hdu 2962 题解

题目

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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minf);
        }else printf("cannot reach destination
");
    }
    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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minn);
        }else printf("cannot reach destination
");
    }
    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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minn);
        }else printf("cannot reach destination
");
    }
    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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minf);
        }else printf("cannot reach destination
");
    }
    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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minn);
        }else printf("cannot reach destination
");
    }
    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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minn);
        }else printf("cannot reach destination
");
    }
    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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minn);
        }else printf("cannot reach destination
");
    }
    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("
");
        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:
",sum);
        if(ans!=0){
            printf("maximum height = %d
",ans);
            printf("length of shortest route = %d
",minn);
        }else printf("cannot reach destination
");
    }
    return 0;
}