<王晓东 算法分析与设计 > 线性规划与网络流24习题
其实早有Beyond The Void 大牛做了解题报告，非常犀利，Orz !
网址：http://www.byvoid.com/blog/lpf24-solution/
我从头做了一遍， 感觉受益匪浅。贴出自己代码，仅供参考。思路可参考Beyond牛。
好不容易找到了两个可提交的网站：
南开大学<可惜只有几个题>
http://acm.nankai.edu.cn/problem_search.php?q=24
南京邮电大学< 可惜没有Sepcial Judge >
http://acm.njupt.edu.cn/acmhome/problemList.do?method=show&page=7
飞行员配对方案问题
#include<iostream>
#include<queue>
using namespace std;
const int maxn = 105 ;
int c[maxn][maxn] , prev[maxn] , n , m , S , T ;
int main()
{
cin>>m>>n ;
int x , y , i , j ;
memset(c , 0 ,sizeof(c));
while( (cin>> x >> y ) && ( x>0 && y>0 )) c[x][y] = 1 ;
S = n + 1 , T = n + 2 ;
for( i = 1 ; i<=m ; ++i ) c[S][i] = 1 ;
for( i = m + 1 ; i<=n ; ++ i ) c[i][T] = 1 ;
int maxf = 0 , v , u , w , del;
while(1)
{
queue<int> Q ; Q.push(S) ; memset(prev , -1 ,sizeof(prev));
while( ! Q.empty() )
{
v = Q.front() ; Q.pop() ;
for( u = 1 ; u <= T ; ++ u )
if( c[v][u] && prev[u] == -1 )
prev[u] = v , Q.push(u);
if( prev[T] !=-1 ) break ;
}
if( prev[T] ==-1 ) break ;
del = 200000000 ;
for( u = T , v = prev[T] ; u != S ; u = v , v = prev[v] )
del = min( del , c[v][u] ) ;
for( u = T , v = prev[T] ; u != S ; u = v , v = prev[v] )
c[v][u] -= del , c[u][v] += del ;
maxf += del ;
}
if( maxf == 0 )
cout<<"No Solution!"<<endl ;
else
{
cout<<maxf<<endl ;
for( i = 1 ; i<=m ; ++i )
{
for( j = m + 1 ; j<=n ; ++j )
if( c[j][i] == 1 )
{ cout<<i<<" "<<j<<endl ; break ; }
}
}
return 0 ;
}
#include<iostream>#include<queue>using namespace std ;const int maxn = 110 ;const int maxe = 2*maxn * maxn ; const int inf = 1<<29 ;struct node
{
int x, y , c , next ;
};node e[maxe] ;int n , m , S , T , N , es , hd[maxn] , used[maxn] ; int cur[maxn] , ps[maxn] , dep[maxn] ;void ins(int x ,int y , int c){ e[es].x = x, e[es].y = y , e[es].c = c, e[es].next = hd[x] , hd[x] = es ++ ; e[es].x = y, e[es].y = x , e[es].c = 0, e[es].next = hd[y] , hd[y] = es ++ ;}int dinic(){ int i ,j , v ,u ,k , top , tr , f ,r , maxf = 0;
while(1){ f = r = 0 ; memset(dep , -1 ,sizeof(dep)); ps[r++] = S ; dep[S] = 0 ; while(f!=r){ v = ps[f++] ; for(i = hd[v] ; i!=-1 ; i = e[i].next) if(e[i].c && dep[e[i].y]==-1) dep[e[i].y] = dep[v] + 1 , ps[r++] = e[i].y ; if(dep[T]!=-1) break; 
} if(dep[T]==-1) break; i = S , top = 0 ; memcpy(cur , hd , sizeof(hd)); while(1){ if(i == T){ for(tr = inf , k = 0 ; k < top ; ++k) if(e[ps[k]].c < tr ) tr = e[ps[f = k]].c ; for(k = 0 ; k < top ; ++k) e[ps[k]].c -= tr , e[ps[k]^1].c += tr ; maxf += tr , i = e[ps[top = f]].x ; } for(j = cur[i] ; j!=-1 ; j=cur[i]=e[j].next) if(e[j].c && dep[e[j].y] == dep[i] + 1) break; if(j!=-1){ ps[top++] = j ; i = e[j].y ; } else{ if( 0 == top ) break ; dep[i] = -1 ; i = e[ps[--top]].x ; } } } return maxf ; }int main(){ int i , j , k , Pi , v , sum = 0; scanf("%d%d",&m,&n); es = 0 ; memset(hd , -1 ,sizeof(hd)); S = m + n + 1 ; T = S + 1 ; N = T ; for(i = 1 ; i<=m ; ++i){ scanf("%d",&Pi); sum += Pi ; ins(n + i , T , Pi ); while(1){ if(getchar() == '\n') break; scanf("%d",&v); ins(v , n + i , inf); } } for(i = 1 ; i<=n ; ++i){ scanf("%d",&Pi); ins(S , i , Pi); } int ret = dinic() ; memset(used , 0 ,sizeof(used)); queue<int> Q ; Q.push(S); used[S] = 1 ; while(!Q.empty()){ v = Q.front() ; Q.pop() ; for(i = hd[v] ; i!=-1 ; i=e[i].next) if(e[i].c && !used[e[i].y]) used[e[i].y] = 1 , Q.push(e[i].y); } for(i = n + 1 ; i<=n+m ; ++i) if(!used[i]) printf("%d " , i - n); printf("\n"); for(i = 1 ; i<=n ; ++i) if(!used[i]) printf("%d " , i); printf("\n"); printf("%d\n",sum - ret); return 0 ;}
#include<iostream>#include<string.h>#include<math.h>#define MAXN ( 155 ) using namespace std ;int gh[MAXN][MAXN] , N , E ;int xM[MAXN] , yM[MAXN] , chk[MAXN] ;bool find(int u){ int v ; for(v = 1 ; v <=N ; ++v) if(gh[u][v]&&!chk[v]){ chk[v] = 1 ; if(yM[v]==-1 || find(yM[v])){ yM[v] = u ; xM[u] = v ; return true ; } } return false;}int MaxMatch(){ int i , ret = 0 ; memset(xM, -1 ,sizeof(xM)); memset(yM, -1 ,sizeof(yM)); for(i = 1 ; i<= N ; ++i ) if(xM[i]==-1){ memset(chk , 0 ,sizeof(chk)); if(find(i)) ++ret ; } return ret ;}int main(){ int i ,j , x , y , used[MAXN]; scanf("%d%d",&N,&E); memset(gh , 0 , sizeof(gh)); for(i = 0 ; i<E ; ++i){ scanf("%d%d",&x,&y); gh[x][y] = 1 ; } int ret = MaxMatch(); memset(used , 0 , sizeof(used)); for(i = 1 ; i<=N ; ++i) if(!used[i]){ printf("%d",i) , used[i] = 1 ; for(j = xM[i] ; j!=-1 ; j = xM[j]) if(!used[j]){ printf(" %d",j) ; used[j] = 1 ; } printf("\n"); } printf("%d\n",N - ret); return 0 ;}
魔术球问题
