hdu 2962 题解
题意
给出一张图，每条道路有限高，给出车子的起点，终点，最高高度，问在保证高度尽可能高的情况下的最短路，如果不存在输出 $ cannot \ reach \ destination $
跟前面 $ hdu5418 $ 一样的，题目挺基础的，但是在细节方面比较抠。要是最高度尽可能高，我们就可以想去枚举可能的高度去跑 $ spfa $ ，但我们可以发现这样效率太低了，那么我们为什么不二分答案呢？给出最高高度了，最低不就是 $ 0 $ 吗？二分答案再去跑 $ spfa $ 加上限制条件。 这题时限 $ 10s $ 枚举其实一样能过，也跑得挺快的。另外我还敲了敲 $ floyd $ 果不其然，数据范围太大，它挂了。dijkstra它我也敲挂了（答案错误）等改对了再说吧。
比较坑的点：每组答案之间输出换行，因为这个格式错误了好几次。
代码(按时间从小到大排序
dijkstra(堆优化)+二分
$ 187MS $
/*
dijkstra(堆优化)+二分
Judge Status:Accepted
Exe.Time:187MS
Exe.Memory:1752K
Code Len:2640 B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}edge[M];
int head[N],ver[M],Next[M],ans,minf,n,m,tot,star,en,sum,addmin;
void add(int x,int y,int z,int hi){
ver[++tot]=y;edge[tot].data=z;edge[tot].h=hi;Next[tot]=head[x];head[x]=tot;
}
struct nod{
int data;
int num;
}minn[M];
int d[N];
bool book[N];
void shiftdownmin(int x){
int t,flag=0;
while(x*2<=addmin&&flag==0){
if(minn[x].data>minn[x*2].data)t=x*2;
else t=x;
if(x*2+1<=addmin){
if(minn[t].data>minn[x*2+1].data)t=x*2+1;
}
if(t!=x){
swap(minn[t],minn[x]);
x=t;
}else flag=1;
}
}
void shiftupmin(int x) {
int flag=0;
if(x==1) return;
while(x!=1&&flag==0){
if(minn[x].data<minn[x/2].data) swap(minn[x],minn[x/2]);
else flag=1;
x=x/2;
}
}
void dijkstra(int mi){
memset(book,0,sizeof(book));
memset(d,0x3f,sizeof(d));addmin=0;
d[star]=0;
minn[++addmin].data=0;
minn[addmin].num=star;
while(addmin){
int x=minn[1].num;
minn[1]=minn[addmin--];
shiftdownmin(1);
if(book[x]) continue;
book[x]=1;
for(int i=head[x];i;i=Next[i]){
int y=ver[i],z=edge[i].data;
if(d[y]>d[x]+z&&edge[i].h>=mi){
d[y]=d[x]+z;
minn[++addmin].num=y;
minn[addmin].data=d[y];
shiftupmin(addmin);
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(head,0,sizeof(head));tot=0;sum++;
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
add(x,y,z,h);
add(y,x,z,h);
}scanf("%d %d %d",&star,&en,&r);
ans=0;minf=0;
while(l<=r){
int mid=(l+r)>>1;
dijkstra(mid);
if(d[en]!=INF){
if(mid>ans){
ans=mid;
minf=d[en];
} l=mid+1;
}else r=mid-1;
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minf);
}else printf("cannot reach destination\n");
}
return 0;
}
spfa+二分
$ 218MS $
/*
spfa+二分
Judge Status:Accepted
Exe.Time:218MS
Exe.Memory:1740K
Code Len:1772 B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}edge[M];
int head[N],ver[M],Next[M],d[N],v[N],ans,minn,n,m,tot,star,en,sum;
void add(int x,int y,int z,int hi){
ver[++tot]=y;edge[tot].data=z;edge[tot].h=hi;Next[tot]=head[x];head[x]=tot;
}
queue<int>q;
void spfa(int mi){
memset(d,0x3f,sizeof(d));
memset(v,0,sizeof(v));
d[star]=0;v[star]=1;
q.push(star);
while(q.size()){
int x=q.front();q.pop();
v[x]=0;
for(int i=head[x];i;i=Next[i]){
int y=ver[i],z=edge[i].data;
if((d[y]>d[x]+z)&&edge[i].h>=mi){
d[y]=d[x]+z;
if(!v[y]) q.push(y),v[y]=1;
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(head,0,sizeof(head));tot=0;sum++;
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
