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

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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; ` `} `

## PHP

\$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
?>

Output:

```11 9 6 5 8 7 10 12 13 15 14
```

Time Complexity: O(n)

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Improved By : Mithun Kumar