Gym - 102346G Getting Confidence
The meaning of problems: n * n grid, each grid having a number required per row could get only a few, such that the product of the maximum, then the output of each column is the number of selected row number.
If it is an addition, then obviously, it is a network flow. But now is how to do multiplication, it is very simple, direct access log, then multiply it converted into an addition, then you can build map.
Every row and column can only take a number equivalent to the ranks of the points is open, because output is required information is listed, then the source built into each column a flow rate of 1, 0 cost side, and each row to Meeting point built a flow rate of 1 at a cost of zero edge.
Then for each grid, each row of the grid it was built to a column flow rate of 1 at a cost of 0 points, and each grid to build a flow rate of 1 to its row at a cost of -log (number on the grid ) side.
Finally, the minimum cost maximum flow run again, look at the traffic that edge of each column is 0
1 #include<cstdio> 2 #include<cmath> 3 #include<queue> 4 #include<algorithm> 5 using namespace std; 6 const int N=2e4+11,M=1e6+11,inf=1e9+7; 7 struct Side{ 8 int v,ne,w; 9 double val; 10 }S[M<<1]; 11 double dis[N]; 12 int n,sn,sb,se,head[N],vis[N],flow[N],lu[N]; 13 void init(){ 14 sn=0; 15 sb=0;se=n*n+2*n+1; 16 for(int i=sb;i<=se;i++) head[i]=-1; 17 } 18 void add(int u,int v,int w,double val){ 19 S[sn].w=w;S[sn].val=val; 20 S[sn].v=v;S[sn].ne=head[u]; 21 head[u]=sn++; 22 } 23 void addE(int u,int v,int w,double val){ 24 add(u,v,w,val);add(v,u,0,-val); 25 } 26 bool spfa(){ 27 queue<int> q; 28 for(int i=sb;i<=se;i++){ 29 dis[i]=inf; 30 vis[i]=0; 31 flow[i]=inf; 32 lu[i]=-1; 33 } 34 dis[sb]=0; 35 vis[sb]=1; 36 q.push(sb); 37 int u,v; 38 while(!q.empty()){ 39 u=q.front();q.pop();vis[u]=0; 40 for(int i=head[u];~i;i=S[i].ne){ 41 v=S[i].v; 42 if(S[i].w>0&&dis[v]>dis[u]+S[i].val){ 43 lu[v]=i; 44 dis[v]=dis[u]+S[i].val; 45 flow[v]=min(flow[u],S[i].w); 46 if(!vis[v]){ 47 vis[v]=1; 48 q.push(v); 49 } 50 } 51 } 52 } 53 return dis[se]!=inf; 54 } 55 void mfml(){ 56 int ans=0,ansc=0; 57 while(spfa()){ 58 ans+=flow[se]; 59 ansc+=flow[se]*dis[se]; 60 for(int i=lu[se];~i;i=lu[S[i^1].v]){ 61 S[i].w-=flow[se]; 62 S[i^1].w+=flow[se]; 63 } 64 } 65 } 66 int main(){ 67 while(~scanf("%d",&n)){ 68 init();; 69 for(int i=1;i<=n;i++){ 70 addE(sb,n*n+n+i,1,0.0); 71 addE(n*n+i,se,1,0.0); 72 } 73 for(int i=1,x;i<=n;i++){ 74 for(int j=1;j<=n;j++){ 75 scanf("%d",&x); 76 addE(n*n+n+j,(i-1)*n+j,1,0.0); 77 addE((i-1)*n+j,n*n+i,1,-log(1.0*x)); 78 } 79 } 80 mfml(); 81 for(int i=1;i<=n;i++) 82 for(int j=head[n*n+n+i];~j;j=S[j].ne){ 83 if(S[j].w||S[j].v==sb) continue; 84 printf("%d%c",(S[j].v-1)/n+1," \n"[i==n]); 85 break; 86 } 87 } 88 return 0; 89 }