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248 lines
7.6 KiB
Python
Executable file
248 lines
7.6 KiB
Python
Executable file
"""#
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### 谜题描述
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Mad scientist Mike does not use slow hard disks. His modification of a hard drive has not one, but n different heads that can read data in parallel.
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When viewed from the side, Mike's hard drive is an endless array of tracks. The tracks of the array are numbered from left to right with integers, starting with 1. In the initial state the i-th reading head is above the track number hi. For each of the reading heads, the hard drive's firmware can move the head exactly one track to the right or to the left, or leave it on the current track. During the operation each head's movement does not affect the movement of the other heads: the heads can change their relative order; there can be multiple reading heads above any of the tracks. A track is considered read if at least one head has visited this track. In particular, all of the tracks numbered h1, h2, ..., hn have been read at the beginning of the operation.
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<image>
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Mike needs to read the data on m distinct tracks with numbers p1, p2, ..., pm. Determine the minimum time the hard drive firmware needs to move the heads and read all the given tracks. Note that an arbitrary number of other tracks can also be read.
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Input
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The first line of the input contains two space-separated integers n, m (1 ≤ n, m ≤ 105) — the number of disk heads and the number of tracks to read, accordingly. The second line contains n distinct integers hi in ascending order (1 ≤ hi ≤ 1010, hi < hi + 1) — the initial positions of the heads. The third line contains m distinct integers pi in ascending order (1 ≤ pi ≤ 1010, pi < pi + 1) - the numbers of tracks to read.
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Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is recommended to use the cin, cout streams or the %I64d specifier.
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Output
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Print a single number — the minimum time required, in seconds, to read all the needed tracks.
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Examples
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Input
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3 4
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2 5 6
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1 3 6 8
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Output
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2
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Input
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3 3
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1 2 3
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1 2 3
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Output
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0
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Input
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1 2
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165
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142 200
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Output
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81
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Note
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The first test coincides with the figure. In this case the given tracks can be read in 2 seconds in the following way:
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1. during the first second move the 1-st head to the left and let it stay there;
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2. move the second head to the left twice;
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3. move the third head to the right twice (note that the 6-th track has already been read at the beginning).
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One cannot read the tracks in 1 second as the 3-rd head is at distance 2 from the 8-th track.
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Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
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```python
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import sys
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from itertools import *
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from math import *
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input = raw_input
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range = xrange
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def solve():
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n, m = map(int, input().split())
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h = list(map(int, input().split()))
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p = list(map(int, input().split()))
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ss, ll = 0, int(2.1e10)
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while ss < ll:
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avg = (ss + ll) // 2
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works = True
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hidx = 0
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pidx = 0
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while hidx < len(h) and pidx < len(p):
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leftget = p[pidx]
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curpos = h[hidx]
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if curpos - leftget > avg:
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works = False
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break
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getbacktime = max(0, 2*(curpos - leftget))
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alsotoright = max(0, avg - getbacktime)
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leftime = max(0, curpos - leftget)
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remtime = max(0, (avg - leftime) // 2)
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furthestright = curpos + max(alsotoright, remtime)
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while pidx < len(p) and p[pidx] <= furthestright: pidx += 1
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hidx += 1
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if pidx != len(p): works = False
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if works: ll = avg
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else: ss = avg + 1
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print(ss)
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if sys.hexversion == 50594544 : sys.stdin = open(\"test.txt\")
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solve()
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```
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请完成上述谜题的训练场环境类实现，包括所有必要的方法。
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"""
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from bootcamp import Basebootcamp
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import random
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import re
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from math import inf
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from bootcamp import Basebootcamp
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def calculate_min_time(n, m, h, p):
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h = sorted(h)
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p = sorted(p)
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ss = 0
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ll = 2 * 10**18 # A sufficiently large upper bound
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while ss < ll:
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avg = (ss + ll) // 2
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works = True
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hidx = 0
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pidx = 0
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while hidx < n and pidx < m:
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current_p = p[pidx]
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current_h = h[hidx]
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if current_h - current_p > avg:
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works = False
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break
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# Calculate the furthest right track covered
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getback_time = max(0, 2 * (current_h - current_p))
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also_to_right = max(0, avg - getback_time)
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left_time = max(0, current_h - current_p)
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remaining_time = max(0, (avg - left_time) // 2)
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furthest_right = current_h + max(also_to_right, remaining_time)
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# Move to the first p not covered by current head
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while pidx < m and p[pidx] <= furthest_right:
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pidx += 1
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hidx += 1
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if pidx < m:
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works = False
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if works:
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ll = avg
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else:
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ss = avg + 1
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return ss
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class Creadtimebootcamp(Basebootcamp):
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def __init__(self, n_range=(1, 5), m_range=(1, 5), h_max=1000, p_max=10000):
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self.n_range = n_range
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self.m_range = m_range
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self.h_max = h_max
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self.p_max = p_max
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def case_generator(self):
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n = random.randint(*self.n_range)
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m = random.randint(*self.m_range)
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# Generate h with sorted unique elements
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h = sorted(random.sample(range(1, self.h_max), n))
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# Generate p with sorted unique elements
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p = sorted(random.sample(range(1, self.p_max), m))
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return {
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"n": n,
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"m": m,
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"h": h,
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"p": p
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}
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@staticmethod
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def prompt_func(question_case) -> str:
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case = question_case
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h_list = ' '.join(map(str, case['h']))
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p_list = ' '.join(map(str, case['p']))
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return f"""You are an AI assistant tasked with solving a hard drive head movement optimization problem. Your goal is to determine the minimal time required for all specified tracks to be read by multiple moving heads.
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**Problem Rules:**
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- There are {case['n']} heads initially positioned at distinct tracks in ascending order.
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- You need to read {case['m']} distinct target tracks in ascending order.
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- Each head can move one track left/right or stay each second. The total time is determined by the longest movement time of any head.
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- All required tracks must be covered by at least one head's path during their movements.
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**Input Format:**
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1. First line: n m (number of heads and target tracks)
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2. Second line: h1 h2 ... hn (initial head positions, sorted)
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3. Third line: p1 p2 ... pm (target tracks, sorted)
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**Output Format:**
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A single integer - the minimal time required.
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**Example:**
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Input:
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3 4
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2 5 6
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1 3 6 8
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Output:
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2
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**Your Task:**
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Given the input below, compute the minimal time required. Enclose your answer within [answer] and [/answer] tags.
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Input:
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{case['n']} {case['m']}
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{h_list}
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{p_list}
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Reason step by step, then provide the final answer within [answer] tags."""
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@staticmethod
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def extract_output(output):
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matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
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if not matches:
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return None
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last_match = matches[-1].strip()
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try:
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return int(last_match)
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except ValueError:
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return None
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@classmethod
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def _verify_correction(cls, solution, identity):
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if solution is None:
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return False
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n = identity["n"]
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m = identity["m"]
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h = identity["h"]
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p = identity["p"]
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correct_time = calculate_min_time(n, m, h, p)
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return solution == correct_time
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