【專題複習4：Dijkstra】1003、1018、1030、1072、1087、1111
阿新 • • 發佈：2022-03-01
1003
點選檢視程式碼
#include <bits/stdc++.h> using namespace std; const int INF=999999999; int n,m,c1,c2; int e[510][510],weight[510],w[510]; int d[510],num[510]; bool vis[510]; void Dijkstra(int s) { fill(d,d+510,INF); d[s]=0; w[s]=weight[s]; num[s]=1; for(int i=0;i<n;i++){ int u=-1,mind=INF; for(int j=0;j<n;j++){ if(vis[j]==false&&d[j]<mind){ u=j; mind=d[j]; } } if(u==-1) return; vis[u]=true; for(int v=0;v<n;v++){ if(vis[v]==false&&e[u][v]!=0){ if(d[u]+e[u][v]<d[v]){ d[v]=d[u]+e[u][v]; w[v]=w[u]+weight[v]; num[v]=num[u]; }else if(d[u]+e[u][v]==d[v]){ if(w[v]<w[u]+weight[v]) w[v]=w[u]+weight[v]; num[v]+=num[u]; } } } } } int main() { #ifdef ONLINE_JUDGE #else freopen("1.txt", "r", stdin); #endif int a,b,dist; cin>>n>>m>>c1>>c2; for(int i=0;i<n;i++) cin>>weight[i]; for(int i=0; i<m; i++) { cin>>a>>b>>dist; e[a][b]=e[b][a]=dist; } Dijkstra(c1); cout<<num[c2]<<" "<<w[c2]; return 0; }
1018
點選檢視程式碼
#include <bits/stdc++.h> using namespace std; const int INF=999999999; int cmax,n,sp,m; int e[510][510],weight[510],numPath=0; int d[510],minNeed=INF,minRemain=INF; vector<int> pre[510]; vector<int> tempPath,path; bool vis[510]; void Dijkstra(int s) { fill(d,d+510,INF); d[s]=0; for(int i=0;i<n;i++){ int u=-1,mind=INF; for(int j=0;j<=n;j++){ if(vis[j]==false&&d[j]<mind){ u=j; mind=d[j]; } } if(u==-1) return; vis[u]=true; for(int v=0;v<=n;v++){ if(vis[v]==false&&e[u][v]!=0){ if(d[u]+e[u][v]<d[v]){ d[v]=d[u]+e[u][v]; pre[v].clear(); pre[v].push_back(u); }else if(d[u]+e[u][v]==d[v]){ pre[v].push_back(u); } } } } } void dfs(int v) { if(v==0){ tempPath.push_back(v); int need=0,remain=0; for(int i=tempPath.size()-1;i>=0;i--){ int id=tempPath[i]; if(weight[id]>0) remain+=weight[id]; else{ if(remain>abs(weight[id])) remain-=abs(weight[id]); else{ need+=abs(weight[id])-remain; remain=0; } } } if(need<minNeed){ minNeed=need; minRemain=remain; path=tempPath; }else if(need==minNeed&&remain<minRemain){ minRemain=remain; path=tempPath; } tempPath.pop_back(); return; } tempPath.push_back(v); for(int i=0;i<pre[v].size();i++) dfs(pre[v][i]); tempPath.pop_back(); } int main() { #ifdef ONLINE_JUDGE #else freopen("1.txt", "r", stdin); #endif int a,b,dist; cin>>cmax>>n>>sp>>m; for(int i=1;i<=n;i++){ cin>>weight[i]; weight[i]-=cmax/2; } for(int i=0; i<m; i++) { cin>>a>>b>>dist; e[a][b]=e[b][a]=dist; } Dijkstra(0); dfs(sp); cout<<minNeed<<" "; for(int i=path.size()-1;i>=0;i--){ cout<<path[i]; if(i>0) cout<<"->"; } cout<<" "<<minRemain; return 0; }
1030
點選檢視程式碼
#include <bits/stdc++.h> using namespace std; const int INF=999999999; int n,m,st,ed; int e[510][510],cost[510][510]; int d[510],minCost=INF; vector<int> pre[510]; vector<int> tempPath,path; bool vis[510]; void Dijkstra(int s) { fill(d,d+510,INF); d[s]=0; for(int i=0;i<n;i++){ int u=-1,mind=INF; for(int j=0;j<n;j++){ if(vis[j]==false&&d[j]<mind){ u=j; mind=d[j]; } } if(u==-1) return; vis[u]=true; for(int v=0;v<n;v++){ if(vis[v]==false&&e[u][v]!