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576 lines
18 KiB
Python
Executable file
576 lines
18 KiB
Python
Executable file
"""#
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### 谜题描述
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Misha was interested in water delivery from childhood. That's why his mother sent him to the annual Innovative Olympiad in Irrigation (IOI). Pupils from all Berland compete there demonstrating their skills in watering. It is extremely expensive to host such an olympiad, so after the first n olympiads the organizers introduced the following rule of the host city selection.
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The host cities of the olympiads are selected in the following way. There are m cities in Berland wishing to host the olympiad, they are numbered from 1 to m. The host city of each next olympiad is determined as the city that hosted the olympiad the smallest number of times before. If there are several such cities, the city with the smallest index is selected among them.
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Misha's mother is interested where the olympiad will be held in some specific years. The only information she knows is the above selection rule and the host cities of the first n olympiads. Help her and if you succeed, she will ask Misha to avoid flooding your house.
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Input
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The first line contains three integers n, m and q (1 ≤ n, m, q ≤ 500 000) — the number of olympiads before the rule was introduced, the number of cities in Berland wishing to host the olympiad, and the number of years Misha's mother is interested in, respectively.
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The next line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ m), where a_i denotes the city which hosted the olympiad in the i-th year. Note that before the rule was introduced the host city was chosen arbitrarily.
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Each of the next q lines contains an integer k_i (n + 1 ≤ k_i ≤ 10^{18}) — the year number Misha's mother is interested in host city in.
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Output
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Print q integers. The i-th of them should be the city the olympiad will be hosted in the year k_i.
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Examples
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Input
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6 4 10
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3 1 1 1 2 2
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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Output
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4
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3
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4
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2
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3
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4
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1
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2
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3
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4
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Input
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4 5 4
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4 4 5 1
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15
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9
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13
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6
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Output
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5
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3
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3
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3
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Note
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In the first example Misha's mother is interested in the first 10 years after the rule was introduced. The host cities these years are 4, 3, 4, 2, 3, 4, 1, 2, 3, 4.
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In the second example the host cities after the new city is introduced are 2, 3, 1, 2, 3, 5, 1, 2, 3, 4, 5, 1.
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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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#!/usr/bin/env python
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from __future__ import division, print_function
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import operator as op
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import os
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import sys
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from bisect import bisect_left, bisect_right, insort
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from io import BytesIO, IOBase
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from itertools import chain, repeat, starmap
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if sys.version_info[0] < 3:
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from __builtin__ import xrange as range
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from future_builtins import ascii, filter, hex, map, oct, zip
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else:
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from functools import reduce
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def main():
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n, m, q = map(int, input().split())
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a = [int(x) for x in input().split()]
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counter = [0] * m
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for ai in a:
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counter[ai - 1] += 1
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count_order = sorted(range(m), key=lambda x: counter[x])
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years = [0] * m
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for i in range(m - 1):
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diff = counter[count_order[i + 1]] - counter[count_order[i]]
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years[i + 1] = years[i] + diff * (i + 1)
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max_k = max(counter) * m - sum(counter)
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k = [int(input()) - n for _ in range(q)]
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k_order = sorted(range(q), key=lambda x: k[x])
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sortedlist = SortedList()
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res, idx = [0] * q, 0
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for i in range(q):
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ki = k[k_order[i]]
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if ki > max_k:
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res[k_order[i]] = ((ki - max_k - 1) % m) + 1
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else:
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while years[idx] < ki:
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sortedlist.add(count_order[idx])
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idx += 1
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ki -= years[idx - 1] + 1
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ki %= idx
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res[k_order[i]] = sortedlist[ki] + 1
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print(*res, sep='\n')
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class SortedList:
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def __init__(self, iterable=[], _load=200):
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\"\"\"Initialize sorted list instance.\"\"\"
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values = sorted(iterable)
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self._len = _len = len(values)
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self._load = _load
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self._lists = _lists = [
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values[i:i + _load] for i in range(0, _len, _load)
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]
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self._mins = [_list[0] for _list in _lists]
