{"id":195,"date":"2010-03-27T17:00:00","date_gmt":"2010-03-27T09:00:00","guid":{"rendered":"http:\/\/localhost\/?p=195"},"modified":"2010-03-27T17:00:00","modified_gmt":"2010-03-27T09:00:00","slug":"jsoi2010_express_service_express_service","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/wjmzbmr\/?p=195","title":{"rendered":"[JSOI2010]Express Service \u5feb\u9012\u670d\u52a1"},"content":{"rendered":"\n

[JSOI2010]Express Service \u5feb\u9012\u670d\u52a1 <\/p>\n

Time Limit:10000MS  Memory Limit:65536K
Total Submit:84 Accepted:20
Case Time Limit:1000MS<\/p>\n

Description <\/strong><\/p>\n

\u300c\u98de\u5954\u300d\u5feb\u9012\u516c\u53f8\u6210立\u4e4b\u540e\uff0c\u5df2\u7ecf\u5206\u522b\u4e0e\u5e02\u5185\u8bb8\u591a\u4e2d\u5c0f\u4f01\u4e1a\u516c\u53f8\u7b7e\u8ba2\u90ae\u4ef6\u6536\u9001\u670d\u52a1契\u7ea6\u3002\u7531\u4e8e\u6709\u4e9b\u516c\u53f8\u662f\u5728\u540c\u4e00\u680b\u5927\u697c\u5185\uff0c\u6240\u4ee5\u300c\u98de\u5954\u300d\u516c\u53f8\u6536\u4ef6\u7684\u5730\u70b9\uff08\u6536\u4ef6\u70b9\uff09 \u6700\u591a\u53ea\u6709m\u70b9 (1, 2, \u2026, m)\uff0c\u56e0\u6b64\u300c\u98de\u5954\u300d\u4ec5\u5148行\u91c7\u8d2d了\u4e09\u8f86\u8d27車\u5e76\u8058\u7528了\u4e09\u540d\u53f8\u673a\uff0c\u6bcf\u5929\u65e9\u4e0a\u5206\u522b\u4ece\u6536\u4ef6\u5730\u70b9 \u300c1\u300d, \u300c2\u300d \u53ca \u300c3\u300d\u51fa\u53d1\u3002\u800c\u5728\u4e0e\u5ba2\u6237\u7684\u670d\u52a1契\u7ea6\u4e2d\u6709\u660e\u786e\u8ba2\u7ea6\uff1a\u300c\u98de\u5954\u300d\u5fc5\u987b\u5728\u5ba2\u6237\u63d0\u51fa\u90ae\u4ef6\u5bc4\u9001\u8981\u6c42\u7684\u9694\u5929\u6d3e\u4eba\u81f3\u8be5\u516c\u53f8\uff08\u5730\u70b9\uff09\u6536\u4ef6\u3002
\u4e3a了\u80fd更\u6709\u6548率\u7684\u670d\u52a1\u5ba2\u6237\u5e76\u8282省\u6536\u4ef6\u65f6\u95f4\uff0c\u8be5\u516c\u53f8\u8bbe立了\u6536\u4ef6\u670d\u52a1\u767b\u8bb0\u7f51\u7ad9\uff0c\u5ba2\u6237\u5982\u6709\u90ae\u4ef6\u9700\u8981\u5bc4\u9001\uff0c\u5fc5\u987b\u5728\u9700\u8981\u6536\u4ef6\u7684\u524d\u4e00\u5929\u5c31\u5148\u4e0a\u7f51\u767b\u8bb0\u3002\u4e3a\u4e86\u8282\u7701 \u6cb9\u91cf\uff0c\u300c\u98de\u5954\u300d\u5c31利\u7528\u665a\u4e0a\u5148行\u5b89\u6392\u4e09\u4f4d\u53f8\u673a\u9694\u5929\u7684\u6536\u4ef6路\u7ebf\u3002\u6bcf\u4f4d\u53f8\u673a\u81f3\u5404\u5730\u70b9\u6536\u4ef6\u7684\u987a\u5e8f\u5e94\u4e0e\u5404\u516c\u53f8\u4e0a\u7f51\u767b\u8bb0\u7684\u987a\u5e8f\u76f8\u7b26\u4e14\u5fc5\u987b\u80fd\u5728\u6700省\u6cb9\u7684\u60c5\u51b5\u4e0b\u5b8c\u6210\u5f53\u5929\u6240 \u6709\u7684\u6536\u4ef6\u670d\u52a1\u3002\u56e0\u6b64\u6bcf\u4f4d\u53f8\u673a\u6709\u53ef\u80fd\u9700\u8981\u5728不\u540c\u65f6\u95f4\u91cd\u590d\u5230\u540c\u4e00\u5730\u70b9\u6536\u4ef6\uff0c\u6216不\u540c\u7684\u53f8\u673a\u6709\u53ef\u80fd\u9700\u5728不\u540c\u7684\u65f6\u95f4\u70b9\u524d\u5f80\u540c\u4e00\u5730\u70b9\u6536\u4ef6\u3002
\u5982\u4e0b\u9762\u8303例\u4e8c(\u6536\u4ef6\u516c\u53f8\u5730\u70b9\u4f9d\u5e8f\u4e3a\uff1a 4 2 4 1 5 4 3 2 1)\u6240\u793a\uff0c\u867d\u7136\u53f8\u673a1\u4e00\u5f00\u59cb\u5c31\u5df2\u7ecf\u5728\u6536\u4ef6\u5730\u70b9\u300c1\u300d了\uff0c\u4f46\u662f\u4ed6\u5374不\u80fd\u5148\u628a\u540e\u9762\u7b2c\u56db\u4e2a\u767b\u8bb0\u7684\u516c\u53f8\uff08\u5730\u70b9\u300c1\u300d\uff09\u90ae\u4ef6\u5148\u6536了\u518d\u524d\u5f80\u7b2c\u4e00\u3001\u7b2c\u4e8c\u3001\u6216\u7b2c\u4e09\u4e2a\u767b\u8bb0\u6536 \u4ef6\u5730\u70b9\uff08\u5730\u70b9\u300c4\u300d,\u300c2\u300d,\u300c4\u300d\uff09\u6536\u4ef6\u3002\u4f46\u662f\u5982\u679c\u524d\u4e09\u4e2a\u767b\u8bb0\u6536\u4ef6\u7684\u670d\u52a1\u662f\u7531\u53f8\u673a2\u62163來\u8d1f\u8d23\uff0c\u5219\u53f8\u673a1\u5c31\u53ef\u4ee5\u5728\u5730\u70b9\u300c1\u300d\u6536了\u7b2c\u56db\u4e2a\u767b\u8bb0\u7684\u90ae\u4ef6\u540e\u518d\u524d \u5f80\u540e\u9762\u6240\u767b\u8bb0\u7684\u5730\u70b9\u6536\u4ef6\u3002\u6b64\u5916\uff0c\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\uff0c不\u4e00\u5b9a\u6bcf\u8f86\u8f66\u90fd\u8981\u6536\u5230\u8d27\uff0c\u4e5f\u5c31\u662f說\uff0c\u6700\u4f73\u6536\u4ef6\u65b9\u5f0f\u4e5f\u6709\u53ef\u80fd\u662f\u53ea\u9700\u51fa\u52a8\u4e00\u6216兩\u8f86\u8f66\u53bb\u6536\u8d27\u3002\u8bf7\u5199\u4e00\u4e2a\u7a0b\u5e8f來\u5e2e \u300c\u98de\u5954\u300d\u516c\u53f8\u8ba1\u7b97\u6bcf\u5929\u4f9d\u9884\u7ea6\u987a\u5e8f\u81f3\u5404\u6536\u4ef6\u5730\u70b9\u6536\u4ef6\u7684\u6700\u5c11\u603b\u8017\u6cb9量\u3002 <\/p>\n

