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Generate a random permutation of elements from range [L, R] (Divide and Conquer)

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  • Difficulty Level : Medium
  • Last Updated : 22 Jun, 2022

Given a range [L, R] where L ≤ R, the task is to generate a random permutation of the sequence [L, L + 1, L + 2, …, R].
Examples: 
 

Input: L = 5, R = 15 
Output: 11 9 6 5 8 7 10 12 13 15 14
Input: L = 10, R = 20 
Output: 16 14 11 10 13 12 15 17 18 20 19 
 

 

Approach: We will use Divide and Conquer algorithm for our solution. We will create a global vector that will store random numbers generated by our recursive function generate_random_permutation()
We will pass two arguments L (start) and R (end) to our recursive function. Inside the function it will call another function give_random_number that will return a number between X and Y. Lets call it N. We will store this random number in our vector and then we will call generate_random_permutation() function recursively for range [L, N – 1] and then for range [N + 1, R]
If L becomes greater than R then we will return from the function without performing any task, as this is our base condition.
Below is the implementation of the above approach: 
 

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// To store the random permutation
vector<int> permutation;
 
// Utility function to print
// the generated permutation
void printPermutation()
{
    for (auto i : permutation)
        cout << i << " ";
}
 
// Function to return a random
// number between x and y
int give_random_number(int l, int r)
{
    int x = rand() % (r - l + 1) + l;
    return x;
}
 
// Recursive function to generate
// the random permutation
void generate_random_permutation(int l, int r)
{
 
    // Base condition
    if (l > r)
        return;
 
    // Random number returned from the function
    int n = give_random_number(l, r);
 
    // Inserting random number in vector
    permutation.push_back(n);
 
    // Recursion call for [l, n - 1]
    generate_random_permutation(l, n - 1);
 
    // Recursion call for [n + 1, r]
    generate_random_permutation(n + 1, r);
}
 
// Driver code
int main()
{
    int l = 5;
    int r = 15;
 
    // Generate permutation
    generate_random_permutation(l, r);
 
    // Print the generated permutation
    printPermutation();
 
    return 0;
}

Java




// Java implementation of the approach
import java.util.Vector;
 
class GFG
{
 
 
// To store the random permutation
static Vector<Integer> permutation = new Vector<>();
 
// Utility function to print
// the generated permutation
static void printPermutation()
{
    permutation.stream().forEach((i) ->
    {
        System.out.print(i+" ");
    });
}
 
// Function to return a random
// number between x and y
static int give_random_number(int l, int r)
{
    int x = (int) (Math.random()% (r - l + 1) + l);
    return x;
}
 
// Recursive function to generate
// the random permutation
static void generate_random_permutation(int l, int r)
{
 
    // Base condition
    if (l > r)
        return;
 
    // Random number returned from the function
    int n = give_random_number(l, r);
 
    // Inserting random number in vector
    permutation.add(n);
 
    // Recursion call for [l, n - 1]
    generate_random_permutation(l, n - 1);
 
    // Recursion call for [n + 1, r]
    generate_random_permutation(n + 1, r);
}
 
// Driver code
public static void main(String[] args)
{
    int l = 5;
    int r = 15;
 
    // Generate permutation
    generate_random_permutation(l, r);
 
    // Print the generated permutation
    printPermutation();
}
}
 
// This code has been contributed by 29AjayKumar

Python3




# Python3 implementation of the approach
import random
 
# To store the random permutation
permutation = []
 
# Utility function to print
# the generated permutation
def printPermutation() :
 
    for i in permutation:
        print(i, end = " ")
 
