Following is the pseudocode: int permutationCoeff(int n,int k) The idea to implement the above recursive relation using a recursion function with base conditions. The value of P(n,k) can be recursively calculated using the below recursive formula: P(n,k) = P(n-1, k) + k * P(n-1, k-1) It is used to represent the number of ways to obtain an ordered subset of k elements from a set of n elements. The permutation coefficient is represented by P(n,k). The number of permutation on a set of n elements is given by n! Permutation refers to the process of arranging all members of a given set to form a sequence.In case of permutation,order of elements is also considered.To understand the permutation,let's take an example: Examine all the different ways in which a pair of objects can be selected from five distinguishable objects - A,B,C,D,E.If both the letters selected and order of selection are considered,then the following 20 outcomes are considered : AB BA AC CA ADĮach of these 20 possible selections is called a permutation.They can be called as permutations of five objects taken two at a time. In this article, first of all we will visit the idea of Permutation coefficient, explore the naive approach and then, go into the dynamic programming approach to solve this efficiently. If we solve this problem using naive algorithm then time complexity would be exponential but we can reduce this to O(n * k) using dynamic programming. Given n and k, we will calculate permutation coefficient using dynamic programming in O(N * K) time complexity. Reading time: 30 minutes | Coding time: 5 minutes
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