=0){ if(d[u]+e[u][v]<d[v]){ d[v]=d[u]+e[u][v]; pre[v].clear(); pre[v].push_back(u); }else if(d[u]+e[u][v]==d[v]){ pre[v].push_back(u); } } } } } void dfs(int v) { if(v==st){ int tempcost=0; tempPath.push_back(v); for(int i=tempPath.size()-1;i>0;i--){ int id=tempPath[i],idnext=tempPath[i-1]; tempcost+=cost[id][idnext]; } if(tempcost<minCost){ minCost=tempcost; path=tempPath; } tempPath.pop_back(); return; } tempPath.push_back(v); for(int i=0;i<pre[v].size();i++) dfs(pre[v][i]); tempPath.pop_back(); } int main() { #ifdef ONLINE_JUDGE #else freopen("1.txt", "r", stdin); #endif int a,b,dist,costt; cin>>n>>m>>st>>ed; for(int i=0; i<m; i++) { cin>>a>>b>>dist>>costt; e[a][b]=e[b][a]=dist; cost[a][b]=cost[b][a]=costt; } Dijkstra(st); dfs(ed); for(int i=path.size()-1;i>=0;i--){ cout<<path[i]<<" "; } cout<<d[ed]<<" "<<minCost; return 0; }
1072
點選檢視程式碼
#include <bits/stdc++.h>
using namespace std;
const int INF=999999999;
int n,m,k,ds;
double e[1020][1020],cost[1020][1020];
double d[1020],minCost=INF;
vector<int> pre[1020];
vector<int> tempPath,path;
bool vis[1020];
void Dijkstra(int s)
{
fill(vis,vis+1020,false);
fill(d,d+1020,INF);
d[s]=0;
for(int i=0;i<n+m;i++){
int u=-1,mind=INF;
for(int j=1;j<=n+m;j++){
if(vis[j]==false&&d[j]<mind){
u=j;
mind=d[j];
}
}
if(u==-1) return;
vis[u]=true;
for(int v=1;v<=n+m;v++){
if(vis[v]==false&&e[u][v]!=0){
if(d[u]+e[u][v]<d[v]){
d[v]=d[u]+e[u][v];
pre[v].clear();
pre[v].push_back(u);
}else if(d[u]+e[u][v]==d[v]){
pre[v].push_back(u);
}
}
}
}
}
int main()
{
#ifdef ONLINE_JUDGE
#else
freopen("1.txt", "r", stdin);
#endif
string s1,s2;
cin>>n>>m>>k>>ds;
for(int i=0; i<k; i++)
{
int a,b;
double dist;
cin>>s1>>s2>>dist;
if(s1[0]!='G')
a=stoi(s1);
else
a=n+stoi(s1.substr(1));
if(s2[0]!='G')
b=stoi(s2);
else
b=n+stoi(s2.substr(1));
e[a][b]=e[b][a]=dist;
}
double ansDis=-1,ansAvg=INF;
int ansID=-1;
for(int i=n+1;i<=n+m;i++){
double minDis=INF,avg=0;
Dijkstra(i);
for(int j=1;j<=n;j++){
if(d[j]>ds){
minDis=-1;
break;
}
if(minDis>d[j]) minDis=d[j];
avg+=d[j]*1.0/n;
}
if(minDis==-1) continue;
if(minDis>ansDis){
ansDis=minDis;
ansID=i;
ansAvg=avg;
}else if(minDis==ansDis&&avg<ansAvg){
ansID=i;
ansAvg=avg;
}
}
if(ansID==-1) cout<<"No Solution";
else{
printf("G%d\n",ansID-n);
printf("%.1f %.1f",ansDis,ansAvg);
}
return 0;
}
1087
點選檢視程式碼
#include <bits/stdc++.h>
using namespace std;
const int MAXV=510;
const int INF=1000000000;
int n,m,k,st,G[MAXV][MAXV],weight[MAXV];
int d[MAXV],numPath,maxW;
double maxAvg;
bool vis[MAXV];
vector<int> pre[MAXV];
vector<int> tempPath,path;
map<string,int> cityToIndex;
map<int,string> indexToCity;
void Dijkstra(int s)
{
fill(d,d+MAXV,INF);
d[s]=0;
for(int i=0;i<n;i++){
int u=-1,MIN=INF;
for(int j=0;j<n;j++){
if(vis[j]==false&&d[j]<MIN){
u=j;
MIN=d[j];
}
}
if(u==-1) return;
vis[u]=true;
for(int v=0;v<n;v++){
if(vis[v]==false&&G[u][v]!=INF){
if(d[u]+G[u][v]<d[v]){
d[v]=d[u]+G[u][v];
pre[v].clear();
pre[v].push_back(u);
}else if(d[v]==d[u]+G[u][v])
pre[v].push_back(u);
}
}
}
}
void DFS(int v)
{
if(v==st){
tempPath.push_back(v);
numPath++;
int tempW=0;
for(int i=tempPath.size()-2;i>=0;i--){