add(x,y,z,h);
add(y,x,z,h);
}scanf("%d %d %d",&star,&en,&r);
ans=0;minn=0;
while(l<=r){
int mid=(l+r)>>1;
spfa(mid);
if(d[en]!=INF){
if(mid>ans){
ans=mid;
minn=d[en];
}
l=mid+1;
}else r=mid-1;
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minn);
}else printf("cannot reach destination\n");
}
return 0;
}
枚举+spfa
$ 390MS $
/*
spfa+枚举
Judge Status:Accepted
Exe.Time:390MS
Exe.Memory:1768K
Code Len:1668 B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}edge[M];
int head[N],ver[M],Next[M],d[N],v[N],ans,minn,n,m,tot,star,en,sum;
void add(int x,int y,int z,int hi){
ver[++tot]=y;edge[tot].data=z;edge[tot].h=hi;Next[tot]=head[x];head[x]=tot;
}
queue<int>q;
void spfa(int mi){
memset(d,0x3f,sizeof(d));
memset(v,0,sizeof(v));
d[star]=0;v[star]=1;
q.push(star);
while(q.size()){
int x=q.front();q.pop();
v[x]=0;
for(int i=head[x];i;i=Next[i]){
int y=ver[i],z=edge[i].data;
if((d[y]>d[x]+z)&&edge[i].h>=mi){
d[y]=d[x]+z;
if(!v[y]) q.push(y),v[y]=1;
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(head,0,sizeof(head));tot=0;sum++;
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
add(x,y,z,h);
add(y,x,z,h);
}scanf("%d %d %d",&star,&en,&r);
ans=0;minn=0;
for(int i=r;i;--i){
spfa(i);
if(d[en]!=INF){
ans=i;
minn=d[en];
break;
}
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minn);
}else printf("cannot reach destination\n");
}
return 0;
}
dijkstra(堆优化)+枚举
$ 405MS $
/*
dijkstra(堆优化)+枚举
Judge Status:Accepted
Exe.Time:405MS
Exe.Memory:1752K
Code Len:2558 B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}edge[M];
int head[N],ver[M],Next[M],ans,minf,n,m,tot,star,en,sum,addmin;
void add(int x,int y,int z,int hi){
ver[++tot]=y;edge[tot].data=z;edge[tot].h=hi;Next[tot]=head[x];head[x]=tot;
}
struct nod{
int data;
int num;
}minn[M];
int d[N];
bool book[N];
void shiftdownmin(int x){
int t,flag=0;
while(x*2<=addmin&&flag==0){
if(minn[x].data>minn[x*2].data)t=x*2;
else t=x;
if(x*2+1<=addmin){
if(minn[t].data>minn[x*2+1].data)t=x*2+1;
}
if(t!=x){
swap(minn[t],minn[x]);
x=t;
}else flag=1;
}
}
void shiftupmin(int x) {
int flag=0;
if(x==1) return;
while(x!=1&&flag==0){
if(minn[x].data<minn[x/2].data) swap(minn[x],minn[x/2]);
else flag=1;
x=x/2;
}
}
void dijkstra(int mi){
memset(book,0,sizeof(book));
memset(d,0x3f,sizeof(d));addmin=0;
d[star]=0;
minn[++addmin].data=0;
minn[addmin].num=star;
while(addmin){
int x=minn[1].num;
minn[1]=minn[addmin--];
shiftdownmin(1);
if(book[x]) continue;
book[x]=1;
for(int i=head[x];i;i=Next[i]){
int y=ver[i],z=edge[i].data;
if(d[y]>d[x]+z&&edge[i].h>=mi){
d[y]=d[x]+z;
minn[++addmin].num=y;
minn[addmin].data=d[y];
shiftupmin(addmin);
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(head,0,sizeof(head));tot=0;sum++;
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
add(x,y,z,h);
add(y,x,z,h);
}scanf("%d %d %d",&star,&en,&r);
ans=0;minf=0;
for(int i=r;i;--i){
dijkstra(i);
if(d[en]!=INF){
