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243 lines
7 KiB
Python
Executable file
243 lines
7 KiB
Python
Executable file
"""#
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### 谜题描述
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There are n balls. They are arranged in a row. Each ball has a color (for convenience an integer) and an integer value. The color of the i-th ball is ci and the value of the i-th ball is vi.
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Squirrel Liss chooses some balls and makes a new sequence without changing the relative order of the balls. She wants to maximize the value of this sequence.
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The value of the sequence is defined as the sum of following values for each ball (where a and b are given constants):
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* If the ball is not in the beginning of the sequence and the color of the ball is same as previous ball's color, add (the value of the ball) × a.
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* Otherwise, add (the value of the ball) × b.
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You are given q queries. Each query contains two integers ai and bi. For each query find the maximal value of the sequence she can make when a = ai and b = bi.
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Note that the new sequence can be empty, and the value of an empty sequence is defined as zero.
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Input
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The first line contains two integers n and q (1 ≤ n ≤ 105; 1 ≤ q ≤ 500). The second line contains n integers: v1, v2, ..., vn (|vi| ≤ 105). The third line contains n integers: c1, c2, ..., cn (1 ≤ ci ≤ n).
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The following q lines contain the values of the constants a and b for queries. The i-th of these lines contains two integers ai and bi (|ai|, |bi| ≤ 105).
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In each line integers are separated by single spaces.
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Output
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For each query, output a line containing an integer — the answer to the query. The i-th line contains the answer to the i-th query in the input order.
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Please, do not write the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.
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Examples
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Input
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6 3
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1 -2 3 4 0 -1
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1 2 1 2 1 1
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5 1
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-2 1
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1 0
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Output
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20
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9
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4
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Input
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4 1
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-3 6 -1 2
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1 2 3 1
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1 -1
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Output
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5
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Note
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In the first example, to achieve the maximal value:
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* In the first query, you should select 1st, 3rd, and 4th ball.
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* In the second query, you should select 3rd, 4th, 5th and 6th ball.
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* In the third query, you should select 2nd and 4th ball.
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Note that there may be other ways to achieve the maximal value.
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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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#include <bits/stdc++.h>
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using namespace std;
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int n, v[100000], c[100000];
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int q, a, b;
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long long f[100000 + 1];
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bool m[100000 + 1];
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int x, y;
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long long query(long long a, long long b) {
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memset(f, 0, sizeof(f));
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memset(m, 0, sizeof(m));
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f[0] = x = y = 0;
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long long res = 0;
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for (int i = 0; i < n; ++i) {
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long long other = c[i] == x ? f[y] : f[x];
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if (m[c[i]]) {
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long long old = f[c[i]];
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f[c[i]] = max(old, max(old + v[i] * a, other + v[i] * b));
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} else {
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f[c[i]] = other + v[i] * b;
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m[c[i]] = 1;
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}
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res = max(res, f[c[i]]);
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if (c[i] == x || c[i] == y) {
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if (f[x] < f[y]) {
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int tmp = x;
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x = y;
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y = tmp;
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}
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} else {
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if (f[c[i]] > f[x]) {
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y = x;
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x = c[i];
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} else if (f[c[i]] > f[y]) {
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y = c[i];
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}
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}
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}
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return res;
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}
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int main(int argc, char *argv[]) {
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cin >> n >> q;
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for (int i = 0; i < n; ++i) {
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cin >> v[i];
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}
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for (int i = 0; i < n; ++i) {
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cin >> c[i];
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}
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for (int i = 0; i < q; ++i) {
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cin >> a >> b;
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cout << query(a, b) << endl;
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}
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return 0;
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}
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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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from bootcamp import Basebootcamp
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class Echoosingballsbootcamp(Basebootcamp):
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def __init__(self, n_min=3, n_max=6, v_min=-5, v_max=5, c_max=3, q_min=1, q_max=3):
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self.n_min = n_min
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self.n_max = n_max
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self.v_min = v_min
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self.v_max = v_max
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self.c_max = c_max
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self.q_min = q_min
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self.q_max = q_max
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def case_generator(self):
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n = random.randint(self.n_min, self.n_max)
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v = [random.randint(self.v_min, self.v_max) for _ in range(n)]
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c = [random.randint(1, self.c_max) for _ in range(n)]
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q = random.randint(self.q_min, self.q_max)
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queries = [(random.randint(-5, 5), random.randint(-5, 5)) for _ in range(q)]
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expected_outputs = [self._compute_query(v, c, a, b) for a, b in queries]
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return {
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'n': n,
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'q': q,
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'v': v,
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'c': c,
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'queries': queries,
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'expected_outputs': expected_outputs
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}
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@staticmethod
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def _compute_query(v_list, c_list, a, b):
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f = {}
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x = None # Largest color
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y = None # Second largest color
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res = 0
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for vi, ci in zip(v_list, c_list):
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other = 0
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if x is not None:
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if ci == x:
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other = f.get(y, 0) if y is not None else 0
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else:
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other = f.get(x, 0)
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current = f.get(ci, -float('inf'))
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new_val = other + vi * b
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if current != -float('inf'):
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new_val = max(new_val, current + vi * a)
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f[ci] = max(current, new_val) if current != -float('inf') else new_val
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res = max(res, f[ci])
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# Update color rankings
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colors = sorted(f.items(), key=lambda x: -x[1])
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x = colors[0][0] if colors else None
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y = colors[1][0] if len(colors) > 1 else None
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return max(res, 0)
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@staticmethod
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def prompt_func(question_case) -> str:
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n = question_case['n']
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q = question_case['q']
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v_str = ' '.join(map(str, question_case['v']))
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c_str = ' '.join(map(str, question_case['c']))
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queries = '\n'.join([f"{a} {b}" for a, b in question_case['queries']])
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return f"""你是一个算法竞赛选手，需要解决以下问题：
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给定{n}个球按序排列，每个球有颜色c和值v。现在有{q}个查询，每个查询给出系数a和b。要求对每个查询找出最大子序列值。规则如下：
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1. 子序列保持原顺序
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2. 第一个球的贡献为v_i × b
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3. 后续球如果颜色与前一个相同，贡献为v_i × a，否则为v_i × b
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输入数据：
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n = {n}, q = {q}
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v数组: {v_str}
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c数组: {c_str}
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查询列表:
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{queries}
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请计算每个查询的最大价值，并按顺序将结果用换行分隔放在[answer]标签内，例如：
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[answer]
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结果1
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结果2
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[/answer]"""
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@staticmethod
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def extract_output(output):
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import re
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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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answers = []
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for line in matches[-1].strip().split('\n'):
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line = line.strip()
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if line:
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try:
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answers.append(int(line))
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except:
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continue
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return answers if answers else None
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@classmethod
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def _verify_correction(cls, solution, identity):
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expected = identity['expected_outputs']
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return isinstance(solution, list) and len(solution) == len(expected) and all(s == e for s, e in zip(solution, expected))
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