Marathon Match 120

Important Links

• Submission-Review You can find your submissions artifacts here. Artifacts will contain output.txt's for both example test cases and provisional test cases with stdout/stderr and individual test case scores.
• Other Details: For other details like Processing Server Specifications, Submission Queue, Example Test Cases Execution.

Overview

You are given a sequence S containing N numbers in the range [0, K). Your task is to sort this sequence into monotonically increasing order, in a way that incurs the smallest penalty. You are allowed to select any contiguous sub-sequence of numbers and reverse their order. Formally, if the sub-sequence is (S[i], S[i+1], ..., S[k-1], S[k]), where 0 <= i < k < N, then its reversal is (S[k], S[k-1], ..., S[i+1], S[i]). The penalty incurred by this reversal is floor[(k-i+1)^X], where X is a given penalty parameter. Your task is to minimize the total penalty incurred by all the reversals.

Here is a solution for seed=1 with N=10, K=5 and X=1.0. The sub-sequences being reversed are shown inside brackets:

Input sequence:
1 1 1 0 3 0 1 1 2 4

Move 1, move score 2, total score 2
1 1 1 0 (3 0) 1 1 2 4

Move 2, move score 3, total score 5
1 1 1 0 0 (3 1 1) 2 4

Move 3, move score 5, total score 10
(1 1 1 0 0) 1 1 3 2 4

Move 4, move score 2, total score 12
0 0 1 1 1 1 1 (3 2) 4

Sorted sequence:
0 0 1 1 1 1 1 2 3 4
 

Input

Your code will receive as input the following values, each on a separate line:

• N, the length of the sequence.
• K, the maximum number of distinct values in the sequence.
• X, the penalty parameter.

This is followed by N lines representing the sequence to be sorted. Each line will contain a single integer in the range [0, K).

Output

Your code should write to output the following:

• On the first line, R, the number of reversal to perform.
• R lines, each representing a single reversal. The format should be "i k" (without the quotes), where i is the starting index and k is the ending index of the reversal (i < k, both 0-based).

Scoring

The scorer will compute the total penalty incurred by the reversals.

If your return was invalid, then your raw score on this test case will be -1. Possible reasons include:

• Using more than floor[(N*N)/2] reversals.
• Using invalid characters or incorrectly formatted reversals.
• Using indices that are out of bounds.

If your raw score for a test case is negative then your normalized score for that test case is 0. Otherwise, your normalized score for each test case is MIN/YOUR, where YOUR is your raw score and MIN is the smallest positive raw score currently obtained on this test case (considering only the last submission from each competitor). Finally, the sum of all your test scores is normalized to 100.

Test Case Generation

Please look at the generate() method in visualizer's source code for the exact details about test case generation. Each test case is generated as follows:

• The length of the sequence N is chosen between 10 and 1000, inclusive.
• The maximum number of distinct values K is chosen between 2 and N, inclusive.
• The penalty parameter X is chosen between 0.0 and 3.0, inclusive.
• Generate N sequence values, each in the range [0, K).
• All values are chosen uniformly at random.

Notes

• The time limit is 10 seconds per test case (this includes only the time spent in your code). The memory limit is 1024 megabytes.
• The compilation time limit is 30 seconds.
• There are 10 example test cases and 100 full submission (provisional) test cases. There will be 2000 test cases in the final testing.
• The match is rated.

Languages Supported

C#, Java, C++ and Python