[USACO07FEB]銀牛派對Silver Cow Party
阿新 • • 發佈：2018-10-08
swa silver 最短路徑 digi edge pop names queue this
題目描述
寒假到了，N頭牛都要去參加一場在編號為X（1≤X≤N）的牛的農場舉行的派對（1≤N≤1000），農場之間有M（1≤M≤100000）條有向路，每條路長Ti（1≤Ti≤100）。
每頭牛參加完派對後都必須回家，無論是去參加派對還是回家，每頭牛都會選擇最短路徑，求這N頭牛的最短路徑（一個來回）中最長的一條路徑長度。
輸入輸出格式
輸入格式：
第一行三個整數N，M, X；
第二行到第M+1行：每行有三個整數Ai，Bi, Ti ,表示有一條從Ai農場到Bi農場的道路，長度為Ti。
輸出格式：
一個整數，表示最長的最短路得長度。
輸入輸出樣例
輸入樣例#1：
4 8 2 1 2 4 1 3 2 1 4 7 2 1 1 2 3 5 3 1 2 3 4 4 4 2 3
輸出樣例#1：
10題解：
的確是水題。
只要跑最短路時建正、反向圖就可以了
代碼：
#include<bits/stdc++.h> #pragma GCC optimize(3) namespace ZDY{ #define res register #define ri res int #define ll long long #define db double #define sht short #define il inline #define MB template <class T> #define Fur(i,x,y) for(ri i=x;i<=y;i++) #define fur(i,x,y) for(i=x;i<=y;i++) #define Fdr(i,x,y) for(ri i=x;i>=y;i--) #define in2(x,y) in(x),in(y) #define in3(x,y,z) in2(x,y),in(z) #define in4(a,b,c,d) in2(a,b);in2(c,d) #define outn(x) out(x),pc('\n') #define clr(x,y) memset(x,y,sizeof(x)) #define cpy(x,y) memcpy(x,y,sizeof(x)) #define fl(i,x) for(ri i=head[x],to;to=e[i].to,i;i=e[i].nxt) #define inf 2147483630 #define fin(s) freopen(s".in","r",stdin) #define fout(s) freopen(s".out","w",stdin) #define gt io.gc() #define l2(n) (log(n)/log(2)) MB il T ABS(T x){return x>0?x:-x;} MB il T MAX(T x,T y){return x>y?x:y;} MB il T MIN(T x,T y){return x<y?x:y;} MB il T GCD(T x,T y){return y?GCD(y,x%y):x;} MB il void SWAP(T x,T y){T t=x;y=t;x=y;} }using namespace ZDY;using namespace std; class IO{ #define fok (ch!=EOF) #define sep (ch==' '||ch=='\n'||ch=='\t') #define dsep !isdigit(ch) #define neq(a,b) ((a)-(b)>1e-6) char rbuf[1<<20],wbuf[1<<20],b,*p1,*p2; int rs,ws,S; public: IO():p1(rbuf),p2(wbuf),S(1000000),rs(1000000),ws(-1),b(1){} ~IO(){fwrite(wbuf,1,ws+1,stdout);} il char gc(){return rs==S&&(p1=rbuf,rs=-1,(S=fread(rbuf,1,S+1,stdin)-1)==-1)?(b=0,EOF):(++rs,*p1++);} il void pc(int x){ws==1000000&&(p2=wbuf,ws=-1,fwrite(wbuf,1,1000001,stdout)),++ws,*p2++=x;} il void puts(const char str[]){fwrite(wbuf,1,ws+1,stdout)?(ws=-1):0,fwrite(str,1,strlen(str),stdout);} il void gl(string& s){for(res char ch;(ch=gc())!='\n'&&fok;)s+=ch;} il IO& operator>>(int& x){x=0;res char f=0,ch=gc();while(dsep&&fok)f|=(ch=='-'),ch=gc();while(isdigit(ch))x=(x<<1)+(x<<3)+(ch^48),ch=gc();return x=f?-x:x,*this;} il IO& operator>>(ll& x){x=0;res char f=0,ch=gc();while(dsep&&fok)f|=(ch=='-'),ch=gc();while(isdigit(ch))x=(x<<1)+(x<<3)+(ch^48),ch=gc();return x=f?-x:x,*this;} il IO& operator>>(char& ch){return ch=gc(),*this;} il IO& operator>>(string& s){res char ch=gc();while(sep&&fok)ch=gc();while(!sep&&fok)s+=ch,ch=gc();return *this;} il IO& operator>>(double& x){x=0;res char f=0,ch=gc();double d=0.1;while(dsep&&fok)f|=(ch=='-'),ch=gc();while(isdigit(ch))x=x*10+(ch^48),ch=gc();if(ch=='.')while(isdigit(ch=gc()))x+=d*(ch^48),d*=0.1;return x=f?