Input <\/strong><\/p>\n

\u8f93\u5165\u6587\u4ef6\u7b2c\u4e00行\u6709\u4e00\u4e2a\u6574\u6570 m\uff083 < = m < = 200\uff09\uff0c\u4ee3\u8868\u300c\u98de\u5954\u300d\u516c\u53f8\u6536\u4ef6\u7684\u5730\u70b9\u6570\uff0c\u4ee51\u81f3m\u4e4b\u95f4\u7684\u6574\u6570\u4ee3\u53f7來\u8868\u793a\u6bcf\u4e2a\u5730\u70b9\u3002
\u63a5\u4e0b來\u7684m行\uff08\u7b2c2\u5230\u7b2cm+1行\uff09\uff0c\u6bcf行\u6709m\u4e2a\u6574\u6570\uff0c\u4ee3\u8868\u4e00\u4e2a\u77e9\u9635D\u3002\u7b2c i +1行\u7684\u7b2c j \u4e2a\u6574\u6570\u662fD(i, j)\uff0cD(i, j) \u4ee3\u8868\u53f8\u673a\u5f00\u8f66\u4ece\u6536\u4ef6\u70b9 i \u5230\u6536\u4ef6\u70b9 j \u6240\u9700\u8017\u6cb9量\u3002\u6700\u540e\u6709\u4e00行\u6570串\uff0c\u6570串\u4e4b\u6570\u5b57\u4f9d\u5e8f\u4e3a\u524d\u4e00\u5929\u4e0a\u7f51\u767b\u8bb0\u8981\u6c42\u6536\u4ef6\u7684\u516c\u53f8\u5730\u70b9\u4ee3\u53f7\uff0c\u6700\u591a\u4f1a\u67091000\u4e2a\u6536\u4ef6\u8bf7\u6c42\u3002\u8f93\u5165\u6587\u4ef6\u4e2d\u4efb兩\u4e2a\u76f8\u90bb\u7684\u6574\u6570\u90fd\u4ee5\u4e00\u4e2a \u7a7a\u767d\u9694\u5f00\u3002 \/\/D(i,j)<=maxint
\u6ce8\u610f\uff1a\u6cb9量\u77e9\u9635D\u6ee1\u8db3\u4e09\u89d2不\u7b49\u5f0f\uff0c\u4e5f\u5c31\u662f說 D(i, j) < = D(i, k) + D(k, j)\uff0c1 < = i, j, k < = m\u3002\u56e0\u6b64\uff0c\u6bcf\u8f86\u8f66\u524d\u5f80\u4e0b\u4e00\u4e2a\u6536\u4ef6\u5730\u70b9\u65f6\u4e00\u5b9a\u662f\u76f4\u63a5\u524d\u5f80\uff0c不\u5fc5\u5148\u7ed5\u9053\u81f3\u5176\u5b83\u5730\u70b9\u518d\u62b5\u8fbe\u4e0b\u4e2a\u6536\u4ef6\u5730\u70b9\u3002 <\/p>\n

Output <\/strong><\/p>\n

\u8f93\u51fa\u4e00\u4e2a\u6574\u6570\uff0c\u4ee3\u8868\u6536\u4ef6\u6240\u9700\u6700\u5c11\u603b\u8017\u6cb9量\u3002 <\/p>\n

Sample Input <\/strong><\/p>\n

4
0 5 0 6
6 0 5 6
1 6 0 6
1 1 1 0
1 1 1 1 4 4 2 2 2 3<\/p>\n

Sample Output <\/strong><\/p>\n

6 <\/p>\n

\u6837\u4f8b\u8bf4\u660e\uff1a\u5230\u6bcf\u4e2a\u8bf7\u6c42\u6536\u4ef6\u5730\u70b9\u7684\u53f8\u673a\u5206\u522b\u4e3a1 1 1 1 3 3 2 2 2 1\uff0c\u56e0\u6b64\u53f8\u673a1\u53ea\u9700\u4ece\u8d77\u4f7f\u70b91\u79fb\u52a8\u5230\u5730\u70b93\uff0c\u53f8\u673a2\u53ea\u9700\u505c留\u5728\u5730\u70b92\uff0c\u53f8\u673a3\u4ece\u8d77\u59cb\u70b93\u79fb\u52a8\u5230\u5730\u70b94\u3002<\/p>\n