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self._list_lens = [len(_list) for _list in _lists]
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self._fen_tree = []
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self._balanced = False
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def _fen_init(self):
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\"\"\"Initialize a fenwick tree instance.\"\"\"
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self._fen_tree[:] = self._list_lens
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_fen_tree = self._fen_tree
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for i in range(len(_fen_tree)):
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if i | i + 1 < len(_fen_tree):
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_fen_tree[i | i + 1] += _fen_tree[i]
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self._balanced = True
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def _fen_update(self, index, value):
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\"\"\"Update `fen_tree[index] += value`.\"\"\"
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if self._balanced:
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_fen_tree = self._fen_tree
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while index < len(_fen_tree):
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_fen_tree[index] += value
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index |= index + 1
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def _fen_query(self, end):
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\"\"\"Return `sum(_fen_tree[:end])`.\"\"\"
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if not self._balanced:
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self._fen_init()
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_fen_tree = self._fen_tree
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x = 0
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while end:
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x += _fen_tree[end - 1]
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end &= end - 1
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return x
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def _fen_findkth(self, k):
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\"\"\"Return a pair of (the largest `idx` such that `sum(_fen_tree[:idx]) <= k`, `k - sum(_fen_tree[:idx])`).\"\"\"
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_list_lens = self._list_lens
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if k < _list_lens[0]:
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return 0, k
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if k >= self._len - _list_lens[-1]:
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return len(_list_lens) - 1, k + _list_lens[-1] - self._len
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if not self._balanced:
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self._fen_init()
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_fen_tree = self._fen_tree
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idx = -1
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for d in reversed(range(len(_fen_tree).bit_length())):
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right_idx = idx + (1 << d)
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if right_idx < len(_fen_tree) and k >= _fen_tree[right_idx]:
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idx = right_idx
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k -= _fen_tree[idx]
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return idx + 1, k
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def _delete(self, pos, idx):
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\"\"\"Delete value at the given `(pos, idx)`.\"\"\"
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_lists = self._lists
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_mins = self._mins
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_list_lens = self._list_lens
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self._len -= 1
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self._fen_update(pos, -1)
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del _lists[pos][idx]
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_list_lens[pos] -= 1
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if _list_lens[pos]:
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_mins[pos] = _lists[pos][0]
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else:
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del _lists[pos]
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del _list_lens[pos]
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del _mins[pos]
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self._balanced = False
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def _loc_left(self, value):
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\"\"\"Return an index pair that corresponds to the first position of `value` in the sorted list.\"\"\"
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if not self._len:
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return 0, 0
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_lists = self._lists
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_mins = self._mins
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lo, pos = -1, len(_lists) - 1
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while lo + 1 < pos:
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mi = (lo + pos) >> 1
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if value <= _mins[mi]:
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pos = mi
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else:
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lo = mi
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if pos and value <= _lists[pos - 1][-1]:
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pos -= 1
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_list = _lists[pos]
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lo, idx = -1, len(_list)
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while lo + 1 < idx:
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mi = (lo + idx) >> 1
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if value <= _list[mi]:
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idx = mi
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else:
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lo = mi
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return pos, idx
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def _loc_right(self, value):
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\"\"\"Return an index pair that corresponds to the last position of `value` in the sorted list.\"\"\"
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if not self._len:
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return 0, 0
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_lists = self._lists
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_mins = self._mins
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pos, hi = 0, len(_lists)
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while pos + 1 < hi:
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mi = (pos + hi) >> 1
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if value < _mins[mi]:
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hi = mi
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else:
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pos = mi
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_list = _lists[pos]
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lo, idx = -1, len(_list)
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while lo + 1 < idx:
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mi = (lo + idx) >> 1
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if value < _list[mi]:
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idx = mi
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else:
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lo = mi
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return pos, idx
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def add(self, value):
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\"\"\"Add `value` to sorted list.\"\"\"
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_load = self._load
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_lists = self._lists
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_mins = self._mins
