Reference no: EM13336646
Task 1.2 Prove this fact rigorously, by mathematical induction.
Please note that the last permutation produced in this sequence is (n, ..., 2, 1). And this is the only permutation that does not have the "next" permutation to it.
Example. Below is the sequence of permutations for n = 3, produced by applying nextPermutation consecutively:
(1 2 3); (1 3 2); (3 1 2); (2 1 3); (2 3 1); (3 2 1)
So, the nextPermutation applied to (1 , 2, 3) produces (1, 3, 2),
applied to (1 , 3, 2) it produces (3, 1, 2),
applied to (3, 1, 2) it produces (2, 1, 3),
etc.
Task 2.2. Iterative version. This is a difficult task, although awarded only two marks.
Using the recursive algorithm, described in the previous section, develop an iterative function with the same functionality as the recursive nextPermutation function. Recall, that the iterative function should not contain recursive calls - it uses only looping constructs.
Task 3. Adding counters to the sorting functions. Develop modified versions of the quickSort and mergeSort functions discussed in the lectures.
I.e. you need to add integer counters to the sorting methods that count the number of comparisons made by each of the functions during the sorting process.
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