#include<iostream>#include<math.h>using namespace std ;const int maxn = 2*2005 ;const int maxe = 70*70*70*2 ;const int inf = 1<<29 ; struct node{ int x , y , c , next ;};node e[maxe] ;int hd[maxn] , es , S ,T , N ;int cur[maxn] , ps[maxn] , dep[maxn] , next[maxn] , used[maxn];bool reach(int x ,int y){ int tp = (int)sqrt((double)(x+y)); return tp*tp == x+y ; }void ins(int x ,int y ,int c ){ e[es].x = x , e[es].y = y , e[es].c = c , e[es].next = hd[x] , hd[x] = es ++ ; e[es].x = y , e[es].y = x , e[es].c = 0 , e[es].next = hd[y] , hd[y] = es ++ ;}int dinic(){ int f , r , top , i , j , k , tr , maxf = 0 , v , u ; while(1){ f = r = 0 ; memset(dep , -1 , sizeof(dep)); ps[r++] = S , dep[S] = 0 ; while(f!=r){ v = ps[f++] ; for(i = hd[v] ; i!=-1 ; i = e[i].next) if(e[i].c && dep[ e[i].y ]==-1) ps[r++] = e[i].y , dep[e[i].y] = dep[v] + 1 ; if(dep[T]!=-1) break; } if(dep[T] == -1) break; i = S , top = 0 ; memcpy(cur , hd , sizeof(hd)); while(1){ if(i == T){ for(k = 0 , tr = inf ; k < top ; ++ k) if(e[ps[k]].c < tr ) tr = e[ ps[f=k] ].c ; for(k = 0 ; k < top ; ++k) e[ps[k]].c -= tr , e[ps[k]^1].c += tr ; maxf += tr ; i = e[ps[top = f]].x ; } for(j = cur[i] ; j!=-1 ; j = cur[i] = e[cur[i]].next) if(e[j].c && dep[e[j].y] == dep[i] + 1) break; if(cur[i]!=-1){ ps[top++] = j ; i = e[j].y ; } else { if(0 == top ) break; dep[i] = -1 ; i = e[ps[--top]].x ; } } } return maxf ;}int main(){ int n , vcnt , i , j ,k , v ; scanf("%d",&n); printf("%d\n",vcnt=(n*n+2*n-1)/2); S = 2*vcnt + 1 ; T = S + 1 ; N = T ; es = 0 ; memset(hd , -1 ,sizeof(hd)); for(i = 1 ; i<=vcnt ;++i) for(j = 1 ; j<i ; ++j) if(reach(i,j)) ins(i , vcnt + j , 1) ; for(i = 1 ; i<=vcnt ; ++i){ ins(S , i , 1); ins(vcnt + i , T , 1); } int ret = dinic(); memset(next , -1 ,sizeof(next)); memset(used , 0 , sizeof(used)); for(i = 1 ; i<=vcnt ; ++i) for(j = hd[i] ; j!=-1 ; j=e[j].next) if((k = e[j].y) > vcnt && k <=2*vcnt && !e[j].c ){ k -= vcnt ; next[k] = i ; } for(i = 1 ; i<=vcnt ; ++i) if(!used[i]){ if(next[i]==-1) printf("%d \n",i) , used[i] = 1 ; else{ printf("%d",i); used[i] = 1 ; for(j = next[i] ; j!=-1 ; j = next[j]) printf(" %d",j), used[j] = 1 ; printf(" \n"); } } return 0 ;}
圆桌问题
#include<iostream>#include<stdlib.h>#include<algorithm>#include<queue>using namespace std ;const int maxn = 150 + 275 ;const int maxe = maxn * maxn ;const int inf = 1<<28 ;struct node{ int x, y , c , next ;} ;node bf[maxe] ;int hd[maxn] , cur[maxn] , ps[maxn] , dep[maxn] , ne , N ,S ,T ;void ins(int x ,int y , int c ){ bf[ne].x = x , bf[ne].y = y ,bf[ne].c = c , bf[ne].next = hd[x] , hd[x] = ne ++ ; bf[ne].y = y , bf[ne].y = x , bf[ne].c = 0, bf[ne].next =hd[y] , hd[y] = ne ++ ;}int maxflow(){ int tr , res = 0 ; int i , j , k , f , r, top ; while(1){ memset(dep , -1 ,sizeof(dep)) ; for( f = dep[S] = 0 , ps[0] = S , r = 1 ; f!=r ; ) for( i = ps[f++] , j = hd[i] ; j !=-1 ; j = bf[j].next ) if( bf[j].c && -1 == dep[ k = bf[j].y ] ) { dep[k] = dep[i] + 1 , ps[r++] = k ; if( k == T ) { f = r ; break ; } } if( -1 == dep[T] ) break ; memcpy(cur , hd , N * sizeof(int) ) ; for( i = S , top = 0 ; ; ){ if( i == T ) { for( k = 0 , tr = inf ; k<top ; ++k ) if( bf[ ps[k] ].c < tr ) tr = bf[ ps[f = k] ].c ; for( k = 0 ; k<top ; ++k ) bf[ps[k]].c -= tr , bf[ps[k]^1].c += tr ; res += tr ; i = bf[ ps[top = f] ].x ; } for( j = cur[i] ; cur[i]!=-1 ; j = cur[i] = bf[cur[i]].next ) if( bf[j].c && dep[i] + 1 == dep[ bf[j].y ] ) break ; if( cur[i]!=-1 ) { ps[top ++ ] = cur[i] ; i = bf[ cur[i] ].y ; } else { if( top == 0 ) break ; dep[i] = -3 , i = bf[ ps[--top] ].x ; } } } return res ; } int main(){ int n , m , r , c , i , j , sup = 0, dmd = 0 ; cin>>n>>m ; N = n + m + 2 ; S = n + m + 1 ; T = n + m + 2 ; memset(hd , -1 , sizeof(hd)) ; ne = 0 ; for( i = 1 ; i<=n; ++i ) { cin>>r ; ins(S , i , r ) ; sup += r ; } for( i = 1 ; i<=m ;++i ) { cin>>c ; ins(n + i , T , c) ; dmd += c ; } for( i = 1 ; i<=n ; ++i ) for( j = m; j>=1; --j ) ins(i , n + j , 1); int ret = maxflow() ; if( ret == sup ) cout<<"1"<<endl ; else cout<<"0"<<endl ; for( i = 1 ; i<=n ; ++ i ) { for( j = hd[i] ; j!=-1 ; j = bf[j].next ) if( bf[j].c == 0 ) cout<<bf[j].y - n <<" "; cout<<endl ; } return 0 ;}
最长递增子序列问题
#include<iostream>using namespace std ;const int SIZE = 501;const int maxn = 2*SIZE + 5 ;const int maxe = maxn * maxn ;const int inf = 1<<29 ;int opt[SIZE] , a[SIZE] , n , ans ;struct node{ int x ,y , c , next; };node e[maxe] ;int es, hd[maxn] , S , T , N ;int cur[maxn] , ps[maxn] , dep[maxn] ;void ins(int x ,int y ,int c){ e[es].x = x, e[es].y = y ,e[es].c = c, e[es].next = hd[x] , hd[x] = es ++ ; e[es].x = y, e[es].y = x ,e[es].c = 0, e[es].next = hd[y] , hd[y] = es ++ ;}int dinic(){ int i ,j , u ,v , k , tr , f, r , maxf = 0 , top ; while(1) { f = r = 0 ; memset(dep , -1 ,sizeof(dep)); ps[r++] = S , dep[S] = 0 ; while(f!=r) { v = ps[f++] ; for(i = hd[v] ; i !=-1 ; i=e[i].next) { u = e[i].y ; if(e[i].c && dep[u] == -1) dep[u] = dep[v] + 1 , ps[r++] = u ; } if( dep[T] !=-1) break; } if( dep[T] == -1) break; i = S ,top = 0 ; memcpy(cur , hd, sizeof(hd)); while(1) { if( i == T){ for(k = 0 , tr = inf ; k < top ; ++ k) if(e[ps[k]].c < tr ) tr = e[ps[k]].c , f = k ; for(k = 0 ; k < top ; ++ k ) e[ps[k]].c -= tr , e[ps[k]^1].c += tr ; maxf += tr , i = e[ ps[top = f] ].x ; } for(j = cur[i] ; j!=-1 ; j = cur[i] = e[j].next) if(e[j].c && dep[i]+1 == dep[ e[j].y ]) break; if(j !