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_list_lens = self._list_lens
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self._len += 1
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if _lists:
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pos, idx = self._loc_right(value)
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self._fen_update(pos, 1)
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_list = _lists[pos]
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_list.insert(idx, value)
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_list_lens[pos] += 1
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_mins[pos] = _list[0]
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if _load + _load < len(_list):
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_lists.insert(pos + 1, _list[_load:])
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_mins.insert(pos + 1, _list[_load])
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_list_lens.insert(pos + 1, len(_list) - _load)
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_list_lens[pos] = _load
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del _list[_load:]
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self._balanced = False
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else:
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_lists.append([value])
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_mins.append(value)
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_list_lens.append(1)
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self._balanced = False
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def discard(self, value):
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\"\"\"Remove `value` from sorted list if it is a member.\"\"\"
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_lists = self._lists
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if _lists:
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pos, idx = self._loc_right(value)
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if idx and _lists[pos][idx - 1] == value:
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self._delete(pos, idx - 1)
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def remove(self, value):
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\"\"\"Remove `value` from sorted list; `value` must be a member.\"\"\"
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_len = self._len
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self.discard(value)
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if _len == self._len:
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raise ValueError('{0!r} not in list'.format(value))
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def bisect_left(self, value):
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\"\"\"Return the first index to insert `value` in the sorted list.\"\"\"
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pos, idx = self._loc_left(value)
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return self._fen_query(pos) + idx
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def bisect_right(self, value):
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\"\"\"Return the last index to insert `value` in the sorted list.\"\"\"
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pos, idx = self._loc_right(value)
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return self._fen_query(pos) + idx
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def count(self, value):
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\"\"\"Return number of occurrences of `value` in the sorted list.\"\"\"
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return self.bisect_right(value) - self.bisect_left(value)
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def pop(self, index=-1):
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\"\"\"Remove and return value at `index` in sorted list.\"\"\"
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pos, idx = self._fen_findkth(index if 0 <= index else self._len -
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index)
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value = self._lists[pos][idx]
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self._delete(pos, idx)
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return value
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def __len__(self):
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\"\"\"Return the size of the sorted list.\"\"\"
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return self._len
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def __getitem__(self, index):
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\"\"\"Lookup value at `index` in sorted list.\"\"\"
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pos, idx = self._fen_findkth(index if 0 <= index else self._len +
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index)
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return self._lists[pos][idx]
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def __delitem__(self, index):
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\"\"\"Remove value at `index` from sorted list.\"\"\"
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pos, idx = self._fen_findkth(index if 0 <= index else self._len +
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index)
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self._delete(pos, idx)
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def __contains__(self, value):
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\"\"\"Return true if `value` is an element of the sorted list.\"\"\"
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_lists = self._lists
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pos, idx = self._loc_left(value)
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return _lists and idx < len(_lists[pos]) and _lists[pos][idx] == value
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def __iter__(self):
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\"\"\"Return an iterator over the sorted list.\"\"\"
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return (value for _list in self._lists for value in _list)
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def __reversed__(self):
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\"\"\"Return a reverse iterator over the sorted list.\"\"\"
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return (value for _list in self._lists[::-1] for value in _list[::-1])
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def __repr__(self):
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\"\"\"Return string representation of sorted list.\"\"\"
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return 'SortedList({0})'.format(
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[value for _list in self._lists for value in _list])
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# region fastio
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BUFSIZE = 8192
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class FastIO(IOBase):
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newlines = 0
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def __init__(self, file):
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self._fd = file.fileno()
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self.buffer = BytesIO()
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self.writable = \"x\" in file.mode or \"r\" not in file.mode
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self.write = self.buffer.write if self.writable else None
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def read(self):
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while True:
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b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
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if not b:
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break
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ptr = self.buffer.tell()
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self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
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self.newlines = 0
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return self.buffer.read()
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def readline(self):
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while self.newlines == 0:
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b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