-x:x,*this;} il IO& operator<<(int x){res char ch[10],i=-1;!x?(pc('0'),0):0,x<0?(pc('-'),x=-x):0;while(x)ch[++i]=x%10+48,x/=10;while(~i)pc(ch[i]),--i;return *this;} il IO& operator<<(ll x){res char ch[20],i=-1;!x?(pc('0'),0):0,x<0?(pc('-'),x=-x):0;while(x)ch[++i]=x%10+48,x/=10;while(~i)pc(ch[i]),--i;return *this;} il IO& operator<<(char ch){return pc(ch),*this;} il IO& operator<<(char str[]){return puts(str),*this;} il IO& operator<<(double x){int y=int(x);*this<<y;x-=y;while(neq(x,int(x)))x*=10;x?*this<<'.'<<int(x):0;return *this;} il operator bool(){return b;} }io; #define N 1001 int n,m,s,cnt,CNT,d[N],D[N],head[N],HEAD[N]; bool v[N]; struct edge{int to,w,nxt;}e[100001],E[100001]; #define FL(i,x) for(ri i=HEAD[x],to;to=E[i].to,i;i=E[i].nxt) struct cmp{bool operator()(int a,int b){return d[a]>d[b];}}; priority_queue<int,vector<int>,cmp>q; il void add(int x,int y,int w){e[++cnt].to=y;e[cnt].w=w;e[cnt].nxt=head[x];head[x]=cnt;} il void ADD(int x,int y,int w){E[++CNT].to=y;E[CNT].w=w;E[CNT].nxt=HEAD[x];HEAD[x]=CNT;} il void spfa(){ clr(d,126);clr(D,126); d[s]=D[s]=0;q.push(s); int x; while(!q.empty()){ v[x=q.top()]=0;q.pop(); fl(i,x) if(d[x]+e[i].w<d[to]){ d[to]=d[x]+e[i].w; if(!v[to])q.push(to),v[to]=1; } FL(i,x) if(D[x]+E[i].w<D[to]){ D[to]=D[x]+E[i].w; if(!v[to])q.push(to),v[to]=1; } } } int main(){ io>>n>>m>>s; int x,y,w,ans=0; Fur(i,1,m)io>>x>>y>>w,add(x,y,w),ADD(y,x,w); spfa(); Fur(i,1,n)ans=MAX(ans,d[i]+D[i]); io<<ans<<'\n'; }
彩蛋：
雙倍經驗題：LUOGU P1629 郵遞員送信
（把所有最大值改成所有總和就可以了）
// luogu-judger-enable-o2 #include<bits/stdc++.h> #pragma GCC optimize(3) namespace ZDY{ #define res register #define ri res int #define ll long long #define db double #define sht short #define il inline #define MB template <class T> #define Fur(i,x,y) for(ri i=x;i<=y;i++) #define fur(i,x,y) for(i=x;i<=y;i++) #define Fdr(i,x,y) for(ri i=x;i>=y;i--) #define in2(x,y) in(x),in(y) #define in3(x,y,z) in2(x,y),in(z) #define in4(a,b,c,d) in2(a,b);in2(c,d) #define outn(x) out(x),pc('\n') #define clr(x,y) memset(x,y,sizeof(x)) #define cpy(x,y) memcpy(x,y,sizeof(x)) #define fl(i,x) for(ri i=head[x],to;to=e[i].to,i;i=e[i].nxt) #define inf 2147483630 #define fin(s) freopen(s".in","r",stdin) #define fout(s) freopen(s".out","w",stdin) #define gt io.gc() #define l2(n) (log(n)/log(2)) MB il T ABS(T x){return x>0?x:-x;} MB il T MAX(T x,T y){return x>y?x:y;} MB il T MIN(T x,T y){return x<y?x:y;} MB il T GCD(T x,T y){return y?GCD(y,x%y):x;} MB il void SWAP(T x,T y){T t=x;y=t;x=y;} }using namespace ZDY;using namespace std; class IO{ #define fok (ch!