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:
Where:
- P(n,r) represents the number of permutations.
- n is the total number of distinct elements.
- r is the number of elements taken at a time.
- n! (read as “n factorial”) represents the product of all positive integers from 1 to n.
If you want to generate all permutations of a given set (where “r” is equal to “n”), the formula simplifies to:
So, for a set of “n” distinct elements, you can generate “n!” (n factorial) permutations. The number of permutations grows rapidly as “n” increases. For example, if you have 3 elements, there are 3! = 6 permutations, but if you have 4 elements, there are 4! = 24 permutations, and so on.
Examples:
Input: nums = [1,2,3]
Output: [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
Explanation: It generates all permutations of the elements in the vector (3!=6) i.e [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]Input: nums = [0,1]
Output: [[0,1],[1,0]]
Explanation: It generates all permutations of the elements in the vector (2!=2) i.e [[0,1],[1,0]]Input: nums = [1]
Output: [[1]]
Explanation: It generates all permutations of the elements in the vector (1!=1) i.e [[1]]
Different Ways to Generate Permutations of an Array
Permutations are like the magic wand of combinatorics, allowing us to explore the countless ways elements can be rearranged within an array. Whether you’re a coder, a math enthusiast, or someone on a quest to solve a complex problem, understanding how to generate all permutations of an array is a valuable skill. In this article, we are going the know Different Ways to Generate Permutations of an Array
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