach: The idea is to use a Deque so that elements can be added from the end and the beginning. Follow the steps below to solve the problem:

  • Initialize a deque to store the element of the resultant bitonic sequence.
  • Initialize a variable i as 0 and start adding elements in the resultant list starting from (R – i) until i less than the minimum of (R – L + 1) and (N – 1).
  • After the above steps if the size of the resultant list is less than N then add add elements from (R – 1) to L from the starting of the list until the size of the resultant list does not become N.
  • After the above steps, if N is greater than (R – L)*2 + 1, then it is not possible to construct such a sequence then print “-1” else print the sequence stored in deque.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to construct bitonic
// sequence of length N from
// integers in the range [L, R]
void bitonicSequence(int num, int lower,
                     int upper)
{
     
    // If sequence is not possible
    if (num > (upper - lower) * 2 + 1)
    {
        cout << -1;
        return;
    }
 
    // Store the resultant list
    deque<int> ans;
    deque<int>::iterator j = ans.begin();
 
    for(int i = 0;
            i < min(upper - lower + 1, num - 1);
            i++)
        ans.push_back(upper - i);
         
    // If size of deque < n
    for(int i = 0;
            i < num - ans.size();
            i++)
          
    // Add elements from start
    ans.push_front(upper - i - 1);
 
    // Print the stored in the list
    cout << '[';
    for(j = ans.begin(); j != ans.end(); ++j)
        cout << ' ' << *j;
         
    cout << ' ' << ']';
}
 
// Driver Code
int main()
{
    int N = 5, L = 3, R = 10;
 
    // Function Call
    bitonicSequence(N, L, R);
 
    return 0;
}
 
// This code is contributed by jana_sayantan

Java




// Java program for the above approach
import java.util.*;
 
class GFG {
 
    // Function to construct bitonic
    // sequence of length N from
    // integers in the range [L, R]
    public static void bitonicSequence(
        int num, int lower, int upper)
    {
        // If sequence is not possible
        if (num > (upper - lower) * 2 + 1) {
            System.out.println(-1);
            return;
        }
 
        // Store the resultant list
        Deque<Integer> ans
            = new ArrayDeque<>();
 
        for (int i = 0;
             i < Math.min(upper - lower + 1,
                          num - 1);
             i++)
            ans.add(upper - i);
 
        // If size of deque < n
        for (int i = 0;
             i < num - ans.size(); i++)
 
            // Add elements from start
            ans.addFirst(upper - i - 1);
 
        // Print the stored in the list
        System.out.println(ans);
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        int N = 5, L = 3, R = 10;
 
        // Function Call
        bitonicSequence(N, L, R);
    }
}

Python3




# Python3 program for the above approach
from collections import deque
 
# Function to construct bitonic
# sequence of length N from
# integers in the range [L, R]
def bitonicSequence(num, lower, upper):
     
    # If sequence is not possible
    if (num > (upper - lower) * 2 + 1):
        print(-1)
        return
 
    # Store the resultant list
    ans = deque()
     
    for i in range(min(upper - lower + 1,
                                 num - 1)):
        ans.append(upper - i)
 
    # If size of deque < n
    for i in range(num - len(ans)):
         
        # Add elements from start
        ans.appendleft(upper - i - 1)
 
    # Print the stored in the list
    print(list(ans))
 
# Driver Code
if __name__ == '__main__':
     
    N = 5
    L = 3
    R = 10
 
    # Function Call
    bitonicSequence(N, L, R)
 
# This code is contributed by mohit kumar 29

C#




// C# program for the above approach
using System;
using System.Collections.Generic;
 
class GFG{
 
// Function to construct bitonic
// sequence of length N from
// integers in the range [L, R]
public static void bitonicSequence(int num,
                                   int lower,
                                   int upper)
{
     
    // If sequence is not possible
    if (num > (upper - lower) * 2 + 1)
    {
        Console.WriteLine(-1);
        return;
    }
 
    // Store the resultant list
    List<int> ans = new List<int>();
 
    for(int i = 0;
            i < Math.Min(upper - lower + 1,
                           num - 1); i++)
        ans.Add(upper - i);
 
    // If size of deque < n
    for(int i = 0;
            i < num - ans.Count; i++)
 
        // Add elements from start
        ans.Insert(0,upper - i - 1);
 
    // Print the stored in the list
    Console.Write("[");
    foreach(int x in ans)
        Console.Write(x + ", ");
         
    Console.Write("]");
}
 
// Driver Code
public static void Main(String[] args)
{
    int N = 5, L = 3, R = 10;
     
    // Function Call
    bitonicSequence(N, L, R);
}
}
 
// This code is contributed by Rajput-Ji

Javascript




<script>
 
// Javascript program for the above approach
 
// Function to construct bitonic
// sequence of length N from
// integers in the range [L, R]
function bitonicSequence(num, lower, upper)
{
     
    // If sequence is not possible
    if (num > (upper - lower) * 2 + 1)
    {
        document.write( -1);
        return;
    }
 
    // Store the resultant list
    var ans = [];
 
    for(var i = 0;
            i < Math.min(upper - lower + 1, num - 1);
            i++)
        ans.push(upper - i);
         
    // If size of deque < n
    for(var i = 0;
            i < num - ans.length;
            i++)
    {
          
            // Add elements from start
            ans.splice(0, 0, upper -i - 1)
    }
 
    // Print the stored in the list
    document.write( '[');
 
    ans.forEach(element => {
        document.write(" "+element);
    });
         
    document.write( ' ' + ']');
}
 
// Driver Code
var N = 5, L = 3, R = 10;
// Function Call
bitonicSequence(N, L, R);
 
 
</script>
Output: 
[9, 10, 9, 8, 7]

 

Time Complexity: O(N)
Auxiliary Space: O(1)




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