=-1 ){ ps[top ++ ] = j , i = e[j].y ; } else{ if(0 == top ) break; dep[i] = -1 , i = e[ps[--top]].x ; } } } return maxf ; } inline int P(int i , int t){ return 2*(i-1)+ t + 1 ;}void ans_1(){ int i ,j ; opt[1] = 1 ; for(i=2; i<=n ; ++i){ opt[i] = 1 ; for(j = 1 ; j<i ; ++j) if(a[i] >= a[j]) opt[i] = max(opt[i] , opt[j] + 1) ; } ans = 0 ; for(i = 1 ; i<=n ; ++i) ans = max(ans , opt[i]); printf("%d\n",ans);}void ans_2(){ int i , j ; es = 0 ; memset(hd , -1 , sizeof(hd)); S = 2*n + 1 , T = 2*n+2 , N = T ; for(i = 1; i<=n ; ++i){ ins(P(i , 0) , P(i , 1) , 1); if(opt[i] == ans) ins(S , P(i,0) , 1); if(opt[i] == 1) ins( P(i,1) , T , 1 ); } for(i = 2; i<=n ; ++i) for(j = 1 ; j<i ; ++j) if(a[i]>=a[j] && opt[i] == opt[j] + 1) ins( P(i , 1) , P(j , 0 ) , 1); int ret = dinic(); printf("%d\n",ret);}void ans_3(){ int i , j ; if(ans == 1) { printf("%d\n",n) ; return ; } es = 0 ; memset(hd , -1 ,sizeof(hd)); S = 2*n + 1 , T = 2*n + 2 ; N = T ; ins(P(1,0) , P(1,1) , inf) ; ins(P(n,0) , P(n,1) , inf) ; ins(P(1,1), T,inf); if(opt[n] == ans) ins(S , P(n,0) , inf ) ; for(i = 2 ; i <=n ; ++i){ ins(P(i,0),P(i,1),1); if(opt[i] == ans) ins(S,P(i,0),1); if(opt[i] == 1) ins(P(i,1),T ,1); } for(i = 2; i<=n ; ++i) for(j = 1 ; j<i ; ++j) if(a[i]>=a[j] && opt[i] == opt[j] + 1) ins( P(i , 1) , P(j , 0 ) , 1); int ret = dinic(); printf("%d\n",ret);}int main(){ int i; scanf("%d",&n); for(i = 1 ; i<=n ; ++i) scanf("%d",&a[i]); ans_1(); ans_2(); ans_3(); return 0 ;}
试题库问题
#include<iostream>#include<queue>#include<stdlib.h>using namespace std ; const int MAXN = 1030;const int maxint = 200000000 ;int c[ MAXN ][ MAXN ] ;int pbm , kind , S , T , N , need; int prev[ MAXN ] ;bool maxflow(){ int maxf = 0 , v , u , w ,del ; while(1) { queue<int> Q ; Q.push(S); memset(prev , -1 , sizeof(prev)); while(! Q.empty() ) { v = Q.front() ; Q.pop() ; for( u = 1 ; u <= N ; ++ u ) if( c[v][u] && prev[u] == -1 ) prev[u] = v , Q.push(u); if( prev[T] > 0 ) break ; } if( prev[T] < 0 ) break ; del = maxint ; for( v = T , u = prev[v] ; v != S ; v = u , u = prev[u] ) if( del > c[u][v] ) del = c[u][v]; for( v = T , u = prev[v] ; v != S ; v = u , u = prev[u] ) c[u][v] -= del , c[v][u] += del ; maxf += del ; } return maxf == need ;}void solve(){ if( ! maxflow() ) { cout<<"No Solution!"<<endl ; return ; } int i , j ; for( i = pbm + 1 ; i <= pbm + kind ; ++ i ) { cout<<i - pbm <<":" ; for( j = 1 ; j<=pbm ; ++ j ) if( c[i][j] == 1 ) cout<<" "<<j ; cout<<endl ; }} void read(){ cin>>kind>>pbm ; memset(c , 0 ,sizeof(c)); S = pbm + kind + 1 ; N = T = pbm + kind + 2 ; need = 0 ; int i , j , cnt , v ; for( i = 1 ; i <= kind ; ++ i ) { cin>>c[ pbm + i ][T] ; need += c[pbm + i][T] ; } for( i = 1 ; i <= pbm ; ++i ) { c[ S ][ i ] = 1 ; cin>> cnt ; for( j = 1 ; j<=cnt ; ++j ) { cin>>v ; c[i][ pbm + v] = 1; } }}int main(){ read(); solve(); return 0 ;}
机器人路径规划问题
方格取数问题
#include<iostream>using namespace std ; const int grid = 30; const int maxn = grid * grid ;const int maxe = maxn * 10 ;const int inf = 200000000 ; int mat[grid][grid] ; int dx[4]={1,0 ,-1,0} , dy[4]={0,1,0,-1}; struct node{ int x , y , c , next ;} ; struct network{ int S , T , N , es , hd[maxn] ; node e[maxe] ; int ps[maxn] , cur[maxn] , dep[maxn] ; void init(int vS , int vT ,int vN) ; void ins(int x,int y ,int c) ; int dinic() ; } ; void network::init(int vS ,int vT ,int vN){ S = vS , T = vT , N = vN ; es = 0 ; memset(hd , -1 ,sizeof(hd));}void network::ins(int x,int y ,int c){ e[es].x = x , e[es].y = y , e[es].c = c, e[es].next = hd[x] , hd[x] = es ++ ; e[es].x = y , e[es].y = x , e[es].c = 0, e[es].next = hd[y] , hd[y] = es ++ ;}int network::dinic(){ int u , v , f , r , i ,j, k , tr , top , maxf = 0 ; while(1) { f = r = 0 ; memset(dep , -1 ,sizeof(dep)); ps[r++] = S , dep[S] = 0 ; while(f != r ) { v = ps[f++] ; for(i = hd[v] ; i !=-1 ; i = e[i].next){ u = e[i].y ; if(e[i].c && dep[u]==-1 ) dep[u] = dep[v] + 1 , ps[r++] = u ; } if(dep[T]!=-1) break; } if(dep[T]==-1) break ; i = S , top = 0 ; memcpy(cur,hd,sizeof(hd)); while(1) { if(i == T) { for(k = 0 , tr = inf ; k < top ; ++ k) if( tr > e[ps[k]].c ) tr = e[ps[k]].c , f = k ; for(k = 0 ; k < top ; ++k) e[ps[k]].c -= tr , e[ps[k]^1].c += tr ; maxf += tr , i = e[ps[top = f]].x ; } for(j = cur[i] ; j!=-1 ; j = cur[i] = e[j].next) if(e[j].c && dep[e[j].y] == dep[i] + 1) break; if(j!=-1) ps[top++] = j , i = e[j].y ; else { if( 0 == top ) break ; // The only end for while(1); dep[i]=-1 , i = e[ps[--top]].x ; } } } return maxf ;}bool out(int x ,int y , int n ,int m){ return x < 0 || y < 0 || x >= n || y >=m ; }int main(){ int n , m , S , T , N , x , tot = 0 ,i , j , k ; cin>>n>>m ; network gh ; S = n * m + 1 ; T = S + 1 ; N = T ; gh.init(S , T , N) ; for(i = 0 ; i<n ; ++ i) for(j = 0 ; j<m ;++j) { cin>>mat[i][j] ; tot += mat[i][j] ; } for(i = 0 ; i < n ; ++ i ) for(j = 0 ; j < m ; ++ j ) if((i + j) % 2 == 0 ) gh.ins(S , i*m+j+1 , mat[i][j]) ; else gh.ins(i*m+j+1 , T , mat[i][j]) ; for(i = 0 ; i<n ; ++i) for(j = 0 ; j<m ; ++j) if((i+j)%2 == 0 ) // set X for(k = 0 ; k < 4 ; ++k) { int cx = i + dx[k] , cy = j + dy[k] ; if(out(cx, cy , n , m) ||(cx + cy)%2 == 0 ) continue ; gh.ins(i * m + j + 1 , cx * m + cy + 1 , inf ) ; } cout<<tot-gh.dinic()<<endl ; //while(getchar()); return 0 ;}
餐巾计划问题
航空路线问题
