Codeforces Bubble Cup 8 - Finals [Online Mirror] F. Bulbo DP

F. Bulbo

Time Limit: 1 Sec  

Memory Limit: 256 MB

题目连接

http://codeforces.com/contest/575/problem/F

Description

Bananistan is a beautiful banana republic. Beautiful women in beautiful dresses. Beautiful statues of beautiful warlords. Beautiful stars in beautiful nights.

In Bananistan people play this crazy game – Bulbo. There’s an array of bulbs and player at the position, which represents one of the bulbs. The distance between two neighboring bulbs is 1. Before each turn player can change his position with cost |posnew - posold|. After that, a contiguous set of bulbs lights-up and player pays the cost that’s equal to the distance to the closest shining bulb. Then, all bulbs go dark again. The goal is to minimize your summed cost. I tell you, Bananistanians are spending their nights playing with bulbs.

Banana day is approaching, and you are hired to play the most beautiful Bulbo game ever. A huge array of bulbs is installed, and you know your initial position and all the light-ups in advance. You need to play the ideal game and impress Bananistanians, and their families.

Input

The first line contains number of turns n and initial position x. Next n lines contain two numbers lstart and lend, which represent that all bulbs from interval [lstart, lend] are shining this turn.

• 1 ≤ n ≤ 5000
• 1 ≤ x ≤ 109
• 1 ≤ lstart ≤ lend ≤ 109

Output

Output should contain a single number which represents the best result (minimum cost) that could be obtained by playing this Bulbo game.

Sample Input

5 4
2 7
9 16
8 10
9 17
1 6

Sample Output

8

HINT

题意

 有n个区间，你一开始站在x位置

然后n个询问，每个询问给你一个线段，是l,r区间

然后你可以选择走到x位置，花费就是距离

然后关闭这个线段的花费是你现在的位置离线段的最短距离

然后问你依次关闭这n个线段最少需要多少花费

题解：

dp咯，dp[i][j]表示第i轮我在j位置的最小花费

dp[i][j]=min(dp[i][j],dp[i-1][k]+abs(d[i]-d[k]))

然后大概单调栈或者维护一下变成o(n^2)的转移就可以AC了

代码：

//qscqesze
#include <cstdio>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <set>
#include <bitset>
#include <vector>
#include <sstream>
#include <queue>
#include <typeinfo>
#include <fstream>
#include <map>
#include <stack>
typedef long long ll;
using namespace std;
//freopen("D.in","r",stdin);
//freopen("D.out","w",stdout);
#define sspeed ios_base::sync_with_stdio(0);cin.tie(0)
#define maxn 110
#define eps 1e-9
int Num;
//const int inf=0x7fffffff;   //¡ì&szlig;¡ì¨¦¡ì¨¤¡ì¨¦¡§f¡ì3
const int inf=0x3f3f3f3f;
inline ll read()
{
    ll x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
//**************************************************************************************

struct node
{
    ll x,y;
};
node a[5005];
vector<ll> Q;
ll dp[15050];
map<ll,int> H;
int main()
{
    int n=read();
    ll x=read();
    Q.push_back(x);
    for(int i=1;i<=n;i++)
    {
        a[i].x=read(),a[i].y=read();
        Q.push_back(a[i].x);
        Q.push_back(a[i].y);
    }
    sort(Q.begin(),Q.end());
    Q.erase(unique(Q.begin(),Q.end()),Q.end());
    for(int i=0;i<Q.size();i++)
        dp[i]=abs(Q[i]-x);
    for(int i=0;i<Q.size();i++)
        H[Q[i]]=i;
    for(int i=1;i<=n;i++)
    {
        ll tmp=dp[0]-Q[0];
        for(int j=1;j<Q.size();j++)
        {
            dp[j]=min(dp[j],tmp+Q[j]);
            tmp=min(tmp,dp[j]-Q[j]);
        }
        tmp=dp[Q.size()-1]+Q[Q.size()-1];
        for(int j=Q.size()-2;j>=0;j--)
        {
            dp[j]=min(dp[j],tmp-Q[j]);
            tmp=min(tmp,dp[j]+Q[j]);
        }
        for(int j=0;j<Q.size();j++)
        {
            if(Q[j]<a[i].x||Q[j]>a[i].y)dp[j]+=min(abs(Q[j]-a[i].y),abs(Q[j]-a[i].x));
        }
     /*   for(int j=0;j<Q.size();j++)
            cout<<dp[j]<<" ";
        cout<<endl;*/
    }
    ll ans = dp[0];
    for(int i=0;i<Q.size();i++)
        ans = min(ans,dp[i]);
    cout<<ans<<endl;
    return 0;
}