=EOF) #define sep (ch==' '||ch=='\n'||ch=='\t') #define dsep !isdigit(ch) #define neq(a,b) ((a)-(b)>1e-6) char rbuf[1<<20],wbuf[1<<20],b,*p1,*p2; int rs,ws,S; public: IO():p1(rbuf),p2(wbuf),S(1000000),rs(1000000),ws(-1),b(1){} ~IO(){fwrite(wbuf,1,ws+1,stdout);} il char gc(){return rs==S&&(p1=rbuf,rs=-1,(S=fread(rbuf,1,S+1,stdin)-1)==-1)?(b=0,EOF):(++rs,*p1++);} il void pc(int x){ws==1000000&&(p2=wbuf,ws=-1,fwrite(wbuf,1,1000001,stdout)),++ws,*p2++=x;} il void puts(const char str[]){fwrite(wbuf,1,ws+1,stdout)?(ws=-1):0,fwrite(str,1,strlen(str),stdout);} il void gl(string& s){for(res char ch;(ch=gc())!='\n'&&fok;)s+=ch;} il IO& operator>>(int& x){x=0;res char f=0,ch=gc();while(dsep&&fok)f|=(ch=='-'),ch=gc();while(isdigit(ch))x=(x<<1)+(x<<3)+(ch^48),ch=gc();return x=f?-x:x,*this;} il IO& operator>>(ll& x){x=0;res char f=0,ch=gc();while(dsep&&fok)f|=(ch=='-'),ch=gc();while(isdigit(ch))x=(x<<1)+(x<<3)+(ch^48),ch=gc();return x=f?-x:x,*this;} il IO& operator>>(char& ch){return ch=gc(),*this;} il IO& operator>>(string& s){res char ch=gc();while(sep&&fok)ch=gc();while(!sep&&fok)s+=ch,ch=gc();return *this;} il IO& operator>>(double& x){x=0;res char f=0,ch=gc();double d=0.1;while(dsep&&fok)f|=(ch=='-'),ch=gc();while(isdigit(ch))x=x*10+(ch^48),ch=gc();if(ch=='.')while(isdigit(ch=gc()))x+=d*(ch^48),d*=0.1;return x=f?-x:x,*this;} il IO& operator<<(int x){res char ch[10],i=-1;!x?(pc('0'),0):0,x<0?(pc('-'),x=-x):0;while(x)ch[++i]=x%10+48,x/=10;while(~i)pc(ch[i]),--i;return *this;} il IO& operator<<(ll x){res char ch[20],i=-1;!x?(pc('0'),0):0,x<0?(pc('-'),x=-x):0;while(x)ch[++i]=x%10+48,x/=10;while(~i)pc(ch[i]),--i;return *this;} il IO& operator<<(char ch){return pc(ch),*this;} il IO& operator<<(char str[]){return puts(str),*this;} il IO& operator<<(double x){int y=int(x);*this<<y;x-=y;while(neq(x,int(x)))x*=10;x?*this<<'.'<<int(x):0;return *this;} il operator bool(){return b;} }io; #define N 1001 int n,m,cnt,CNT,d[N],D[N],head[N],HEAD[N]; bool v[N]; struct edge{int to,w,nxt;}e[100001],E[100001]; #define FL(i,x) for(ri i=HEAD[x],to;to=E[i].to,i;i=E[i].nxt) struct cmp{bool operator()(int a,int b){return d[a]>d[b];}}; priority_queue<int,vector<int>,cmp>q; il void add(int x,int y,int w){e[++cnt].to=y;e[cnt].w=w;e[cnt].nxt=head[x];head[x]=cnt;} il void ADD(int x,int y,int w){E[++CNT].to=y;E[CNT].w=w;E[CNT].nxt=HEAD[x];HEAD[x]=CNT;} il void spfa(){ clr(d,126);clr(D,126); d[1]=D[1]=0;q.push(1); int x; while(!q.empty()){ v[x=q.top()]=0;q.pop(); fl(i,x) if(d[x]+e[i].w<d[to]){ d[to]=d[x]+e[i].w; if(!v[to])q.push(to),v[to]=1; } FL(i,x) if(D[x]+E[i].w<D[to]){ D[to]=D[x]+E[i].w; if(!v[to])q.push(to),v[to]=1; } } } int main(){ io>>n>>m; int x,y,w,ans=0; Fur(i,1,m)io>>x>>y>>w,add(x,y,w),ADD(y,x,w); spfa(); Fur(i,2,n)ans+=d[i]+D[i]; io<<ans<<'\n'; }
[USACO07FEB]銀牛派對Silver Cow Party