#include<iostream>#include<stdio.h>#include<stdlib.h>#include<queue>#include<vector>#include<string.h>using namespace std ; const int maxn = 110 ;const int maxe = maxn * maxn ;const int inf = 1<<28 ;struct node { int v , c , cost , next ;} ;struct network{ int S ,T , N , hd[maxn] , es ; int vis[maxn] , prev[maxn] , pos[maxn] , d[maxn] ; node e[maxe] ; void init(int vS , int vT , int vN ) ; void ins(int u ,int v ,int c ,int cost) ; bool spfa() ; int mcmf() ;} ;void network::init(int vS ,int vT ,int vN){ S = vS , T =vT , N = vN ; es = 0 , memset(hd , -1,sizeof(hd)) ;}void network::ins(int u ,int v,int c,int cost){ e[es].v = v , e[es].c = c, e[es].cost =cost ,e[es].next = hd[u] , hd[u] = es ++ ; e[es].v = u , e[es].c = 0, e[es].cost =-cost,e[es].next = hd[v] , hd[v] = es ++ ; }bool network::spfa(){ int u , v , i ; queue<int> Q ; for( i = 1 ; i<=N ; ++i ) vis[i] = 0 , prev[i]=-1 ,d[i] = inf ; vis[S] = 1 , Q.push(S) , d[S] = 0 ; while(!Q.empty() ) { v = Q.front() ; Q.pop() ; vis[v] = 0 ; for( i = hd[v] ; i!=-1 ; i=e[i].next ) { u = e[i].v ; if( e[i].c && d[u] > d[v] + e[i].cost ) { d[u] = d[v] + e[i].cost ; prev[u] = v ; pos[u]=i ; if(!vis[u]) vis[u]=1 ,Q.push(u) ; } } } return prev[T]!=-1 ;}int network::mcmf(){ int take = 0 , del , u ; while(spfa()) { del = inf ; for( u = T ; u!=S ; u=prev[u] ) del = min( del , e[pos[u]].c ) ; for( u = T ; u!=S ; u=prev[u] ) e[pos[u]].c -= del , e[pos[u]^1].c += del ; take += del * d[T] ; } return take ;}struct city { char cy[41] ; } ; city vec[100] ;int city_cnt , route_cnt ; int find(char * s ){ int i ; for( i = 1 ; i<=city_cnt ; ++ i) if( !strcmp(s , vec[i].cy) ) return i ;}void solve(){ int i , j , vs , vt , S , T , N , ret , x, y; char fst[41] , sec[41] ; network gh ; cin>>city_cnt>>route_cnt ; N = 2*city_cnt , S = 1 , T = 2*city_cnt ; gh.init(S , T , N ) ; gh.ins(1 , 2 , 2 , -1 ) ; gh.ins(T - 1 , T , 2 , -1 ) ; for( i = 2 ; i<city_cnt ; ++ i ) gh.ins(2*i - 1 , 2*i , 1 , -1 ) ; for( i = 1 ; i <= city_cnt ; ++ i ) cin>>vec[i].cy ; for( i = 1 ; i<=route_cnt ; ++ i ) { cin>>fst>>sec ; vs = find(fst) ; vt = find(sec) ; if( vs > vt ) swap(vs , vt) ; gh.ins(2*vs , 2*vt - 1 , 1 , 0 ) ; } ret = gh.mcmf() + 2 ; cout<<-ret<<endl ;}int main(){ solve() ; return 0 ;}
软件补丁问题
本题书上描述有误：
原文：
补丁pi将修复某些错误而同时加入某些错误，设错误集合Fi-、Fi+，使用过补丁pi之后，Fi-中的任何错误都不会在软件中出现，而软件将包含Fi+中的所有错误， 同样Fi-、Fi+交集为空。另外，使用每个补丁都要耗一定的时间（即补丁程序的运行时间）。
错误原因：
王晓东书中将F1[]与F2[]正好搞反了。 害的我查了半天错误。
#include<iostream>#include<queue>#define shl(x,i) ((x)<<(i))#define shr(x,i) ((x)>>(i))#define bit(x,i) ((x)&shl(1,i) ? 1:0)#define rev(x,i) ((x)^(shl(1,i)-1) )using namespace std ;const int maxn = (1<<20) + 5 ;const int ms = 101 ;const int inf = 1<<29 ;int d[maxn] , t[ms] , b1[ms] , b2[ms] , f1[ms] , f2[ms];bool vis[maxn] ;int scnt , n ;inline int getp(int a ,int i ){ if( ((a&b1[i]) == b1[i]) && ((a&b2[i]) == 0) ) return (a|f1[i])&rev(f2[i],n) ; else return -1 ;}int work(){ int i , j ,v , u , S , T; queue<int> Q ; for(i = 0 ; i<(1<<n) ; ++i) d[i] = inf , vis[i] = 0 ; S = (1<<n)-1 ; T = 0 ; d[S] = 0 , vis[S] = 1 , Q.push(S); while(!Q.empty()){ v = Q.front() ; Q.pop() ; vis[v] = 0 ; for(i = 0 ; i<scnt ; ++i) if((u = getp(v , i))!=-1 && d[u] > d[v] + t[i] ){ d[u] = d[v] + t[i] ; if(vis[u] == 0){ vis[u] = 1 ; Q.push(u); } } } return d[T] == inf ? 0 : d[T] ;}int main(){ int i , j , ret ; char B[25],F[25] ; scanf("%d%d",&n,&scnt); for(i = 0 ; i<scnt ;++i){ b1[i]=b2[i]=f1[i]=f2[i]=0 ; scanf("%d%s%s",&t[i],B,F); for(j = 0 ; j<n ; ++j){ if(B[j]=='+') b1[i] += 1<<j ; // need if(B[j]=='-') b2[i] += 1<<j ; // not need if(F[j]=='+') f1[i] += 1<<j ; // repair if(F[j]=='-') f2[i] += 1<<j ; // produce } } ret = work(); printf("%d\n",ret); return 0 ;}
星际转移问题
#include<iostream>#include<queue>using namespace std ;const int inf = 1<<29 ;const int MaxT = 1000 ;const int MaxN = 25 ;const int MaxM = 20 ;const int MaxK = 55 ;const int maxn = (MaxN + 2)*( MaxT + 2 ) ;const int maxe = 3*(MaxT + 1)*(MaxN + MaxM + 2) ;struct node{ int x, y , c, next ;};node e[maxe] ;int es , hd[maxn] , S , T , N , maxf ; int n , m , K ; int pos[MaxN][MaxN] , circle[MaxN] , H[MaxN] ;int used[MaxN] , chk[MaxN][MaxN];int cur[maxn] , ps[maxn] , dep[maxn] ;void ins(int x,int y ,int c){ e[es].x = x, e[es].y = y ,e[es].c = c , e[es].next = hd[x] , hd[x] = es ++ ; e[es].x = y ,e[es].y = x ,e[es].c = 0 , e[es].next = hd[y] , hd[y] = es ++ ;}int dinic(){ int i ,j , v ,u ,k , top , tr , f ,r ;; while(1){ f = r = 0 ; memset(dep , -1 ,sizeof(dep)); ps[r++] = S ; dep[S] = 0 ; while(f!=r){ v = ps[f++] ; for(i = hd[v] ; i!=-1 ; i = e[i].next) if(e[i].c && dep[e[i].y]==-1) dep[e[i].y] = dep[v] + 1 , ps[r++] = e[i].y ; if(dep[T]!=-1) break; } if(dep[T]==-1) break; i = S , top = 0 ; memcpy(cur , hd , sizeof(hd)); while(1){ if(i == T){ for(tr = inf , k = 0 ; k < top ; ++k) if(e[ps[k]].c < tr ) tr = e[ps[f = k]].c ; for(k = 0 ; k < top ; ++k) e[ps[k]].c -= tr , e[ps[k]^1].c += tr ; maxf += tr , i = e[ps[top = f]].x ; } for(j = cur[i] ; j!=-1 ; j=cur[i]=e[j].next) if(e[j].c && dep[e[j].y] == dep[i] + 1) break; if(j!