int id=tempPath[i];
tempW+=weight[id];
}
double tempAvg=1.0*tempW/(tempPath.size()-1);
if(tempW>maxW){
maxW=tempW;
maxAvg=tempAvg;
path=tempPath;
}else if(tempW==maxW&&tempAvg>maxAvg){
maxAvg=tempAvg;
path=tempPath;
}
tempPath.pop_back();
return;
}
tempPath.push_back(v);
for(int i=0;i<pre[v].size();i++)
DFS(pre[v][i]);
tempPath.pop_back();
}
int main()
{
#ifdef ONLINE_JUDGE
#else
freopen("1.txt", "r", stdin);
#endif
string start,city1,city2;
cin>>n>>m>>start;
cityToIndex[start]=0;
indexToCity[0]=start;
for(int i=1;i<=n-1;i++){
cin>>city1>>weight[i];
cityToIndex[city1]=i;
indexToCity[i]=city1;
}
fill(G[0],G[0]+MAXV*MAXV,INF);
for(int i=0;i<m;i++){
cin>>city1>>city2;
int c1=cityToIndex[city1],c2=cityToIndex[city2];
cin>>G[c1][c2];
G[c2][c1]=G[c1][c2];
}
Dijkstra(0);
int rom=cityToIndex["ROM"];
DFS(rom);
cout<<numPath<<" "<<d[rom]<<" "<<maxW<<" "<<(int)maxAvg<<endl;
for(int i=path.size()-1;i>=0;i--){
cout<<indexToCity[path[i]];
if(i>0) cout<<"->";
}
return 0;
}
1111
點選檢視程式碼
#include <bits/stdc++.h>
using namespace std;
const int INF=999999999;
int n,m,st,fin;
int e[510][510],w[510][510],dispre[510],Timepre[510];
int dis[510],Time[510];
int weight[510],nodenum[510];
vector<int> dispath,Timepath;
bool vis[510];
void dfsdispath(int v)
{
dispath.push_back(v);
if(v==st) return;
dfsdispath(dispre[v]);
}
void dfsTimepath(int v)
{
Timepath.push_back(v);
if(v==st) return;
dfsTimepath(Timepre[v]);
}
int main()
{
#ifdef ONLINE_JUDGE
#else
freopen("1.txt", "r", stdin);
#endif
fill(dis,dis+510,INF);
fill(Time,Time+510,INF);
fill(weight,weight+510,INF);
cin>>n>>m;
for(int i=0; i<m; i++)
{
int a,b,one;
cin>>a>>b>>one;
cin>>e[a][b]>>w[a][b];
if(one!=1){
e[b][a]=e[a][b];
w[b][a]=w[a][b];
}
}
cin>>st>>fin;
dis[st]=0;
for(int i=0;i<n;i++){
int u=-1,minn=INF;
for(int j=0;j<n;j++){
if(vis[j]==false&&dis[j]<minn){
u=j;
minn=dis[j];
}
}
if(u==-1) break;
vis[u]=true;
for(int v=0;v<n;v++){
if(vis[v]==false&&e[u][v]!=0){
if(dis[u]+e[u][v]<dis[v]){
dis[v]=dis[u]+e[u][v];
dispre[v]=u;
weight[v]=weight[u]+w[u][v];
}else if(dis[u]+e[u][v]==dis[v]&&weight[v]>weight[u]+w[u][v]){
dispre[v]=u;
weight[v]=weight[u]+w[u][v];
}
}
}
}
dfsdispath(fin);
Time[st]=0;
fill(vis,vis+510,false);
for(int i=0;i<n;i++){
int u=-1,minn=INF;
for(int j=0;j<n;j++){
if(vis[j]==false&&Time[j]<minn){
u=j;
minn=Time[j];
}
}
if(u==-1) break;
vis[u]=true;
for(int v=0;v<n;v++){
if(vis[v]==false&&w[u][v]!=0){
if(Time[u]+w[u][v]<Time[v]){
Time[v]=Time[u]+w[u][v];
Timepre[v]=u;
nodenum[v]=nodenum[u]+1;
}else if(Time[u]+w[u][v]==Time[v]&&nodenum[u]+1<nodenum[v]){
Timepre[v]=u;
nodenum[v]=nodenum[u]+1;
}
}
}
}
dfsTimepath(fin);
printf("Distance = %d",dis[fin]);
if(dispath==Timepath)
printf("; Time = %d: ",Time[fin]);
else{
printf(": ");
for(int i=dispath.size()-1;i>=0;i--){
printf("%d",dispath[i]);
if(i!=0) printf(" -> ");
}
printf("\nTime = %d: ",Time[fin]);
}
for(int i=Timepath.size()-1;i>=0;i--){
printf("%d",Timepath[i]);
if(i!=0) printf(" -> ");
}
return 0;
}
本文來自部落格園，作者：勇往直前的力量，轉載請註明原文連結：https://www.cnblogs.com/moonlight1999/p/15952694.html