USACO Seciton 5.4 Canada Tour(dp)-优快云博客

本文介绍了一种解决加拿大旅游路线规划问题的算法实现。通过给出的代码示例，展示了如何利用动态规划方法来确定最优的旅游路线，使得在遵循特定条件的前提下，尽可能多地游览城市。算法考虑了城市之间的直接航班连接，并且确保路线的起点和终点一致，同时避免重复访问城市（除了起始城市）。代码中详细解释了状态转移方程和初始化步骤，最后通过遍历结果输出可能的最大访问城市数量。

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因为dp(i,j)=dp(j,i),所以令i>j. dp(i,j)=max(dp(k,j))+1(0<=k<i),若此时dp(i,j)=1则让dp(i,j)=0.(因为无法到达此状态,等于1是因为后来加1了).初始：dp(0,0)=1.answer: max(dp(i,n-1))(0<=i<n).比较难理解的是为什么状态转移时为什么不会出现重复,只要我们每次计算时没有计算重复点，那么之前的计算也不会有(因为是同样的dp计算方式),所以就不会重复.

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#include<cstdio>

#include<iostream>

#include<map>

#include<cstring>

#include<string>

#define rep(i,n) for(int i=0;i<n;i++)

#define Rep(i,l,r) for(int i=l;i<=r;i++)

#define clr(x,c) memset(x,c,sizeof(x))

using namespace std;

const int maxn=100;

map<string,int> Map;

int ok[maxn][maxn];

int d[maxn][maxn];

int n;

int dp(int a,int b) {

if(a<b) swap(a,b);

int &ans=d[a][b];

if(ans>=0) return ans;

ans=0;

if(a==b) return ans;

rep(i,a) if(ok[i][a] && a-b) ans=max(ans,dp(i,b));

return ans ? ++ans : ans;

}

void init() {

clr(d,-1); d[0][0]=1;

clr(ok,0);

int m;

string s[2];

cin>>n>>m;

rep(i,n) {

cin>>s[0];

Map[s[0]]=i;

}

rep(i,m) {

rep(j,2) cin>>s[j];

int a=Map[s[0]],b=Map[s[1]];

ok[a][b]=ok[b][a]=1;

}

void work() {

int ans=1;

rep(i,n) if(ok[i][n-1]) ans=max(ans,dp(i,n-1));

printf("%d\n",ans);

}

int main()

{

freopen("tour.in","r",stdin);

freopen("tour.out","w",stdout);

init();

work();

return 0;

}

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Canada Tour

You have won a contest sponsored by an airline. The prize is a ticket to travel around Canada, beginning in the most western point served by this airline, then traveling only from west to east until you reach the most eastern point served, and then coming back only from east to west until you reach the starting city. No city may be visited more than once, except for the starting city, which must be visited exactly twice (at the beginning and the end of the trip). You are not allowed to use any other airline or any other means of transportation.

Given a list of cities served by the airline and a list of direct flights between pairs of cities, find an itinerary which visits as many cities as possible and satisfies the above conditions beginning with the first city and visiting the last city on the list and returning to the first city.

PROGRAM NAME: tour

INPUT FORMAT

Line 1:	The number N of cities served by the airline and the number V of direct flights that will be listed. N will be a positive integer not larger than 100. V is any positive integer.
Lines 2..N+1:	Each line contains a name of a city served by the airline. The names are ordered from west to east in the input file. There are no two cities in the same meridian. The name of each city is a string of, at most, 15 digits and/or characters of the Latin alphabet; there are no spaces in the name of a city.
Lines N+2..N+2+V-1:	Each line contains two names of cities (taken from the supplied list), separated by a single blank space. This pair is connected by a direct, two-way airline flight.

SAMPLE INPUT (file tour.in)

8 9	 Vancouver		 Yellowknife	 Edmonton Calgary Winnipeg Toronto	 Montreal Halifax	 Vancouver Edmonton Vancouver Calgary	 Calgary Winnipeg Winnipeg Toronto Toronto Halifax Montreal Halifax Edmonton Montreal Edmonton Yellowknife Edmonton Calgary