{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"hlce","formal_name":"Humanity's Last Code Exam","introduction":"Humanity's Last Code Exam evaluates problem solving and code generation using ICPC World Finals and IOI problems. The project describes 235 problems; this import selects its public ICPC dataset of 146 problems.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://humanity-s-last-code-exam.github.io/website/","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"0f37ab73-41cd-5e4d-8a2d-7aed59d145e5","task_key":"ICPC~2dWorld~2dFinals--examples--2014~5fG","task_revision_id":"2","upstream_id":"2014_G","short_description":"Metal Processing Plant","config":"ICPC-World-Finals","split":"examples","body":"{\"platform\":\"atcoder\",\"question_content\":\"## Problem Description\\n\\nYulia works for a metal processing plant in Ekaterinburg. This plant processes ores mined in the Ural mountains, extracting precious metals such as chalcopyrite, platinum, and gold from the ores. Every month, the plant receives \\\\( n \\\\) shipments of unprocessed ore. Yulia needs to partition these shipments into two groups based on their similarity. Each group is then sent to one of two ore processing buildings of the plant.\\n\\nTo perform this partitioning, Yulia first calculates a numeric distance \\\\( d(i, j) \\\\) for each pair of shipments \\\\( 1 \\\\leq i \\\\leq n \\\\) and \\\\( 1 \\\\leq j \\\\leq n \\\\), where the smaller the distance, the more similar the shipments \\\\( i \\\\) and \\\\( j \\\\) are. For a subset \\\\( S \\\\subseteq \\\\{1, \\\\ldots, n\\\\} \\\\) of shipments, she defines the disparity \\\\( D \\\\) of \\\\( S \\\\) as the maximum distance between a pair of shipments in the subset, that is:\\n\\n\\\\[\\nD(S) = \\\\max_{i,j \\\\in S} d(i, j)\\n\\\\]\\n\\nYulia then partitions the shipments into two subsets \\\\( A \\\\) and \\\\( B \\\\) in such a way that the sum of their disparities \\\\( D(A) + D(B) \\\\) is minimized. Your task is to help her find this partitioning.\\n\\n## Input\\n\\nThe input consists of a single test case. The first line contains an integer \\\\( n \\\\) \\\\((1 \\\\leq n \\\\leq 200)\\\\) indicating the number of shipments. The following \\\\( n-1 \\\\) lines contain the distances \\\\( d(i, j) \\\\). The \\\\( i \\\\)-th of these lines contains \\\\( n-i \\\\) integers and the \\\\( j \\\\)-th integer of that line gives the value of \\\\( d(i, i+j) \\\\). The distances are symmetric, so \\\\( d(j, i) = d(i, j) \\\\), and the distance of a shipment to itself is 0. All distances are integers between 0 and \\\\( 10^9 \\\\) (inclusive).\\n\\n## Output\\n\\nDisplay the minimum possible sum of disparities for partitioning the shipments into two groups.\\n\\n## Sample Input 1\\n\\n```\\n5\\n4 5 0 2\\n1 3 7\\n2 0\\n4\\n```\\n\\n## Sample Output 1\\n\\n```\\n4\\n```\\n\\n## Sample Input 2\\n\\n```\\n7\\n1 10 5 5 5 5\\n5 10 5 5 5\\n100 100 5 5\\n10 5 5\\n98 99\\n3\\n```\\n\\n## Sample Output 2\\n\\n```\\n15\\n```\",\"question_title\":\"Metal Processing Plant\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://humanity-s-last-code-exam.github.io/website/","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}