High Load CodeForces - 828D

本文探讨了如何构建一个包含特定数量节点和出口节点的高速互联网交换点。通过最小化出口节点间的最大距离来提高网络效率,并提供了一种有效的二分搜索算法实现方案。

摘要生成于 C知道 ,由 DeepSeek-R1 满血版支持, 前往体验 >

Arkady needs your help again! This time he decided to build his own high-speed Internet exchange point. It should consist of n nodes connected with minimum possible number of wires into one network (a wire directly connects two nodes). Exactly k of the nodes should be exit-nodes, that means that each of them should be connected to exactly one other node of the network, while all other nodes should be connected to at least two nodes in order to increase the system stability.

Arkady wants to make the system as fast as possible, so he wants to minimize the maximum distance between two exit-nodes. The distance between two nodes is the number of wires a package needs to go through between those two nodes.

Help Arkady to find such a way to build the network that the distance between the two most distant exit-nodes is as small as possible.

Input

The first line contains two integers n and k (3 ≤ n ≤ 2·1052 ≤ k ≤ n - 1) — the total number of nodes and the number of exit-nodes.

Note that it is always possible to build at least one network with nnodes and k exit-nodes within the given constraints.

Output

In the first line print the minimum possible distance between the two most distant exit-nodes. In each of the next n - 1 lines print two integers: the ids of the nodes connected by a wire. The description of each wire should be printed exactly once. You can print wires and wires' ends in arbitrary order. The nodes should be numbered from 1to n. Exit-nodes can have any ids.

If there are multiple answers, print any of them.

Example

Input
3 2
Output
2
1 2
2 3
Input
5 3
Output
3
1 2
2 3
3 4
3 5

Note

In the first example the only network is shown on the left picture.

In the second example one of optimal networks is shown on the right picture.

Exit-nodes are highlighted.





该题解法挺多,我对题目所需要的最小值进行二分。判断该二分值时,已知二分假设的最短距离以及总点数。可以按照这个假设值构成一棵树的最长边,在该边中心处连点,求出所需要的最少叶子数。若该最小叶子数小于等于k,那么该假设成立可以继续缩小,否则增大;最后找到边界值。





#include"stdio.h"
#include"algorithm"
#include"string.h"
#include"cstdio"
using namespace std;
const int max_n=2*(1e5)+10;
int n,k;
int len(int mid)
{
    int maxx=mid/2;
    if(maxx==0)
    return k;
    int less=(n-mid-1)%maxx==0?(n-mid-1)/maxx:(n-mid-1)/maxx+1;
    return less;
}
int EF()
{
    int l=2,r=n-1,mid;
    mid=(l+r)>>1;
    while(l<=r)
    {
        int maxx=mid/2;
        int less=len(mid);
        if(less+2<=k)
        r=mid-1;
        else 
        l=mid+1;
        mid=(l+r)>>1;//printf("&&  %d %d mid:%d\n",l,r,mid);//printf("**\n");
    }
    if(len(r)+2<=k)
    return r;
    return l;
}
int main()
{
    while(scanf("%d%d",&n,&k)!=EOF)
    {
         int ret=EF();
         printf("%d\n",ret);
        int i,num=0;
        int point[max_n],root=0;
        for(i=1;i<=ret;i++)
        printf("%d %d\n",i,i+1);
        i++;
        for(int j=0;j<k-2;j++)
            {
                printf("%d %d\n",(ret+2)/2,i);
                point[++root]=i++;
            }
        while(i<=n)
        {
            
            printf("%d %d\n",point[root--],i++);
            for(int p=0;p<(ret/2-2)&&i<=n;)
            {
                printf("%d %d\n",i-1,i);
                i++; p++;
            }
        }
    }
}



内容概要:本文探讨了在MATLAB/SimuLink环境中进行三相STATCOM(静态同步补偿器)无功补偿的技术方法及其仿真过程。首先介绍了STATCOM作为无功功率补偿装置的工作原理,即通过调节交流电压的幅值和相位来实现对无功功率的有效管理。接着详细描述了在MATLAB/SimuLink平台下构建三相STATCOM仿真模型的具体步骤,包括创建新模型、添加电源和负载、搭建主电路、加入控制模块以及完成整个电路的连接。然后阐述了如何通过对STATCOM输出电压和电流的精确调控达到无功补偿的目的,并展示了具体的仿真结果分析方法,如读取仿真数据、提取关键参数、绘制无功功率变化曲线等。最后指出,这种技术可以显著提升电力系统的稳定性与电能质量,展望了STATCOM在未来的发展潜力。 适合人群:电气工程专业学生、从事电力系统相关工作的技术人员、希望深入了解无功补偿技术的研究人员。 使用场景及目标:适用于想要掌握MATLAB/SimuLink软件操作技能的人群,特别是那些专注于电力电子领域的从业者;旨在帮助他们学会建立复杂的电力系统仿真模型,以便更好地理解STATCOM的工作机制,进而优化实际项目中的无功补偿方案。 其他说明:文中提供的实例代码可以帮助读者直观地了解如何从零开始构建一个完整的三相STATCOM仿真环境,并通过图形化的方式展示无功补偿的效果,便于进一步的学习与研究。
评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值