【算法竞赛入门经典】6.5[图的概念和拓扑序] 例题6-21 UVa506

【算法竞赛入门经典】6.5[图的概念和拓扑序] 例题6-21 UVa506

算法竞赛入门经典65图的概念和拓扑序 例题6-21 UVa506
例题UVa506

拓扑

本题储存结构

思路

样例实现代码

例题UVa506

Components of computer systems often have dependencies—other components that must be installed before they will function properly. These dependencies are frequently shared by multiple components. For example, both the TELNET client program and the FTP client program require that the TCP/IP networking software be installed before they can operate. If you install TCP/IP and the TELNET client program, and later decide to add the FTP client program, you do not need to reinstall TCP/IP.

For some components it would not be a problem if the components on which they depended were reinstalled; it would just waste some resources. But for others, like TCP/IP, some component configuration may be destroyed if the component was reinstalled.

It is useful to be able to remove components that are no longer needed. When this is done, components that only support the removed component may also be removed, freeing up disk space, memory, and other resources. But a supporting component, not explicitly installed, may be removed only if all components which depend on it are also removed. For example, removing the FTP client program and TCP/IP would mean the TELNET client program, which was not removed, would no longer operate. Likewise, removing TCP/IP by itself would cause the failure of both the TELNET and the FTP client programs. Also if we installed TCP/IP to support our own development, then installed the TELNET client (which depends on TCP/IP) and then still later removed the TELNET client, we would not want TCP/IP to be removed.

We want a program to automate the process of adding and removing components. To do this we will maintain a record of installed components and component dependencies. A component can be installed explicitly in response to a command (unless it is already installed), or implicitly if it is needed for some other component being installed. Likewise, a component, not explicitly installed, can be explicitly removed in response to a command (if it is not needed to support other components) or implicitly removed if it is no longer needed to support another component. Installing an already implicitly-installed component won’t make that component become explicity installed.

Input

The input file contains several test cases, each of them as described below. The input will contain a sequence of commands (as described below), each on a separate line containing no more than eighty characters. Item names are case sensitive, and each is no longer than ten characters. The command names (DEPEND, INSTALL, REMOVE and LIST) always appear in uppercase starting in column one, and item names are separated from the command name and each other by one or more spaces. All appropriate DEPEND commands will appear before the occurrence of any INSTALL command that uses them. There will be no circular dependencies. The end of the input is marked by a line containing only the word END.



Output

For each test case, the output must follow the description below. Echo each line of input. Follow each echoed INSTALL or REMOVE line with the actions taken in response, making certain that the actions are given in the proper order. Also identify exceptional conditions (see Sample Output, below, for examples of all cases). For the LIST command, display the names of the currently installed components in the installation order. No output, except the echo, is produced for a DEPEND command or the line containing END. There will be at most one dependency list per item

Sample Input

DEPEND TELNET TCPIP NETCARD

DEPEND TCPIP NETCARD

DEPEND DNS TCPIP NETCARD

DEPEND BROWSER TCPIP HTML

INSTALL NETCARD

INSTALL TELNET

INSTALL foo

REMOVE NETCARD

INSTALL BROWSER

INSTALL DNS

LIST

REMOVE TELNET

REMOVE NETCARD

REMOVE DNS

REMOVE NETCARD

INSTALL NETCARD

REMOVE TCPIP

REMOVE BROWSER

REMOVE TCPIP

END

Sample Output

DEPEND TELNET TCPIP NETCARD

DEPEND TCPIP NETCARD

DEPEND DNS TCPIP NETCARD

DEPEND BROWSER TCPIP HTML

INSTALL NETCARD

Installing NETCARD

INSTALL TELNET

Installing TCPIP

Installing TELNET

INSTALL foo

Installing foo

REMOVE NETCARD

NETCARD is still needed.