=-1){ ps[top++] = j ; i = e[j].y ; } else{ if( 0 == top ) break ; dep[i] = -1 ; i = e[ps[--top]].x ; } } } return maxf ; }inline int P(int ti ,int vi){ return ti * (n + 2) + vi + 1;}int no_answer(){ int i , j , v ; memset(chk , 0 ,sizeof(chk)); memset(used, 0 ,sizeof(used)); for(i = 0 ; i < m ; ++i) for(j = 0 ; j < circle[i] ; ++j) chk[pos[i][j]][pos[i][j+1]] = 1 ; queue<int> Q ; Q.push(0) ; used[0] = 1 ; while(!Q.empty()){ v = Q.front() ; Q.pop() ; for( i = 0 ; i < n + 2 ; ++i) if(chk[v][i]&&!used[i]) used[i] = 1 , Q.push(i) ; if(used[n+1] == 1) break ; } return used[n+1]==0 ;}int work(){ int v , u , i , j , t ; es = 0 ; memset(hd , -1 ,sizeof(hd)); scanf("%d%d%d",&n,&m,&K); // n station , m boat , K people for(i = 0 ; i < m ; ++i){ scanf("%d%d",&H[i],&circle[i]); for(j = 0 ; j < circle[i] ; ++j){ scanf("%d",&pos[i][j]); if( pos[i][j] == -1 ) pos[i][j] = n + 1 ; } pos[i][j] = pos[i][0] ; } if(no_answer()) return 0 ; S = maxn - 3; T = S + 1 ; ins(S , P(0,0) , inf) ; ins(P(0,n+1),T ,inf) ; for(t = 1 , maxf = 0 ; maxf < K ; ++t){ ins(S , P(t,0) , inf ) ; ins(P(t,n+1),T ,inf) ; for(i = 0 ; i < n + 2 ; ++ i) ins( P(t-1,i) , P(t,i) , inf) ; for(i = 0 ; i < m ; ++ i){ v = pos[i][(t-1)%circle[i]] ; u = pos[i][t%circle[i]] ; ins( P(t-1,v), P(t,u) , H[i]) ; } dinic() ; } return t - 1 ; }int main(){ printf("%d\n",work()) ; return 0 ;}
孤岛营救问题
#include<iostream>#include<stdlib.h>#include<queue>#include<memory.h>#define WALL 0#define YES (-1) using namespace std ; const int maxkey = 11 ;const int grid = 11 ; struct node{ int x , y , key ; node() {} node(int vX ,int vY ,int vKey): x(vX) , y(vY) , key(vKey) {} } ; int dx[]={1,0,-1,0} , dy[]={0,1,0,-1} ; int used[ grid * grid ][ (1<<maxkey) ] ;int bd[grid][grid] ; int nbr[grid * grid][4] ;int n , m , K , keycnt , P ;inline int hash(int x ,int y){ return x * m + y ;}inline int out(int x ,int y){ return x<0 || y<0 || x>=n || y>=m ;}inline int fdir(int x1 ,int y1 , int x2 ,int y2){ for(int i = 0 ; i<4 ; ++i) if( (x1 + dx[i] == x2 ) && (y1 + dy[i] == y2) ) return i ;}inline bool End(node cur){ return cur.x == n-1 && cur.y == m-1 ;}int can(){ memset(used , -1 ,sizeof(used)); int i , j , t ; queue<node> Q ; node cur(0 , 0 , 0 ) , son ; if(bd[0][0] !=0 ) cur.key |= (1<<bd[0][0]) ; used[hash(cur.x,cur.y)][cur.key] = 0 ; Q.push(cur) ; while(! Q.empty()) { cur = Q.front() ; Q.pop() ; for(i = 0 ; i<4 ; ++i) { son=node(cur.x + dx[i] , cur.y+dy[i] , cur.key ); t = nbr[ hash(cur.x , cur.y) ][ i ] ; if( out(son.x,son.y) || t == WALL || ( t > 0 && !( cur.key & (1<<t )) ) ) continue ; if(bd[son.x][son.y]) son.key |= bd[son.x][son.y] ; if( used[hash(son.x,son.y)][son.key] != -1) continue ; t = used[hash(son.x,son.y)][son.key] = used[hash(cur.x,cur.y)][cur.key] + 1 ; if( End(son) ) return t ; Q.push(son); } } return -1 ;}int main(){ int i , x1 , y1 , x2 , y2 , gi ,j, keycnt , keyid; memset(bd , 0 , sizeof(bd)); memset(nbr, YES , sizeof(nbr)); cin>>n>>m>>P ; cin>>K ; for(i = 0 ; i<K ; ++i) { cin>>x1>>y1>>x2>>y2>>gi ; -- x1 , -- y1 , -- x2, -- y2 ; j = fdir(x1, y1,x2,y2); nbr[ x1*m + y1 ][j] = gi ; j = fdir(x2, y2,x1,y1); nbr[ x2*m + y2 ][j] = gi ; } cin>>keycnt ; for(i = 0 ; i<keycnt ; ++i) { cin>>x1>>y1>>keyid ; -- x1 , -- y1 ; bd[x1][y1] |= (1<<keyid) ; } int take = can() ; cout<< take <<endl ; return 0 ;}
汽车加油行驶问题
#include<iostream>#include<queue>using namespace std ; const int grid = 105 ; const int maxn = grid * grid * 11 ;const int maxe = 4 * maxn ; const int inf = 1<<30 ;struct node{ int y , c, next;} ;int hd[maxn] , S ,T , Vcnt, es ;node e[maxe] ;int N , K , A , B ,C , bd[grid][grid];int dx[4] = {1,0,-1,0} , dy[4] = {0,1,0,-1} , oil[4] ; int hash(int x , int y ,int t ){ return t*N*N + x*N + y + 1 ;}void ins(int x , int y , int w){ e[es].y = y , e[es].c = w, e[es].next = hd[x] , hd[x] = es ++ ;}bool out(int x,int y){ return x < 0 || y < 0 || x>=N || y>=N ; } void readln(){ int i , j , t , u , x , y , cost; cin>>N>>K>>A>>B>>C ; for(i = 0 ; i < N ; ++i) for( j = 0 ; j < N ; ++j) cin>>bd[i][j] ; S = hash(0,0,K) , T = hash(N-1,N-1,K) + 1 , Vcnt = T ; es = 0 ; memset(hd , -1 , sizeof(hd)) ; oil[0]=0 , oil[1] = 0 , oil[2] = B , oil[3] = B ; for(i = 0 ;i < N ; ++i) for(j = 0 ; j < N ; ++j) for(t = 0 ; t <= K ; ++ t) { if( bd[i][j] && t < K) { ins( hash(i , j ,t ) , hash(i ,j , K ) , A ) ; continue ; } if( t == 0 ) { ins( hash(i, j , 0 ) , hash(i ,j , K) , C + A) ; continue ; } for(u = 0 ; u < 4 ; ++ u) { x = i + dx[u] , y = j + dy[u] ; if( out(x ,y ) ) continue ; ins( hash(i , j , t ) , hash(x ,y , t -1 ) , oil[u] ) ; } } for(i = 0 ; i <= K ; ++i) ins( hash(N-1,N-1,i) , T , 0 );}int dist[maxn] , vis[maxn]; int SPFA(){ int i , j ,v , u; queue<int> Q ; for(i = 1 ; i <= Vcnt ; ++i) dist[i] = inf , vis[i] = 0 ; Q.push(S) ; dist[S] = 0 ; vis[S] = 1 ; while(!Q.empty()) { v = Q.front() ; Q.pop() ; vis[v] = 0 ; for(i = hd[v] ; i!=-1 ; i = e[i].next) { u = e[i].y ; if(dist[u] > dist[v] + e[i].c ) { dist[u] = dist[v] + e[i].c ; if(vis[u]==0) vis[u] = 1 , Q.push(u) ; } } } return dist[T] ;}int main(){ readln(); int ret = SPFA(); cout<<ret<<endl; return 0 ;}
数字梯形问题