ans=i;
minf=d[en];
break;
}
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minf);
}else printf("cannot reach destination\n");
}
return 0;
}
dijkstra+二分
$ 1154MS $
/*
dijkstra+二分
Judge Status:Accepted
Exe.Time:1154MS
Exe.Memory:9376K
Code Len:2376 B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}dis[N][N];
int ans,minn,n,m,tot,star,en,sum;
node d[N];
bool book[N];
void dijkstra(int x){
memset(book,0,sizeof(book));
memset(d,0x3f,sizeof(d));
for(int i=1;i<=n;++i){
if(dis[star][i].h>=x) d[i].data=dis[star][i].data;
d[i].h=dis[star][i].h;
}
d[star].data=0;book[star]=1;
for(int i=1;i<n;++i){
int minx=INF;
int op=-1;
for(int j=1;j<=n;++j){
if(d[j].data<minx&&book[j]!=1&&d[j].h>=x){
minx=d[j].data;
op=j;
}
}
if(op!=-1){
book[op]=1;
for(int j=1;j<=n;++j){
if(d[j].data>d[op].data+dis[op][j].data&&(!book[j])&&(dis[op][j].h>=x)&&(d[op].h>=x)){
d[j].data=d[op].data+dis[op][j].data;
d[j].h=min(d[op].h,dis[op][j].h);
}
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(dis,0,sizeof(dis));sum++;
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if(i==j) dis[i][j].data=0;
else dis[i][j].data=INF;
}
}
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
if(h>dis[x][y].h){
dis[x][y].data=z;
dis[x][y].h=h;
}
dis[y][x].data=dis[x][y].data;
dis[y][x].h=dis[x][y].h;
}scanf("%d %d %d",&star,&en,&r);
ans=0;minn=0;
while(l<=r){
int mid=(l+r)>>1;
dijkstra(mid);
if(d[en].data!=INF){
if(mid>ans){
ans=mid;
minn=d[en].data;
} l=mid+1;
}else r=mid-1;
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minn);
}else printf("cannot reach destination\n");
}
return 0;
}
以下是非AC代码
/*
dijkstra+枚举
Judge Status:Time Limit Exceeded
Exe.Time:10000MS
Exe.Memory:9332K
Code Len:2287B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}dis[N][N];
int ans,minn,n,m,tot,star,en,sum;
node d[N];
bool book[N];
void dijkstra(int x){
memset(book,0,sizeof(book));
memset(d,0x3f,sizeof(d));
for(int i=1;i<=n;++i){
if(dis[star][i].h>=x) d[i].data=dis[star][i].data;
d[i].h=dis[star][i].h;
}
d[star].data=0;book[star]=1;
for(int i=1;i<n;++i){
int minx=INF;
int op=-1;
for(int j=1;j<=n;++j){
if(d[j].data<minx&&book[j]!=1&&d[j].h>=x){
minx=d[j].data;
op=j;
}
}
if(op!=-1){
book[op]=1;
for(int j=1;j<=n;++j){
if(d[j].data>d[op].data+dis[op][j].data&&(!book[j])&&(dis[op][j].h>=x)&&(d[op].h>=x)){
d[j].data=d[op].data+dis[op][j].data;
d[j].h=min(d[op].h,dis[op][j].h);
}
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(dis,0,sizeof(dis));sum++;
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if(i==j) dis[i][j].data=0;
else dis[i][j].data=INF;
}
}
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
if(h>dis[x][y].h){
dis[x][y].data=z;
dis[x][y].h=h;
}
dis[y][x].data=dis[x][y].data;
dis[y][x].h=dis[x][y].h;
}scanf("%d %d %d",&star,&en,&r);
ans=0;minn=0;
for(int i=r;i;--i){
dijkstra(i);
if(d[en].data!=INF){
ans=i;
minn=d[en].data;
break;
}