INSTALL BROWSER

Installing HTML

Installing BROWSER

INSTALL DNS

Installing DNS

LIST

NETCARD

TCPIP

TELNET

foo

HTML

BROWSER

DNS

REMOVE TELNET

Removing TELNET

REMOVE NETCARD

NETCARD is still needed.

REMOVE DNS

Removing DNS

REMOVE NETCARD

NETCARD is still needed.

INSTALL NETCARD

NETCARD is already installed.

REMOVE TCPIP

TCPIP is still needed.

REMOVE BROWSER

Removing BROWSER

Removing HTML

Removing TCPIP

REMOVE TCPIP

TCPIP is not installed.

END

拓扑

对一个有向无环图(Directed Acyclic Graph简称DAG)G进行拓扑排序，是将G中所有顶点排成一个线性序列，使得图中任意一对顶点u和v，若边(u,v)∈E(G)，则u在线性序列中出现在v之前。通常，这样的线性序列称为满足拓扑次序(Topological Order)的序列，简称拓扑序列。

本题储存结构

为编号便于使用，采用了STL MAP的结构

map<string, int>info1;

每一个系统看成一个节点，系统之间是单向的图，由于不涉及到边上的信息，只需要储存其指向哪个节点和被哪个节点指向即可。已安装的节点也用一个vector储存。

vector<int>d[MAX];
vector<int>bd[MAX];
vector<int>installinfo;

这题的拓扑直接使用数组记录入度和出度即可。

TIP：安装方式需要保留，删除组件时有用

思路

直接利用两个vector数组记录每个节点的入度和出度。安装和删除进行dfs。

样例实现代码

TIP:本代码没有在UVa测试，仅保证样例通过。

#include<iostream>
#include<map>
#include<string>
#include<sstream>
#include<vector>
#include<algorithm>
#define MAX 1000
using namespace std;
vector<int>d[MAX];
vector<int>bd[MAX];
vector<int>installinfo;
int installed[MAX];
map<string, int>info1;
string info2[MAX];
int cnt = 0;
int ID(const string &s) {
if (!info1.count(s)) {
info2[cnt] = s;
info1[s] = cnt++;
}
return info1[s];
}
void list() {
for (int i = 0; i < installinfo.size(); i++)
cout << "   " << info2[installinfo[i]] << "\n";
}
void install(int s,int level) {
if (!installed[s]) {
installed[s] = level;
for (int i = 0; i < d[s].size(); i++)
install(d[s][i], 2);
cout << "   Installing " << info2[s] << endl;
installed[s] = level;
installinfo.push_back(s);
}
}
bool need(int s) {
for (int i = 0; i < bd[s].size(); i++)
if (installed[bd[s][i]])
return true;
return false;
}
void remove(int s,int level) {
if ((installed[s]==2||level==1)&&installed[s]&&!need(s)) {
installed[s] = 0;
cout << "   Removing " << info2[s] << endl;
installinfo.erase(remove(installinfo.begin(), installinfo.end(), s), installinfo.end());
for (int i = 0; i < d[s].size(); i++)
remove(d[s][i], 2);
}
}
int main() {
memset(installed, 0, sizeof(installed));
string raw, cmd;
string s1, s2;
int st1, st2;
while (getline(cin, raw)) {
stringstream ss(raw);
ss >> cmd;
if (cmd == "END")
break;
else if (cmd == "LIST")
list();
else if (cmd == "DEPEND") {
ss >> s1;
st1=ID(s1);
while (ss >> s2) {
st2 = ID(s2);
d[st1].push_back(st2);
bd[st2].push_back(st1);
}
}
else if (cmd == "INSTALL") {
ss >> s1;
st1 = ID(s1);
if (installed[st1])
cout << "   " << s1 << " is already installed." << endl;
else
install(st1,1);
}
else if (cmd == "REMOVE") {
ss >> s1;
st1 = ID(s1);
if (!installed[st1])
cout << "   " << s1 << " is not installed." << endl;
else if (need(st1))
cout << "   " << s1 << " is still needed." << endl;
else
remove(st1,1);
}
}
return 0;
}