#include<iostream>#include<queue>using namespace std ;const int grid = 21 ;const int maxn = 2 * (grid +grid)* grid + 5 ;const int maxe = 8 * maxn ;const int inf = 1<<28;struct node{ int y , c , cost , next ;} ;int S ,T , N , hd[maxn] , es ;node e[maxe] ;int vis[maxn] , d[maxn] , pos[maxn] , prev[maxn] ; int n , m , data[grid][grid] , cnt[grid][grid] ;inline int P(int x,int y ,int t) { return 2*cnt[x][y] + t ; } void readln(){ int i , j , CH = 1 ; cin>>m>>n ; for(i = 1 ; i<= n ; ++i ) for(j = 1 ; j <= m+i-1 ; ++j) cin>>data[i][j] , cnt[i][j] = CH++ ;}void init(){ S = maxn - 2 , T = maxn - 1 , N = T ; es = 0 ; memset(hd, -1 ,sizeof(hd));}void ins(int x,int y ,int c,int cost ){ e[es].y = y, e[es].c = c, e[es].cost = cost, e[es].next = hd[x] , hd[x] = es ++ ; e[es].y = x, e[es].c = 0, e[es].cost = -cost,e[es].next = hd[y] , hd[y] = es ++ ;}bool SPFA(){ int i , v ,u ; queue<int> Q ; for(i = 1; i <=N ; ++i) d[i] = inf , vis[i] = 0 , prev[i] = -1 ; Q.push( S ); d[S] = 0 ; vis[S] = 1 ; while(!Q.empty()) { v = Q.front() ; Q.pop() ; vis[v]=0 ; for(i = hd[v] ; i!=-1 ; i = e[i].next) { u = e[i].y ; if( e[i].c && d[u] > d[v] + e[i].cost) { d[u] = d[v] + e[i].cost ; prev[u] = v ; pos[u] = i ; if( vis[u] == 0) vis[u] = 1 , Q.push(u); } } } return prev[T]!=-1;}int MCMF(){ int res = 0 , del , u ; while(SPFA()) { del = inf ; for(u = T ; u!=S ; u = prev[u] ) if(del > e[pos[u]].c ) del = e[pos[u]].c; for(u = T ; u!=S ; u= prev[u]) e[pos[u]].c -= del , e[pos[u]^1].c += del ; res += del * d[T] ; } return res ; }void ans_1(){ int i , j; init(); for(i = 1 ; i<=m ; ++i) ins( S , P(1 ,i ,0) , 1 , 0 ); for(i = 1 ; i<=n+m-1 ; ++i) { ins( P(n , i , 1 ) , T , 1 , 0 ); ins( P(n , i , 0 ) , P(n , i , 1 ) , 1 , -data[n][i]); } for(i = 1 ; i<=n-1 ; ++i) for(j = 1 ; j<=m+i-1; ++j) { ins( P(i,j,0) , P(i,j,1) , 1 , -data[i][j]); ins( P(i,j,1) , P(i+1,j,0) , 1 , 0 ); ins( P(i,j,1) , P(i+1,j+1,0) , 1 , 0 ); } int ret = MCMF(); cout<< - ret<<endl;}void ans_2(){ int i , j; init(); for(i = 1 ; i<=m ; ++i) ins(S , cnt[1][i] , 1 , -data[1][i]) ; for(i = 1 ; i<=n+m-1 ;++i) ins(cnt[n][i] , T , m , 0); for(i = 1 ; i<=n-1; ++i ) for(j = 1 ; j<=m+i-1 ; ++j) { ins(cnt[i][j] , cnt[i+1][j] , 1 , - data[i+1][j] ) ; ins(cnt[i][j] , cnt[i+1][j+1] , 1 , - data[i+1][j+1]); } int ret = MCMF(); cout<< - ret<<endl; }void ans_3(){ int i , j ; init(); for(i = 1 ; i<=m ; ++i) ins( S , P(1 ,i ,0) , 1 , 0 ); for(i = 1 ; i<=n+m-1 ; ++i) { ins( P(n , i , 1 ) , T , m , 0 ); ins( P(n , i , 0 ) , P(n , i , 1 ) , m , -data[n][i]); } for(i = 1 ; i<=n-1 ; ++i) for(j = 1 ; j<=m+i-1; ++j) { ins( P(i,j,0) , P(i,j,1) , m , -data[i][j]); ins( P(i,j,1) , P(i+1,j,0) , m , 0 ); ins( P(i,j,1) , P(i+1,j+1,0) , m , 0 ); } int ret = MCMF(); cout<<-ret<<endl;}int main(){ readln(); ans_1(); ans_2(); ans_3(); return 0 ;}
运输问题
#include<iostream>#include<stdio.h>#include<stdlib.h>#include<queue>using namespace std ; const int maxn = 210 ;const int maxe = maxn * maxn ;const int inf = 1<<28 ;struct node { int v , c , cost , next ;} ;struct network{ int S ,T , N , hd[maxn] , es ; int vis[maxn] , prev[maxn] , pos[maxn] , d[maxn] ; node e[maxe] ; void init(int vS , int vT , int vN ) ; void ins(int u ,int v ,int c ,int cost) ; bool spfa() ; int mcmf() ;} ;void network::init(int vS ,int vT ,int vN){ S = vS , T =vT , N = vN ; es = 0 , memset(hd , -1,sizeof(hd)) ;}void network::ins(int u ,int v,int c,int cost){ e[es].v = v , e[es].c = c, e[es].cost =cost ,e[es].next = hd[u] , hd[u] = es ++ ; e[es].v = u , e[es].c = 0, e[es].cost =-cost,e[es].next = hd[v] , hd[v] = es ++ ; }bool network::spfa(){ int u , v , i ; queue<int> Q ; for( i = 1 ; i<=N ; ++i ) vis[i] = 0 , prev[i]=-1 ,d[i] = inf ; vis[S] = 1 , Q.push(S) , d[S] = 0 ; while(!Q.empty() ) { v = Q.front() ; Q.pop() ; vis[v] = 0 ; for( i = hd[v] ; i!=-1 ; i=e[i].next ) { u = e[i].v ; if( e[i].c && d[u] > d[v] + e[i].cost ) { d[u] = d[v] + e[i].cost ; prev[u] = v ; pos[u]=i ; if(!vis[u]) vis[u]=1 ,Q.push(u) ; } } } return prev[T]!=-1 ;}int network::mcmf(){ int take = 0 , del , u ; while(spfa()) { del = inf ; for( u = T ; u!=S ; u=prev[u] ) del = min( del , e[pos[u]].c ) ; for( u = T ; u!=S ; u=prev[u] ) e[pos[u]].c -= del , e[pos[u]^1].c += del ; take += del * d[T] ; } return take ;}int main(){ network gh ; int n , m , S, T , N , i , j , sup[maxn] , dmd[maxn] , cost[maxn][maxn] ; cin>>m>>n ; S = n + m + 1 , T = S + 1 , N = T ; gh.init(S , T , N) ; for( i = 1 ; i<=m ; ++i ) { cin>>sup[i] ; gh.ins(S , i , sup[i] , 0) ; } for( i = 1 ; i <= n ; ++i ) { cin>>dmd[i] ; gh.ins(m + i ,T , dmd[i], 0) ; } for( i = 1 ; i<=m ; ++i ) for( j = 1 ; j<=n ; ++j) { cin>>cost[i][j] ; gh.ins(i , j + m , inf , cost[i][j]) ; } int ret = gh.mcmf() ; cout<<ret<<endl ; gh.init(S, T , N); for( i = 1 ; i<=m ; ++i ) gh.ins(S , i , sup[i], 0); for( i = 1 ; i<=n ; ++i ) gh.ins(m + i ,T , dmd[i] , 0) ; for( i = 1 ; i<=m ;++i) for( j = 1; j<=n ;++j ) gh.ins(i , m + j , inf , - cost[i][j] ) ; ret = gh.mcmf() ; cout<<-ret<<endl ; return 0 ; }
分配问题