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self.newlines = b.count(b\"\n\") + (not b)
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ptr = self.buffer.tell()
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self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
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self.newlines -= 1
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return self.buffer.readline()
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def flush(self):
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if self.writable:
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os.write(self._fd, self.buffer.getvalue())
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self.buffer.truncate(0), self.buffer.seek(0)
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class IOWrapper(IOBase):
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def __init__(self, file):
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self.buffer = FastIO(file)
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self.flush = self.buffer.flush
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self.writable = self.buffer.writable
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self.write = lambda s: self.buffer.write(s.encode(\"ascii\"))
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self.read = lambda: self.buffer.read().decode(\"ascii\")
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self.readline = lambda: self.buffer.readline().decode(\"ascii\")
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def print(*args, **kwargs):
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\"\"\"Prints the values to a stream, or to sys.stdout by default.\"\"\"
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sep, file = kwargs.pop(\"sep\", \" \"), kwargs.pop(\"file\", sys.stdout)
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at_start = True
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for x in args:
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if not at_start:
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file.write(sep)
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file.write(str(x))
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at_start = False
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file.write(kwargs.pop(\"end\", \"\n\"))
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if kwargs.pop(\"flush\", False):
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file.flush()
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if sys.version_info[0] < 3:
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sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
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else:
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sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
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input = lambda: sys.stdin.readline().rstrip(\"\r\n\")
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# endregion
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if __name__ == \"__main__\":
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main()
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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 bisect
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import re
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from bootcamp import Basebootcamp
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class Dirrigationbootcamp(Basebootcamp):
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def __init__(self, m_max=1000, n_max=1000):
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"""
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初始化城市数量上限和前n届数量上限
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"""
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super().__init__()
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self.m_max = max(1, m_max) # 确保最小值为1
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self.n_max = max(1, n_max) # 确保最小值为1
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def case_generator(self):
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"""
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生成完整的问题实例，包含输入参数和预计算的正确答案
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"""
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import random
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m = random.randint(1, self.m_max) # m至少为1
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n = random.randint(1, self.n_max) # n至少为1
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a = [random.randint(1, m) for _ in range(n)] # 保证城市编号有效
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k_val = random.randint(n + 1, n + 10**6) # 确保k > n
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# 生成完整的问题描述字典
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case = {
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'n': n,
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'm': m,
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'a': a,
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'k': k_val,
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'answer': self._compute_answer(n, m, a, k_val) # 预存正确答案
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}
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return case # 返回单一字典
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def _compute_answer(self, n, m, a, k_val):
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"""计算正确答案的核心算法"""
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if m == 0 or not a:
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return None
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counter = [0] * m
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for ai in a:
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counter[ai-1] += 1
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# 双重排序键：先按次数升序，再按编号升序
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count_order = sorted(range(m), key=lambda x: (counter[x], x))
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years = [0] * m
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# 计算阶段边界
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for i in range(m-1):
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if i+1 >= len(count_order):
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break
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diff = counter[count_order[i+1]] - counter[count_order[i]]
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years[i+1] = years[i] + diff * (i + 1)
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# 计算最大有效年份
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max_k = max(counter) * m - sum(counter)
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query_k = k_val - n
|
||
|
||
# 处理超大规模年份
|
||
if query_k > max_k:
|
||
return ((query_k - max_k - 1) % m) + 1
|
||
else:
|
||
# 二分查找阶段边界
|
||
idx = bisect.bisect_right(years, query_k) - 1
|
||
# 获取候选城市列表
|
||
candidates = sorted(count_order[:idx+1])
|
||
# 计算最终位置
|
||
return candidates[(query_k - years[idx] - 1) % len(candidates)] + 1
|
||
|
||
@staticmethod
|
||
def prompt_func(question_case):
|
||
"""生成符合规范的问题描述"""
|
||
return (
|
||
f"## 奥林匹克主办城市选择问题\n\n"
|
||
f"**已知条件**\n"
|
||
f"- 前 {question_case['n']} 届主办城市：{question_case['a']}\n"
|
||
f"- 共有 {question_case['m']} 个候选城市（编号1-{question_case['m']}）\n\n"
|
||
f"**选择规则**\n"
|
||
f"1. 从第 {question_case['n']+1} 届开始，每年选择历史上主办次数最少的城市\n"
|
||
f"2. 若有多个城市次数相同，选择编号最小的\n\n"
|
||
f"**查询请求**\n"
|
||
f"请计算第 {question_case['k']} 届的主办城市编号，并将答案放置于[answer]和[/answer]之间\n\n"
|
||
f"**答案格式示例**\n"
|
||
f"[answer]3[/answer]"
|
||
)
|
||
|
||
@staticmethod
|
||
def extract_output(output):
|
||
"""从模型输出中严格提取答案"""
|
||
matches = re.findall(r'\[answer\](.*?)\[/answer\]', output)
|
||
if not matches:
|
||
return None
|
||
try:
|
||
return int(matches[-1].strip())
|
||
except (ValueError, TypeError):
|
||
return None
|
||
|
||
@classmethod
|
||
def _verify_correction(cls, solution, identity):
|
||
"""严格验证答案，identity即case_generator的输出"""
|
||
return solution == identity.get('answer', None)
|
||
|
||
# 单元测试保障
|
||
if __name__ == "__main__":
|
||
# 测试案例1：官方样例输入1
|
||
test_case1 = {
|
||
'n': 6,
|
||
'm': 4,
|
||
'a': [3,1,1,1,2,2],
|
||
'k': 16,
|
||
'answer': 4
|
||
}
|
||
assert Dirrigationbootcamp._verify_correction(4, test_case1)
|
||
|
||
# 测试案例2：边界值测试
|
||
test_case2 = {
|
||
'n': 1,
|
||
'm': 1,
|
||
'a': [1],
|
||
'k': 2,
|
||
'answer': 1
|
||
}
|
||
assert Dirrigationbootcamp._verify_correction(1, test_case2)
|
||
|
||
print("所有基本测试通过")
|