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minn);
}else printf("cannot reach destination\n");
}
return 0;
}
/*
floyd+枚举
Judge Status:Time Limit Exceeded
Exe.Time:10000MS
Exe.Memory:9740K
Code Len:1819 B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}dis[N][N];
int ans,minn,n,m,tot,star,en,sum;
node d[N][N];
queue<int>q;
void floyd(int x){
memset(d,0x3f,sizeof(d));
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if(dis[i][j].h>=x) d[i][j].data=dis[i][j].data;
d[i][j].h=dis[i][j].h;
}
}
for(int k=1;k<=n;++k){
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if((d[i][j].data>d[i][k].data+d[k][j].data)&&(d[i][k].h>=x)&&(d[k][j].h>=x)){
d[i][j].data=d[i][k].data+d[k][j].data;
d[i][j].h=min(d[i][k].h,d[k][j].h);
}
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(dis,0,sizeof(dis));sum++;
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if(i==j) dis[i][j].data=0;
else dis[i][j].data=INF;
}
}
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
if(h>dis[x][y].h){
dis[x][y].data=z;
dis[x][y].h=h;
}
dis[y][x].data=dis[x][y].data;
dis[y][x].h=dis[x][y].h;
}scanf("%d %d %d",&star,&en,&r);
ans=0;minn=0;
for(int i=r;i;--i){
floyd(i);
if(d[star][en].data!=INF){
ans=i;
minn=d[star][en].data;
break;
}
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minn);
}else printf("cannot reach destination\n");
}
return 0;
}
/*
/*
floyd+二分
Judge Status:Time Limit Exceeded
Exe.Time:10000MS
Exe.Memory:12212K
Code Len:1891 B
*/
#include<bits/stdc++.h>
using namespace std;
const int N=1010;
const int M=1000010;
const int INF=0x3f3f3f3f;
struct node{
int h;
int data;
}dis[N][N];
int ans,minn,n,m,tot,star,en,sum;
node d[N][N];
queue<int>q;
void floyd(int x){
memset(d,0x3f,sizeof(d));
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if(dis[i][j].h>=x) d[i][j].data=dis[i][j].data;
d[i][j].h=dis[i][j].h;
}
}
for(int k=1;k<=n;++k){
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if((d[i][j].data>d[i][k].data+d[k][j].data)&&(d[i][k].h>=x)&&(d[k][j].h>=x)){
d[i][j].data=d[i][k].data+d[k][j].data;
d[i][j].h=min(d[i][k].h,d[k][j].h);
}
}
}
}
}
int main(){
while(scanf("%d %d",&n,&m)){
if((!n)&&(!m)) return 0;
if(sum) printf("\n");
memset(dis,0,sizeof(dis));sum++;
for(int i=1;i<=n;++i){
for(int j=1;j<=n;++j){
if(i==j) dis[i][j].data=0;
else dis[i][j].data=INF;
}
}
int l=0,r=0;
for(int i=1;i<=m;++i){
int x,y,z,h;
scanf("%d %d %d %d",&x,&y,&h,&z);
if(h==-1) h=INF;
if(h>dis[x][y].h){
dis[x][y].data=z;
dis[x][y].h=h;
}
dis[y][x].data=dis[x][y].data;
dis[y][x].h=dis[x][y].h;
}scanf("%d %d %d",&star,&en,&r);
ans=0;minn=0;
while(l<=r){
int mid=(l+r)>>1;
floyd(mid);
if(d[star][en].data!=INF){
if(mid>ans){
ans=mid;
minn=d[star][en].data;
} l=mid+1;
}else r=mid-1;
}
printf("Case %d:\n",sum);
if(ans!=0){
printf("maximum height = %d\n",ans);
printf("length of shortest route = %d\n",minn);
}else printf("cannot reach destination\n");
}
return 0;
}