#include<iostream>#include<stdio.h>#include<stdlib.h>#include<queue>using namespace std ; const int maxn = 200 ; const int maxe = maxn * maxn ; const int inf = 1<<28 ;struct node{ int v , c , cost , next ; } ;struct network{ int S , T , hd[maxn] , es , N ; int vis[maxn] , d[maxn] , pos[maxn] , prev[maxn] ; node e[maxe] ; void init(int vS , int vT , int vcnt); void ins(int u , int v ,int c ,int cost) ; bool spfa() ; int mcmf() ; } ; void network::init(int vS , int vT , int vcnt ){ S = vS ; T = vT ; N = vcnt ; es = 0 ; memset(hd , -1 ,sizeof(hd));}void network::ins(int u ,int v,int c ,int cost){ e[es].v = v , e[es].c = c , e[es].cost = cost , e[es].next = hd[u] ; hd[u] = es ++ ; e[es].v = u , e[es].c = 0 , e[es].cost = -cost, e[es].next = hd[v] ; hd[v] = es ++ ;}bool network::spfa(){ queue<int> Q ; int u , v , i ; for( i = 1 ; i<=N ; ++i ) vis[i] = 0 , d[i] = inf , prev[i] = -1 ; vis[S] = 1 , Q.push(S) , d[S] = 0 ; while(! Q.empty()) { v = Q.front() ; Q.pop() ; vis[v] = 0 ; for( i = hd[v] ; i!=-1 ; i = e[i].next ) { u = e[i].v ; if( e[i].c && d[u] > d[v] + e[i].cost ) { d[u] = d[v] + e[i].cost ; prev[u] = v ; pos[u] = i ; if( vis[u] == 0 ) vis[u] = 1 , Q.push(u); } } } return prev[T]!=-1 ; } int network::mcmf(){ int take = 0 , del ,u ; while(spfa()) { del = inf ; for( u = T ; u != S ; u = prev[u] ) del = min( del , e[pos[u]].c ) ; for( u = T ; u != S ; u = prev[u] ) e[pos[u]].c -= del , e[pos[u]^1].c += del ; take += del * d[T] ; } return take ; }int main(){ network gh ; int n , i , j , cost , S , T , mat[maxn][maxn] ; cin>>n ; S = 2*n + 1 , T = 2*n + 2 ; gh.init(S , T , T) ; for( i = 1 ; i<=n ;++i ) { gh.ins(S , i ,1 , 0 ) ; gh.ins(n + i , T , 1 , 0 ) ; } for( i = 1 ; i<=n ; ++ i ) for( j = 1 ; j<=n ; ++j ) { cin>>mat[i][j] ; gh.ins(i , j + n , 1 , mat[i][j] ) ; } int ret = gh.mcmf() ; cout<<ret<<endl ; gh.init(S , T , T) ; for( i = 1 ; i<=n ;++i ) { gh.ins(S , i ,1 , 0) ; gh.ins(n + i ,T ,1, 0) ; } for( i = 1 ;i<=n; ++i ) for( j = 1 ; j<=n ; ++j ) gh.ins(i , j+n , 1, -mat[i][j]) ; ret = gh.mcmf() ; cout<<-ret<<endl ; return 0 ;}
负载平衡问题
#include<iostream>#include<stdio.h>#include<stdlib.h>#include<queue>using namespace std ; const int maxn = 110 ;const int maxe = maxn * maxn ;const int inf = 1<<28 ;struct node { int v , c , cost , next ;} ;struct network{ int S ,T , N , hd[maxn] , es ; int vis[maxn] , prev[maxn] , pos[maxn] , d[maxn] ; node e[maxe] ; void init(int vS , int vT , int vN ) ; void ins(int u ,int v ,int c ,int cost) ; bool spfa() ; int mcmf() ;} ;void network::init(int vS ,int vT ,int vN){ S = vS , T =vT , N = vN ; es = 0 , memset(hd , -1,sizeof(hd)) ;}void network::ins(int u ,int v,int c,int cost){ e[es].v = v , e[es].c = c, e[es].cost =cost ,e[es].next = hd[u] , hd[u] = es ++ ; e[es].v = u , e[es].c = 0, e[es].cost =-cost,e[es].next = hd[v] , hd[v] = es ++ ; }bool network::spfa(){ int u , v , i ; queue<int> Q ; for( i = 1 ; i<=N ; ++i ) vis[i] = 0 , prev[i]=-1 ,d[i] = inf ; vis[S] = 1 , Q.push(S) , d[S] = 0 ; while(!Q.empty() ) { v = Q.front() ; Q.pop() ; vis[v] = 0 ; for( i = hd[v] ; i!=-1 ; i=e[i].next ) { u = e[i].v ; if( e[i].c && d[u] > d[v] + e[i].cost ) { d[u] = d[v] + e[i].cost ; prev[u] = v ; pos[u]=i ; if(!vis[u]) vis[u]=1 ,Q.push(u) ; } } } return prev[T]!=-1 ;}int network::mcmf(){ int take = 0 , del , u ; while(spfa()) { del = inf ; for( u = T ; u!=S ; u=prev[u] ) del = min( del , e[pos[u]].c ) ; for( u = T ; u!=S ; u=prev[u] ) e[pos[u]].c -= del , e[pos[u]^1].c += del ; take += del * d[T] ; } return take ;}int main(){ network gh ; int n , w[maxn] , S ,T , N , ret , i , j , sum ; cin>> n ; S = n + 1 , T = S + 1 , N = T ; gh.init(S , T , N ) ; for( i = 1 , sum = 0 ; i <=n ;++i ) cin>>w[i] , w[i] *= n , sum += w[i] ; sum /=n ; for( i = 1 ; i<=n ; ++i ) if( sum >= w[i] ) gh.ins(S , i , sum - w[i] , 0 ) ; else gh.ins(i , T , w[i]-sum , 0 ) ; for( i = 1 ; i<n ;++i ) gh.ins(i , i + 1, inf , 1 ) , gh.ins(i + 1, i , inf , 1) ; gh.ins(n , 1 , inf , 1 ) ; gh.ins(1 , n , inf , 1 ) ; ret = gh.mcmf() ; cout<< ret/n <<endl ; return 0 ;}
深海机器人问题
最长k可重区间集问题
#include<iostream>#include<queue>#include<set>#include<vector>using namespace std ;const int INF = 1<<29 ;const int MaxSeg = 505 ;const int MaxPnt = 2*MaxSeg ;const int maxn = 2*(MaxPnt + 5) ;const int maxe = 10*maxn ;struct node{ int x , y , c , cost , next ;};node e[maxe] ;int S , T , N , es , hd[maxn] ; int dist[maxn] , vis[maxn] , ps[maxn] , prev[maxn] ;int l[MaxSeg] , r[MaxSeg] , sgnt , K ;set<int> ch ;vector<int> vec ;void ins(int x ,int y ,int c ,int cost){ e[es].x = x , e[es].y = y , e[es].c = c , e[es].cost = cost , e[es].next = hd[x] , hd[x] = es ++ ; e[es].x = y , e[es].y = x , e[es].c = 0 , e[es].cost =-cost , e[es].next = hd[y] , hd[y] = es ++ ;}bool spfa(){ int i , u , v ; queue<int> Q ; for(i = 0 ; i <= N ; ++i) dist[i] = INF , vis[i] = 0 , prev[i] = -1 ; dist[S] = 0 ; vis[S] = 1 ; Q.push(S) ; while(!Q.empty()){ v = Q.front() ; Q.pop() ; vis[v] = 0 ; for(i = hd[v] ; i!=-1 ; i=e[i].next){ u = e[i].y ; if( e[i].c && dist[u] > dist[v] + e[i].cost){ dist[u] = dist[v] + e[i].cost ; prev[u] = v ; ps[u] = i ; if(vis[u] == 0 ) vis[u] = 1 , Q.push(u) ; } } } return prev[T]!=-1 ;}int mcmf(){ int del , v , u , res = 0 ; while(spfa()){ del = INF ; for(v = T ; v!=S ; v = prev[v]) del = min(del , e[ps[v]].c) ; for(v = T ; v!=S ; v = prev[v]) e[ps[v]].c -= del , e[ps[v]^1].c += del ; res += del * dist[T] ; } return res ;}void readin(){ int i ; set<int>::iterator it ; ch.clear() ; vec.clear(); scanf("%d%d",&sgnt ,&K); for(i = 0 ; i < sgnt ; ++i){ scanf("%d%d",&l[i] , &r[i]) ; ch.insert(l[i]); ch.insert(r[i]); } for(it = ch.begin() ; it!=ch.end() ; it++) vec.push_back(*it);} int bbs(int x){ int mid , i , low = 0 , up = vec.size() - 1 ; while(low <= up){ mid = (low + up)/2 ; if(x == vec[mid]) return mid + 1; if(x < vec[mid]) up = mid - 1 ; else low = mid + 1 ; } return 0 ; }int work() { int i , j , k , low , up , ret ; es = 0 ; memset(hd , -1 ,sizeof(hd)); S = vec.size() + 1 ; T = vec.size() + 2 ; N = T ; ins(S , 1 , K , 0 ) ; ins(vec.size() , T , K , 0) ; for(i = 1 ; i < vec.size() ; ++ i) ins(i , i + 1 , K , 0 ) ; for(i = 0 ; i < sgnt ; ++ i){ low = bbs(l[i]); up = bbs(r[i]) ; ins(low , up , 1 , l[i] - r[i] ) ; } ret = mcmf() ; return ret ;}int main(){ readin() ; printf("%d\n",-work()) ; return 0 ;}