# Function to return a random
# number between x and y
def give_random_number(l, r) :
 
    x = random.randint(l, r)
    return x
 
# Recursive function to generate
# the random permutation
def generate_random_permutation(l, r) :
 
    # Base condition
    if (l > r) :
        return
 
    # Random number returned from the function
    n = give_random_number(l, r)
 
    # Inserting random number in vector
    permutation.append(n)
 
    # Recursion call for [l, n - 1]
    generate_random_permutation(l, n - 1)
 
    # Recursion call for [n + 1, r]
    generate_random_permutation(n + 1, r)
 
# Driver code
l = 5
r = 15
 
# Generate permutation
generate_random_permutation(l, r)
 
# Print the generated permutation
printPermutation()
 
# This code is contributed by ihritik

C#




// C# implementation of the approach
using System;
using System.Collections.Generic;
 
class GFG
{
 
 
// To store the random permutation
static List<int> permutation = new List<int>();
 
// Utility function to print
// the generated permutation
static void printPermutation()
{
    foreach(int i in permutation)
        Console.Write(i+" ");
}
 
// Function to return a random
// number between x and y
static int give_random_number(int l, int r)
{
    Random rnd = new Random();
    int num = rnd.Next(l, r);
    int x = (int) (num % (r - l + 1) + l);
    return x;
}
 
// Recursive function to generate
// the random permutation
static void generate_random_permutation(int l, int r)
{
 
    // Base condition
    if (l > r)
        return;
 
    // Random number returned from the function
    int n = give_random_number(l, r);
 
    // Inserting random number in vector
    permutation.Add(n);
 
    // Recursion call for [l, n - 1]
    generate_random_permutation(l, n - 1);
 
    // Recursion call for [n + 1, r]
    generate_random_permutation(n + 1, r);
}
 
// Driver code
public static void Main(String[] args)
{
    int l = 5;
    int r = 15;
 
    // Generate permutation
    generate_random_permutation(l, r);
 
    // Print the generated permutation
    printPermutation();
}
}
 
/* This code contributed by PrinciRaj1992 */

PHP




<?php
// PHP implementation of the approach
 
// To store the random permutation
$permutation = array();
 
// Utility function to print
// the generated permutation
function printPermutation()
{
    global $permutation;
    foreach ($permutation as $i)
        echo $i . " ";
}
 
// Function to return a random
// number between x and y
function give_random_number($l, $r)
{
    $x = rand() % ($r - $l + 1) + $l;
    return $x;
}
 
// Recursive function to generate
// the random permutation
function generate_random_permutation($l, $r)
{
    global $permutation;
 
    // Base condition
    if ($l > $r)
        return;
 
    // Random number returned from the function
    $n = give_random_number($l, $r);
 
    // Inserting random number in vector
    array_push($permutation, $n);
 
    // Recursion call for [l, n - 1]
    generate_random_permutation($l, $n - 1);
 
    // Recursion call for [n + 1, r]
    generate_random_permutation($n + 1, $r);
}
 
// Driver code
$l = 5;
$r = 15;
 
// Generate permutation
generate_random_permutation($l, $r);
 
// Print the generated permutation
printPermutation();
 
// This code is contributed by mits
?>

Javascript




<script>
 
// Javascript implementation of the approach
 
// To store the random permutation
var permutation = [];
 
// Utility function to print
// the generated permutation
function printPermutation()
{
    for (var i of permutation)
        document.write(i + " ");
}
 
// Function to return a random
// number between x and y
function give_random_number(l, r)
{
    var x = Math.floor(Math.random() * l + r) % (r - l + 1) + l;
    return x;
}
 
// Recursive function to generate
// the random permutation
function generate_random_permutation(l, r)
{
 
    // Base condition
    if (l > r)
        return;
 
    // Random number returned from the function
    var n = give_random_number(l, r);
 
    // Inserting random number in vector
    permutation.push(n);
 
    // Recursion call for [l, n - 1]
    generate_random_permutation(l, n - 1);
 
    // Recursion call for [n + 1, r]
    generate_random_permutation(n + 1, r);
}
 
// Driver code
var l = 5;
var r = 15;
 
// Generate permutation
generate_random_permutation(l, r);
 
// Print the generated permutation
printPermutation();
 
// This code is contributed by rrrtnx.
</script>

Output: 

11 9 6 5 8 7 10 12 13 15 14

 

Time Complexity: O(n)

Auxiliary Space: O(1)
 


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