Source <\/strong><\/p>\n

JSOI2010\u7b2c\u4e8c\u8f6eContest1
\u8fd9\u9898\u80af\u5b9a\u662f\u8981Dp\u7684\uff0c\u5173\u952e\u662f\u72b6\u6001\uff0c\u8bb0\u5f55Dp(i,j,k)\u8868\u793a\u524di\u4e2a\u8ba2\u5355\uff0c\u4e00\u4e2a\u8f66\u5728\u7b2ci\u4e2a\u8ba2\u5355\u7684\u4f4d\u7f6e\uff0c\u53e6\u4e00\u4e2a\u5728\u7b2cj\u4e2a\u4f4d\u7f6e\uff0c\u53e6\u4e00\u4e2a\u5728\u7b2ck\u4e2a\u4f4d\u7f6e\u65f6\u7684\u6700\u5c0f\u6536\u5165\uff0c\u90a3\u4e48\u76f4\u63a5Dp\u5c31OK\u4e86\u3002\u3002
\u4e00\u5f00\u59cb\u6211\u770b\u5230\u90a3\u4e2aD(i,j)<=maxint\u4ee5\u4e3a\u8981\u7528long long\uff0c\u7ed3\u679cTLE\uff0c\u5176\u5b9e\u8fd9\u4e2amaxint\u5c31\u662fmax integer\u7684\u610f\u601d\u56e7\u3002\u3002\u6240\u4ee5int\u5c31\u53ef\u4ee5\u4e86\u3002\u3002
\u5b9e\u9645\u4e0a\u8fd8\u80fd\u518d\u5feb1\u500d\u7684\uff0c\u56e0\u4e3a\u53e6\u5916\u4e24\u8f86\u7684\u987a\u5e8f\u662f\u65e0\u6240\u8c13\u7684\uff0c\u6240\u4ee5\u72b6\u6001\u6570\u8fd8\u53ef\u4ee5\u51cf\u5c11\u4e00\u534a\uff0c\u4e0d\u8fc7\u61d2\u5f97\u4e86\u56e7\u3002\u3002<\/p>\n

Code\uff1a<\/p>\n

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<cstring>
#define rep(i,n) for(int i=0;i<n;i++)
#define pb push_back
using namespace std;
typedef long long ll;
const int maxn=200+10,maxp=1000+10;
const int inf=~0U>>1;
int Dist[maxn][maxn];
int Dp[2][maxn][maxn];
int A[maxp],n,p=0;
void Init()
{
scanf("%d",&n);
rep(i,n) rep(j,n)scanf("%d",&Dist[i][j]);
A[p++]=0;
while(scanf("%d",A+p)==1)–A[p++];
}
inline void Update(int&x,int c){x=min(x,c);}
void Work()
{
int now=0,next=1;int cost;
rep(j,n) rep(k,n) Dp[next][j][k]=inf;
Dp[next][1][2]=0;
rep(i,p-1)
{
swap(now,next);
rep(j,n) rep(k,n) Dp[next][j][k]=inf;
rep(j,n) rep(k,n) if((cost=Dp[now][j][k])!=inf)
{
\/\/use the car in previous place
Update(Dp[next][j][k],cost+Dist[A[i]][A[i+1]]);
\/\/use other two car
Update(Dp[next][A[i]][j],cost+Dist[k][A[i+1]]);
Update(Dp[next][A[i]][k],cost+Dist[j][A[i+1]]);
}
}
int Ans=inf;
rep(j,n) rep(k,n) Update(Ans,Dp[next][j][k]);
cout<<Ans<<endl;
}
int main()
{
\/\/freopen("in","r",stdin);
Init();
Work();
} <\/p>\n","protected":false},"excerpt":{"rendered":"