最长k可重线段集问题
火星探险问题
#include<iostream>#include<queue>using namespace std ;const int grid = 40 ;const int maxn = 2*grid*grid ;const int maxe = 5 * maxn ;const int INF = 1<<29 ;struct node{ int y , c , cost ,next ;};node e[maxe] ;int es , hd[maxn] , S ,T , N ;int vis[maxn] , d[maxn] , ps[maxn] , prev[maxn] ;int car , row , col , bd[grid][grid]; void ins(int x ,int y ,int c ,int cost ){ e[es].y = y , e[es].c = c, e[es].cost = cost , e[es].next = hd[x] , hd[x] = es ++ ; e[es].y = x , e[es].c = 0, e[es].cost =-cost , e[es].next = hd[y] , hd[y] = es ++ ;}inline int V(int x ,int y) { return x * col + y + 1;}inline bool out(int x,int y){ return x<0 || y<0 || x>=row || y>=col ;}bool spfa(){ queue<int> Q ; int i , v , u ; for(i = 0 ; i <= N ; ++i) d[i] = INF , vis[i] = 0 , prev[i] = -1 ; d[S] = 0 ; vis[S] = 1 ; Q.push(S) ; while(!Q.empty()){ v = Q.front() ; Q.pop() ; for(i = hd[v] ; i!=-1 ; i=e[i].next){ u = e[i].y ; if(e[i].c && d[u] > d[v] + e[i].cost){ d[u] = d[v] + e[i].cost ; prev[u] = v ; ps[u] = i ; if(vis[u] == 0) vis[u] = 1 , Q.push(u) ; } } } return prev[T]!=-1 ;}int MCMF(){ int res = 0 , del , i , v ; while(spfa()){ del = INF ; for(v = T ; v!=S ; v=prev[v]) del = min(del , e[ps[v]].c) ; for(v = T ; v!=S ; v=prev[v]) e[ps[v]].c -= del , e[ps[v]^1].c += del ; res += del * d[T] ; } return res ;}int work(){ int i , j , cnt = 0 , idx = 0; scanf("%d%d%d",&car,&col,&row); for(i = 0 ; i < row ; ++i) for(j = 0 ; j < col ; ++j){ scanf("%d",&bd[i][j]); if(bd[i][j] == 1) cnt ++ ; } S = V(row-1,col-1) + cnt + 1 ; T = S + 1 ; N = T ; es = 0 ; memset(hd , -1 ,sizeof(hd)) ; ins(S , V(1,1) , car , 0 ) ; ins(V(row-1,col-1) , T , car , 0) ; for(i = 0 ; i < row ; ++ i) for(j = 0 ; j < col ; ++j) if( bd[i][j]!=1 ){ if(!out(i+1,j) && bd[i+1][j]!=1 ) ins(V(i,j) , V(i+1,j) , INF , 0 ) ; if(!out(i,j+1) && bd[i][j+1]!=1 ) ins(V(i,j) , V(i,j+1) , INF , 0 ); if( bd[i][j] == 2 ){ idx ++ ; int vertex = V(row - 1 , col - 1) + idx ; ins(V(i,j) , vertex , 1 , -1 ) ; if(!out(i+1,j) && bd[i+1][j]!=1 ) ins(vertex , V(i+1,j) , 1 , 0 ) ; if(!out(i,j+1) && bd[i][j+1]!=1 ) ins(vertex , V(i,j+1) , 1 , 0 ) ; } } return -MCMF() ;}int main(){ printf("%d\n",work()) ; return 0 ;}
骑士共存问题
#include<iostream>#include<memory.h>#include<algorithm>using namespace std ;const int grid = 201;const int maxn = grid * grid ;const int maxe = maxn * 16;const int inf = 1<<30 ;int n , m ; int dx[]={2,1,-1,-2,-2,-1,1,2} , dy[]={1,2,2,1,-1,-2,-2,-1} ;int bd[grid][grid] ;inline bool out(int x,int y){ return x < 0 || y < 0 || x >=n || y>=n ; }struct node{ int x,y,c,next ;};int S ,T ,N , es ,hd[maxn] ;int cur[maxn] , ps[maxn] , dep[maxn] ; node e[maxe] ;void ins(int x ,int y ,int c){ e[es].x = x ,e[es].y = y ,e[es].c = c, e[es].next = hd[x] , hd[x] = es ++ ; e[es].x = y ,e[es].y = x ,e[es].c = 0 ,e[es].next = hd[y] , hd[y] = es ++ ;}int dinic(){ int i ,j , u ,v , k , tr , f, r , maxf = 0 , top ; while(1) { f = r = 0 ; memset(dep , -1 ,sizeof(dep)); ps[r++] = S , dep[S] = 0 ; while(f!=r) { v = ps[f++] ; for(i = hd[v] ; i !=-1 ; i=e[i].next) { u = e[i].y ; if(e[i].c && dep[u] == -1) dep[u] = dep[v] + 1 , ps[r++] = u ; } if( dep[T] !=-1) break; } if( dep[T] == -1) break; i = S ,top = 0 ; memcpy(cur , hd, sizeof(hd)); while(1) { if( i == T){ for(k = 0 , tr = inf ; k < top ; ++ k) if(e[ps[k]].c < tr ) tr = e[ps[k]].c , f = k ; for(k = 0 ; k < top ; ++ k ) e[ps[k]].c -= tr , e[ps[k]^1].c += tr ; maxf += tr , i = e[ ps[top = f] ].x ; } for(j = cur[i] ; j!=-1 ; j = cur[i] = e[j].next) if(e[j].c && dep[i]+1 == dep[ e[j].y ]) break; if(j !=-1 ){ ps[top ++ ] = j , i = e[j].y ; } else{ if(0 == top ) break; dep[i] = -1 , i = e[ps[--top]].x ; } } } return maxf ; } int main(){ int vS , vT , vN , i , j , x, y , k , vx ,vy; scanf("%d%d",&n,&m); S = n*n + 1 , T = S + 1 , N = T ; es = 0 ; memset(hd, -1 ,sizeof(hd)); memset(bd, 0 ,sizeof(bd)); for(i = 0 ; i<m ;++i) scanf("%d%d",&x,&y) , bd[--x][--y] = 1 ; vx = vy = 0 ; for(i = 0 ; i < n ; ++i) for(j = 0 ;j < n ; ++j) if(!bd[i][j]) { if( (i+j)%2 == 0 ) ins(S , i*n+j+1 , 1) , vx ++ ; else ins(i*n+j+1,T ,1) , vy ++ ; } for(i = 0 ;i<n; ++i) for(j = 0 ; j<n ;++j) if(!bd[i][j] && (i+j)%2==0) for(k = 0 ;k<8;++k) { x=i+dx[k],y=j+dy[k]; if(out(x,y) || bd[x][y]) continue; ins(i*n+j+1,x*n+y+1,inf); } printf("%d\n",vx+vy-dinic()); return 0 ;}
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