mirror of
https://github.com/InternLM/InternBootcamp.git
synced 2026-04-19 12:58:04 +00:00
305 lines
8.6 KiB
Python
Executable file
305 lines
8.6 KiB
Python
Executable file
"""#
|
||
|
||
### 谜题描述
|
||
Mike is a bartender at Rico's bar. At Rico's, they put beer glasses in a special shelf. There are n kinds of beer at Rico's numbered from 1 to n. i-th kind of beer has ai milliliters of foam on it.
|
||
|
||
<image>
|
||
|
||
Maxim is Mike's boss. Today he told Mike to perform q queries. Initially the shelf is empty. In each request, Maxim gives him a number x. If beer number x is already in the shelf, then Mike should remove it from the shelf, otherwise he should put it in the shelf.
|
||
|
||
After each query, Mike should tell him the score of the shelf. Bears are geeks. So they think that the score of a shelf is the number of pairs (i, j) of glasses in the shelf such that i < j and <image> where <image> is the greatest common divisor of numbers a and b.
|
||
|
||
Mike is tired. So he asked you to help him in performing these requests.
|
||
|
||
Input
|
||
|
||
The first line of input contains numbers n and q (1 ≤ n, q ≤ 2 × 105), the number of different kinds of beer and number of queries.
|
||
|
||
The next line contains n space separated integers, a1, a2, ... , an (1 ≤ ai ≤ 5 × 105), the height of foam in top of each kind of beer.
|
||
|
||
The next q lines contain the queries. Each query consists of a single integer integer x (1 ≤ x ≤ n), the index of a beer that should be added or removed from the shelf.
|
||
|
||
Output
|
||
|
||
For each query, print the answer for that query in one line.
|
||
|
||
Examples
|
||
|
||
Input
|
||
|
||
5 6
|
||
1 2 3 4 6
|
||
1
|
||
2
|
||
3
|
||
4
|
||
5
|
||
1
|
||
|
||
|
||
Output
|
||
|
||
0
|
||
1
|
||
3
|
||
5
|
||
6
|
||
2
|
||
|
||
Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
|
||
```python
|
||
#include <bits/stdc++.h>
|
||
using namespace std;
|
||
int arr[1000000], val[1000000], mark[1000000];
|
||
int freq[1000000];
|
||
void sieve() {
|
||
int i, j;
|
||
for (i = 2; i * i <= 500000; ++i) {
|
||
if (arr[i] == 0) {
|
||
for (j = i + i; j <= 500000; j += i) {
|
||
if (!arr[j]) arr[j] = i;
|
||
}
|
||
}
|
||
}
|
||
for (i = 2; i <= 500000; ++i) {
|
||
if (!arr[i]) arr[i] = i;
|
||
}
|
||
}
|
||
int main() {
|
||
sieve();
|
||
int tmp, n, q, i, j, k, a, b, c, x, y, z, lim, tot;
|
||
long long int ans;
|
||
scanf(\"%d\", &n);
|
||
scanf(\"%d\", &q);
|
||
for (i = 1; i <= n; ++i) {
|
||
scanf(\"%d\", &val[i]);
|
||
}
|
||
ans = 0ll;
|
||
tot = 0;
|
||
int c1 = 0;
|
||
while (q--) {
|
||
scanf(\"%d\", &x);
|
||
a = val[x];
|
||
vector<int> v;
|
||
while (a != 1) {
|
||
k = arr[a];
|
||
v.push_back(k);
|
||
while (a % k == 0) a /= k;
|
||
}
|
||
lim = (1 << v.size());
|
||
tmp = 0;
|
||
for (i = 1; i < lim; ++i) {
|
||
if (__builtin_popcount(i) & 1) {
|
||
a = 1;
|
||
} else {
|
||
a = -1;
|
||
}
|
||
y = 1;
|
||
for (j = 0; j < v.size(); ++j) {
|
||
if (i & (1 << j)) y *= v[j];
|
||
}
|
||
tmp += (a * freq[y]);
|
||
}
|
||
if (mark[x] == 0) {
|
||
mark[x] = 1;
|
||
ans += (tot - tmp);
|
||
tot++;
|
||
for (i = 1; i < lim; ++i) {
|
||
y = 1;
|
||
for (j = 0; j < v.size(); ++j) {
|
||
if (i & (1 << j)) {
|
||
y *= v[j];
|
||
}
|
||
}
|
||
freq[y]++;
|
||
}
|
||
} else {
|
||
mark[x] = 0;
|
||
if (val[x] == 1)
|
||
ans -= (tot - 1);
|
||
else
|
||
ans -= (tot - tmp);
|
||
tot--;
|
||
for (i = 1; i < lim; ++i) {
|
||
y = 1;
|
||
for (j = 0; j < v.size(); ++j) {
|
||
if (i & (1 << j)) {
|
||
y *= v[j];
|
||
}
|
||
}
|
||
freq[y]--;
|
||
}
|
||
}
|
||
printf(\"%lld\n\", ans);
|
||
}
|
||
return 0;
|
||
}
|
||
```
|
||
|
||
|
||
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。
|
||
"""
|
||
|
||
from bootcamp import Basebootcamp
|
||
import random
|
||
import re
|
||
from collections import defaultdict
|
||
from bootcamp import Basebootcamp
|
||
|
||
def prime_factors(n):
|
||
"""返回唯一质因数列表（已排序）"""
|
||
if n == 1:
|
||
return []
|
||
factors = set()
|
||
while n % 2 == 0:
|
||
factors.add(2)
|
||
n = n // 2
|
||
i = 3
|
||
max_i = int(n**0.5) + 1
|
||
while i <= max_i and n > 1:
|
||
