Codeforces 30D King's Problem? 模拟

首先将n个点排序，找出排序后的K，然后分情况讨论。

当 k == n+1时，显然是 k->1->n || k->n->1这两种的较小值，因为三角形的两边之和大于第三边。

当1 <= k && k <= n 时：

1 ， k -> 1 -> n+1 -> k+1 ->n  ||  k -> n -> n+1 -> k-1 -> 1，当k+1 || k-1 不存在时将对应步骤忽略。

2 ， k - > 1 -> n+1 -> n -> k+1 || k ->n -> n+1 -> 1 -> k-1，当k+1 || k-1 不存在时将对应步骤忽略。

3，这是一种比较奇葩的策略，刚开始做时直觉上认为这种情况是不会存在的，可是.....5个WA教做人。

k -> i -> n -> n+1 -> i-1 -> 1 (i < k)  ||   k -> i -> 1 -> n+1 - > i+1 -> n (i > k) 。

可以理解为花费了 abs(site[k]-site[i]) 的代价以更换起点使得总价值最小，智商好捉急。

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <queue>
#include <cmath>
#include <stack>
#include <map>
#include <ctime>
#include <iomanip>

#pragma comment(linker, "/STACK:1024000000");
#define EPS (1e-6)
#define _LL long long
#define ULL unsigned long long
#define LL __int64
#define INF 0x3f3f3f3f
#define Mod 1000000007

/** I/O Accelerator Interface .. **/
#define g (c=getchar())
#define d isdigit(g)
#define p x=x*10+c-'0'
#define n x=x*10+'0'-c
#define pp l/=10,p
#define nn l/=10,n
template<class T> inline T& RD(T &x)
{
    char c;
    while(!d);
    x=c-'0';
    while(d)p;
    return x;
}
template<class T> inline T& RDD(T &x)
{
    char c;
    while(g,c!='-'&&!isdigit(c));
    if (c=='-')
    {
        x='0'-g;
        while(d)n;
    }
    else
    {
        x=c-'0';
        while(d)p;
    }
    return x;
}
inline double& RF(double &x)      //scanf("%lf", &x);
{
    char c;
    while(g,c!='-'&&c!='.'&&!isdigit(c));
    if(c=='-')if(g=='.')
        {
            x=0;
            double l=1;
            while(d)nn;
            x*=l;
        }
        else
        {
            x='0'-c;
            while(d)n;
            if(c=='.')
            {
                double l=1;
                while(d)nn;
                x*=l;
            }
        }
    else if(c=='.')
    {
        x=0;
        double l=1;
        while(d)pp;
        x*=l;
    }
    else
    {
        x=c-'0';
        while(d)p;
        if(c=='.')
        {
            double l=1;
            while(d)pp;
            x*=l;
        }
    }
    return x;
}
#undef nn
#undef pp
#undef n
#undef p
#undef d
#undef g
using namespace std;

LL num[100010];

double Cal(LL x,LL x0,LL y0)
{
    return sqrt((x-x0)*(x-x0) + y0*y0);
}

int main()
{
    int n,i;
    LL x,y,k;

    scanf("%d %I64d",&n,&k);

    for(i = 1;i <= n; ++i)
        scanf("%I64d",&num[i]);
    scanf("%I64d %I64d",&x,&y);

    if(k == n+1)
    {
        sort(num+1,num+n+1);

        double anw = num[n]-num[1] + min( Cal(num[n],x,y),Cal(num[1],x,y) );

        for(i = 2;i < n; ++i)
            anw = min(anw,min(num[n]-num[i],num[i]-num[1]) + num[n]-num[1] + Cal(num[i],x,y));

        printf("%.10lf\n",anw);

        return 0;
    }

    k = num[k];
    sort(num+1,num+n+1);
    for(i = 1;i <= n && num[i] != k; ++i)
        ;
    k = i;

    double Min = 1000000000;

    double tmp;

    tmp = num[k]-num[1] + num[n]-num[1];
    for(i = 2;i <= n; ++i)
        Min = min(Min,tmp + Cal(num[i-1],x,y) + Cal(num[i],x,y) - (num[i]-num[i-1]));
    tmp = num[n]-num[k] + num[n]-num[1];
    for(i = 2;i <= n; ++i)
        Min = min(Min,tmp + Cal(num[i-1],x,y) + Cal(num[i],x,y) - (num[i]-num[i-1]));

    tmp = num[n]-num[1];

    if(k-1)
    {
        Min = min(Min,tmp + Cal(num[n],x,y) + Cal(num[k-1],x,y) - (num[k]-num[k-1]));
        Min = min(Min,tmp + Cal(num[n],x,y) + Cal(num[1],x,y) - (num[k]-num[k-1]));
    }
    else
    {
        Min = min(Min,tmp + Cal(num[n],x,y));
    }
    if(k+1 <= n)
    {
        Min = min(Min,tmp + Cal(num[1],x,y) + Cal(num[k+1],x,y) - (num[k+1]-num[k]) );
        Min = min(Min,tmp + Cal(num[1],x,y) + Cal(num[n],x,y) - (num[k+1]-num[k]) );
    }
    else
    {
        Min = min(Min,tmp + Cal(num[1],x,y));
    }

    Min = min(Min,num[n]-num[1]+num[k]-num[1] + Cal(num[n],x,y));
    Min = min(Min,num[n]-num[1]+num[n]-num[k] + Cal(num[1],x,y));

    for(i = k+1;i <= n; ++i)
    {
        if(i!=n)
        {
            Min = min(Min,num[i]-num[k]+num[i]-num[1]+Cal(num[1],x,y)+Cal(num[i+1],x,y)+num[n]-num[i+1]);
        }
        else
        {
            Min = min(Min,num[i]-num[k]+num[i]-num[1]+Cal(num[1],x,y)+Cal(num[i+1],x,y));
        }
    }

    for(i = k-1;i >= 1; --i)
    {
        if(i!=1)
        {
            Min = min(Min,num[k]-num[i]+num[n]-num[i]+Cal(num[n],x,y)+Cal(num[i-1],x,y)+num[i-1]-num[1]);
        }
        else
        {
            Min = min(Min,num[k]-num[i]+num[n]-num[i]+Cal(num[n],x,y)+Cal(num[i-1],x,y));
        }
    }

    printf("%.10lf\n",Min);

    return 0;
}

Codeforces 30D King's Problem? 模拟