Please show all pseudocode and actual code for the first problem :)

1. We want to deriza a function NEXT-PERMUTATION (n,) that given an integer n and a permutation of {1,2,,n} outputs the "rext permutation of {1,2,,n} after in the lexicographical order. For example, on an input (3,1,3,2), NEXT-PERMUTATION should output 2,1,3 and on an input (5,2,3,5,4,1), NEXT-PERMUTATION should output 2,4,1,3,5. (a) Giye pseudocode for the function NEXT-PERMUTATION. (b) Determine the worst case running time of NEXT-PERMUTATION. (c) Implement your pudocode for NEXT-PERMUTation using C/C+ +/ Jay 2. Prose that for all k,nk is O(2r)