Iterative Algorithm for Generating All Permutations of an Array

What does Permutations of an Array Means?

Imagine you have three letters, A, B, and C, and you want to make words out of them. You can arrange them in different orders, and those arrangements are called permutations. Here are the possibilities: ABC, ACB, BAC, BCA, CBA, CAB. This is all about permutations, where order matters....

How Many Permutations Can Be Generated?

The number of permutations that can be generated from a set of elements depends on the size of the set/array. In combinatorics, the formula for calculating the number of permutations of a set of “n” distinct elements taken “r” at a time is given by:...

Different Ways to Generate Permutations of an Array:

Simple Recursive Algorithm for Generating All Permutations of an ArrayIterative Algorithm for Generating All Permutations of an ArrayHeap’s Algorithm for Generating All Permutations of an ArraySteinhaus Johnson Trotter Algorithm for Generating All Permutations of an Array...

1. Simple Recursive Algorithm for Generating All Permutations of an Array:

The simple recursive algorithm for generating all permutations of an array works like a branching tree. It starts with one element, explores all possible choices for the next element, and repeats this process for each subsequent element. This recursive “tree” expands until it covers all permutations, ensuring that no arrangement is missed. It’s like systematically trying out different orders for the elements, gradually building each permutation, one step at a time....

2. Iterative Algorithm for Generating All Permutations of an Array:

The iterative algorithm for generating permutations efficiently arranges array elements in a systematic order, avoiding the complexities of backtracking. It consistently creates the next lexicographically greater permutation and ensures complete coverage without needing to backtrack, making it a straightforward and efficient approach to generating all possible permutations....

3. Heap’s Algorithm:

Heaps algorithms are used to generate all the possible permutations of n-decimals of a number. This algorithm minimizes the movements, basically, it generates each permutation from the previous one by interchanging a single element while other elements are not disturbed....

4. Steinhaus Johnson Trotter Algorithm:

The Steinhaus Johnson Trotter algorithm’s intuitive idea is to explore permutations by moving elements in a coordinated, directional manner. It ensures that every permutation is generated, and it can be particularly useful for problems where understanding the order of permutations is essential. The algorithm provides a different perspective on permutation generation compared to more traditional methods like Heap’s Algorithm or recursive approaches....