Moving Tables(贪心)

本文介绍了一种解决表格移动问题的算法,通过优化走廊使用,最小化完成所有移动所需的时间。具体包括输入处理、计数走廊使用情况并找出最大使用量,从而计算出最短移动时间。

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链接:http://acm.hdu.edu.cn/showproblem.php?pid=1050

原题:

Moving Tables

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 19651    Accepted Submission(s): 6709


Problem Description
The famous ACM (Advanced Computer Maker) Company has rented a floor of a building whose shape is in the following figure. 



The floor has 200 rooms each on the north side and south side along the corridor. Recently the Company made a plan to reform its system. The reform includes moving a lot of tables between rooms. Because the corridor is narrow and all the tables are big, only one table can pass through the corridor. Some plan is needed to make the moving efficient. The manager figured out the following plan: Moving a table from a room to another room can be done within 10 minutes. When moving a table from room i to room j, the part of the corridor between the front of room i and the front of room j is used. So, during each 10 minutes, several moving between two rooms not sharing the same part of the corridor will be done simultaneously. To make it clear the manager illustrated the possible cases and impossible cases of simultaneous moving. 



For each room, at most one table will be either moved in or moved out. Now, the manager seeks out a method to minimize the time to move all the tables. Your job is to write a program to solve the manager’s problem.
 

Input
The input consists of T test cases. The number of test cases ) (T is given in the first line of the input. Each test case begins with a line containing an integer N , 1<=N<=200 , that represents the number of tables to move. Each of the following N lines contains two positive integers s and t, representing that a table is to move from room number s to room number t (each room number appears at most once in the N lines). From the N+3-rd line, the remaining test cases are listed in the same manner as above.
 

Output
The output should contain the minimum time in minutes to complete the moving, one per line.
 

Sample Input
  
3 4 10 20 30 40 50 60 70 80 2 1 3 2 200 3 10 100 20 80 30 50
 

Sample Output
  
10 20 30
 

Source
 

#include<iostream>
#include<algorithm>
using namespace std;
int cnt[222];
struct node{
int s;
int e;
}a[222];
//bool cmp(node a,node b)
//{
// if(a.s!=b.s)
// return a.s<b.s;
// else
// return a.e<b.e;
//}
int main()
{
int cas,n,i,j,t,max;
while(scanf("%d",&cas)!=EOF)
{
while(cas--)
{
scanf("%d",&n);
max=0;
memset(cnt,0,sizeof(cnt));
for(i=0;i<n;i++)
{
scanf("%d%d",&a[i].s,&a[i].e);
if(a[i].s>a[i].e)
{
t=a[i].s;
a[i].s=a[i].e;
a[i].e=t;
}
for(j=(a[i].s+1)/2;j<=(a[i].e+1)/2;j++)
{
cnt[j]++;
if(cnt[j]>max)
max=cnt[j];
}
}
printf("%d\n",max*10);
}
}
return 0;
}

### 7-2 Moving Tables C语言解决方案 #### 算法思路 为了最小化移动所有桌子所需的时间,采用贪心算法是一个有效的方法。核心思想是在任何时刻尽可能多地利用走廊资源来搬运桌子。具体来说: 对于每一个需要移动的桌子,记录下它所占用的走廊区间的起始位置和结束位置,并统计这些区间重叠的最大次数。因为每次只能有一个桌子通过同一段走廊,所以最大重叠数决定了最少需要多少次5分钟才能完成全部桌子的移动。 #### 实现方法 下面展示了一个完整的C语言程序用于求解此问题[^1]。 ```c #include <stdio.h> int main() { int n, m; scanf("%d", &n); while (n--) { // 处理多组测试数据 int i, j, k, t; int begin, end; int a[200] = {0}; // 记录各个时间段是否有桌椅经过 scanf("%d", &m); for (i = 0; i < m; ++i) { scanf("%d%d", &begin, &end); if (begin > end) { // 如果起点大于终点,则交换两者的位置 t = begin; begin = end; end = t; } // 统计每个时间片内的最大并发量 for (k = (begin - 1) / 2; k <= (end - 1) / 2; ++k){ a[k]++; } } int max = -1; // 找到最大的并发数量作为最终的结果乘以单位时间得到总耗时 for (i = 0; i < 200; ++i) { if (a[i] > max) { max = a[i]; } } printf("%d\n", max * 10); // 输出结果并换行 } return 0; } ``` 这段代码实现了上述提到的逻辑流程,能够有效地处理多个案例的数据输入,并给出相应的最优解。需要注意的是,在实际编程过程中应当仔细考虑边界条件以及变量初始化等问题,确保程序运行稳定可靠[^4]。
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