[luoguP3068] [USACO13JAN]派对邀请函Party Invitations(stl大乱交)

本文介绍了一种使用数据结构解决竞赛编程问题的方法。通过维护每个组的成员列表(set)和成员所属组的链接列表(vector),实现了高效地模拟邀请过程。具体地,使用队列(queue)来跟踪被邀请的人,并更新其所在组的状态,最终输出被邀请的总人数。

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传送门

 

记录每一个编号在那些组中,可以用vector,这里选择链式前向星。

每一组用set

将被邀请的放到queue中

 

#include <set>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iostream>
#define N 1000001

using namespace std;

int n, g, cnt, ans;
int head[N], to[N], next[N];
queue <int> q;
set <int> s[N];
set <int> :: iterator it;
bool b[N];

inline int read()
{
	int x = 0, f = 1;
	char ch = getchar();
	for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = -1;
	for(; isdigit(ch); ch = getchar()) x = (x << 1) + (x << 3) + ch - '0';
	return x * f;
}

inline void add(int x, int y)
{
	to[cnt] = y;
	next[cnt] = head[x];
	head[x] = cnt++;
}

int main()
{
	int i, j, k, x, u, v;
	n = read();
	g = read();
	memset(head, -1, sizeof(head));
	for(i = 1; i <= g; i++)
	{
		k = read();
		for(j = 1; j <= k; j++)
		{
			x = read();
			s[i].insert(x);
			add(x, i);
		}
	}
	q.push(1);
	while(!q.empty())
	{
		ans++;
		u = q.front();
		q.pop();
		for(i = head[u]; i ^ -1; i = next[i])
		{
			v = to[i];
			s[v].erase(u);
			it = s[v].begin();
			if(s[v].size() == 1 && !b[*it])
			{
				b[*it] = 1;
				q.push(*it);
			}
		}
	}
	printf("%d\n", ans);
	return 0;
}

  

转载于:https://www.cnblogs.com/zhenghaotian/p/7373333.html

### USACO 2016 January Contest Subsequences Summing to Sevens Problem Solution and Explanation In this problem from the USACO contest, one is tasked with finding the size of the largest contiguous subsequence where the sum of elements (IDs) within that subsequence is divisible by seven. The input consists of an array representing cow IDs, and the goal is to determine how many cows are part of the longest sequence meeting these criteria; if no valid sequences exist, zero should be returned. To solve this challenge efficiently without checking all possible subsequences explicitly—which would lead to poor performance—a more sophisticated approach using prefix sums modulo 7 can be applied[^1]. By maintaining a record of seen remainders when dividing cumulative totals up until each point in the list by 7 along with their earliest occurrence index, it becomes feasible to identify qualifying segments quickly whenever another instance of any remainder reappears later on during iteration through the dataset[^2]. For implementation purposes: - Initialize variables `max_length` set initially at 0 for tracking maximum length found so far. - Use dictionary or similar structure named `remainder_positions`, starting off only knowing position `-1` maps to remainder `0`. - Iterate over given numbers while updating current_sum % 7 as you go. - Check whether updated value already exists inside your tracker (`remainder_positions`). If yes, compare distance between now versus stored location against max_length variable's content—update accordingly if greater than previous best result noted down previously. - Finally add entry into mapping table linking latest encountered modulus outcome back towards its corresponding spot within enumeration process just completed successfully after loop ends normally. Below shows Python code implementing described logic effectively handling edge cases gracefully too: ```python def find_largest_subsequence_divisible_by_seven(cow_ids): max_length = 0 remainder_positions = {0: -1} current_sum = 0 for i, id_value in enumerate(cow_ids): current_sum += id_value mod_result = current_sum % 7 if mod_result not in remainder_positions: remainder_positions[mod_result] = i else: start_index = remainder_positions[mod_result] segment_size = i - start_index if segment_size > max_length: max_length = segment_size return max_length ```
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