[JSOI2010]Express Service \u5feb\u9012\u670d\u52a1 Time Limit:10000MS  Memory Limit:65536KTotal Submit:84 Accepted:20 Case Time Limit:1000MS Description \u300c\u98de\u5954\u300d\u5feb\u9012\u516c\u53f8\u6210立\u4e4b\u540e\uff0c\u5df2\u7ecf\u5206\u522b\u4e0e\u5e02\u5185\u8bb8\u591a\u4e2d\u5c0f\u4f01\u4e1a\u516c\u53f8\u7b7e\u8ba2\u90ae\u4ef6\u6536\u9001\u670d\u52a1契\u7ea6\u3002\u7531\u4e8e\u6709\u4e9b\u516c\u53f8\u662f\u5728\u540c\u4e00\u680b\u5927\u697c\u5185\uff0c\u6240\u4ee5\u300c\u98de\u5954\u300d\u516c\u53f8\u6536\u4ef6\u7684\u5730\u70b9\uff08\u6536\u4ef6\u70b9\uff09 \u6700\u591a\u53ea\u6709m\u70b9 (1, 2, \u2026, m)\uff0c\u56e0\u6b64\u300c\u98de\u5954\u300d\u4ec5\u5148行\u91c7\u8d2d了\u4e09\u8f86\u8d27車\u5e76\u8058\u7528了\u4e09\u540d\u53f8\u673a\uff0c\u6bcf\u5929\u65e9\u4e0a\u5206\u522b\u4ece\u6536\u4ef6\u5730\u70b9 \u300c1\u300d, \u300c2\u300d \u53ca \u300c3\u300d\u51fa\u53d1\u3002\u800c\u5728\u4e0e\u5ba2\u6237\u7684\u670d\u52a1契\u7ea6\u4e2d\u6709\u660e\u786e\u8ba2\u7ea6\uff1a\u300c\u98de\u5954\u300d\u5fc5\u987b\u5728\u5ba2\u6237\u63d0\u51fa\u90ae\u4ef6\u5bc4\u9001\u8981\u6c42\u7684\u9694\u5929\u6d3e\u4eba\u81f3\u8be5\u516c\u53f8\uff08\u5730\u70b9\uff09\u6536\u4ef6\u3002 \u4e3a了\u80fd更\u6709\u6548率\u7684\u670d\u52a1\u5ba2\u6237\u5e76\u8282省\u6536\u4ef6\u65f6\u95f4\uff0c\u8be5\u516c\u53f8\u8bbe立了\u6536\u4ef6\u670d\u52a1\u767b\u8bb0\u7f51\u7ad9\uff0c\u5ba2\u6237\u5982\u6709\u90ae\u4ef6\u9700\u8981\u5bc4\u9001\uff0c\u5fc5\u987b\u5728\u9700\u8981\u6536\u4ef6\u7684\u524d\u4e00\u5929\u5c31\u5148\u4e0a\u7f51\u767b\u8bb0\u3002\u4e3a\u4e86\u8282\u7701 \u6cb9\u91cf\uff0c\u300c\u98de\u5954\u300d\u5c31利\u7528\u665a\u4e0a\u5148行\u5b89\u6392\u4e09\u4f4d\u53f8\u673a\u9694\u5929\u7684\u6536\u4ef6路\u7ebf\u3002\u6bcf\u4f4d\u53f8\u673a\u81f3\u5404\u5730\u70b9\u6536\u4ef6\u7684\u987a\u5e8f\u5e94\u4e0e\u5404\u516c\u53f8\u4e0a\u7f51\u767b\u8bb0\u7684\u987a\u5e8f\u76f8\u7b26\u4e14\u5fc5\u987b\u80fd\u5728\u6700省\u6cb9\u7684\u60c5\u51b5\u4e0b\u5b8c\u6210\u5f53\u5929\u6240 \u6709\u7684\u6536\u4ef6\u670d\u52a1\u3002\u56e0\u6b64\u6bcf\u4f4d\u53f8\u673a\u6709\u53ef\u80fd\u9700\u8981\u5728不\u540c\u65f6\u95f4\u91cd\u590d\u5230\u540c\u4e00\u5730\u70b9\u6536\u4ef6\uff0c\u6216不\u540c\u7684\u53f8\u673a\u6709\u53ef\u80fd\u9700\u5728不\u540c\u7684\u65f6\u95f4\u70b9\u524d\u5f80\u540c\u4e00\u5730\u70b9\u6536\u4ef6\u3002 \u5982\u4e0b\u9762\u8303例\u4e8c(\u6536\u4ef6\u516c\u53f8\u5730\u70b9\u4f9d\u5e8f\u4e3a\uff1a 4 2 4 1 5 4 3 2 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