Creating a Random Permutation with Fixed Indices in Python

Creating a Random Permutation with Fixed Indices in Python

When working with permutations in Python, there might be instances where you need certain elements to be fixed at specific positions while the rest of the elements are shuffled randomly. This tutorial will guide you through creating a uniformly random permutation with some fixed indices in Python.

Overview

To achieve this, we will:

1. Create a list of elements to be permuted.
2. Remove the fixed elements from this list.
3. Shuffle the remaining elements.
4. Insert the fixed elements back into their specified positions.

This approach ensures that the permutation is random for all elements except for those that are fixed.

Step-by-Step Guide

Step 1: Import the Random Module

First, you need to import Python’s random module which contains the shuffle method used to randomize the order of elements in a list.

import random

Step 2: Define the Fixed Index Permutation Function

Next, define a function that generates a ra