while n % i == 0:
|
||
factors.add(i)
|
||
n = n // i
|
||
max_i = int(n**0.5) + 1
|
||
i += 2
|
||
if n > 1:
|
||
factors.add(n)
|
||
return sorted(factors)
|
||
|
||
def generate_correct_output(n, q, a, queries):
|
||
"""生成正确的输出序列"""
|
||
mark = defaultdict(bool)
|
||
freq = defaultdict(int)
|
||
ans = 0
|
||
tot = 0
|
||
output = []
|
||
|
||
for x in queries:
|
||
val = a[x-1]
|
||
factors = prime_factors(val)
|
||
lim = 1 << len(factors)
|
||
|
||
# 计算互质的元素数量
|
||
tmp = 0
|
||
for mask in range(1, lim):
|
||
bits = bin(mask).count('1')
|
||
sign = 1 if bits % 2 else -1
|
||
product = 1
|
||
for j in range(len(factors)):
|
||
if mask & (1 << j):
|
||
product *= factors[j]
|
||
tmp += sign * freq[product]
|
||
|
||
if not mark[x]:
|
||
# 添加操作
|
||
ans += (tot - tmp)
|
||
tot += 1
|
||
# 更新素数组合频率
|
||
for mask in range(1, lim):
|
||
product = 1
|
||
for j in range(len(factors)):
|
||
if mask & (1 << j):
|
||
product *= factors[j]
|
||
freq[product] += 1
|
||
mark[x] = True
|
||
else:
|
||
# 移除操作
|
||
ans -= (tot - 1 - tmp) if val == 1 else (tot - tmp)
|
||
tot -= 1
|
||
# 更新素数组合频率
|
||
for mask in range(1, lim):
|
||
product = 1
|
||
for j in range(len(factors)):
|
||
if mask & (1 << j):
|
||
product *= factors[j]
|
||
freq[product] -= 1
|
||
if freq[product] == 0:
|
||
del freq[product]
|
||
mark[x] = False
|
||
|
||
output.append(ans)
|
||
|
||
return output
|
||
|
||
class Cmikeandfoambootcamp(Basebootcamp):
|
||
def __init__(self, **params):
|
||
self.params = params
|
||
self.max_beer = params.get('max_beer', 5)
|
||
self.max_queries = params.get('max_queries', 8)
|
||
self.max_foam = params.get('max_foam', 20)
|
||
|
||
def case_generator(self):
|
||
"""生成有效测试案例（保证至少有一个解）"""
|
||
while True:
|
||
try:
|
||
n = random.randint(2, self.max_beer)
|
||
q = random.randint(3, self.max_queries)
|
||
a = [random.randint(1, self.max_foam) for _ in range(n)]
|
||
queries = [random.randint(1, n) for _ in range(q)]
|
||
output = generate_correct_output(n, q, a, queries)
|
||
return {
|
||
'n': n,
|
||
'q': q,
|
||
'a': a,
|
||
'queries': queries,
|
||
'correct_output': output
|
||
}
|
||
except:
|
||
continue
|
||
|
||
@staticmethod
|
||
def prompt_func(question_case):
|
||
"""生成符合要求的题目描述"""
|
||
problem_desc = (
|
||
"Mike is a bartender at Rico's bar. Your task is to track beer glasses "
|
||
"on a shelf and calculate coprime pairs after each query.\n\n"
|
||
f"Parameters:\n"
|
||
f"- {question_case['n']} beer types\n"
|
||
f"- {question_case['q']} queries\n"
|
||
f"- Foam amounts: {', '.join(map(str, question_case['a']))}\n"
|
||
f"- Query sequence: {', '.join(map(str, question_case['queries']))}\n\n"
|
||
"Rules:\n"
|
||
"1. For each query, toggle the presence of the specified beer type\n"
|
||
"2. After each query, count all (i,j) pairs where i<j and gcd(a_i, a_j)=1\n"
|
||
"3. Output the count immediately after each query\n\n"
|
||
"Output Format:\n"
|
||
"Put each query's result on a separate line within [answer] tags.\n"
|
||
"Example:\n"
|
||
"[answer]\n0\n1\n3\n5\n6\n2\n[/answer]\n"
|
||
"Now provide the answer for the given queries:"
|
||
)
|
||
return problem_desc
|
||
|
||
@staticmethod
|
||
def extract_output(output):
|
||
"""增强答案提取的鲁棒性"""
|
||
answer_pattern = re.compile(r'\[answer\][\s]*(.*?)[\s]*\[/answer\]', re.DOTALL)
|
||
matches = answer_pattern.findall(output)
|
||
|
||
if not matches:
|
||
return None
|
||
|
||
# 取最后一个答案块并解析数字
|
||
last_answer = matches[-1].strip()
|
||
valid_numbers = []
|
||
for line in last_answer.split('\n'):
|
||
line = line.strip()
|
||
if line and line.isdigit():
|
||
valid_numbers.append(int(line))
|
||
|
||
return valid_numbers if valid_numbers else None
|
||
|
||
@classmethod
|
||
def _verify_correction(cls, solution, identity):
|
||
"""严格验证答案顺序和数值"""
|
||
correct = identity.get('correct_output', [])
|
||
return solution == correct
|
||
|
||
# 示例用法
|
||
if __name__ == "__main__":
|
||
bootcamp = Cmikeandfoambootcamp()
|
||
case = bootcamp.case_generator()
|
||
print("Generated Case:", case)
|
||
prompt = Cmikeandfoambootcamp.prompt_func(case)
|
||
print("\nPrompt Example:")
|
||
print(prompt)
|