[Network Flow 24 questions] questions of question Bank

Description

Suppose a question bank has $n$ road questions, each question is marked with the category, the same problem may have more than one category attribute. Now to take $m$ from the question bank to form a test paper, and asked to include a specific type of test paper. A group volume scheme that satisfies the requirements.

Input

The $1$ line has a $2$ positive integer $n,k,k$ represents the total number of question types in the bank, $n $ indicates the total number of questions in the library.

Line $2$ has a $k$ positive integer, and the $i$ positive integer indicates the number of $i$ of the type to be selected $a_i$. The sum of the $k$ number is the total number of questions to be selected $m$.

The next $n$ line gives the type information for each question in the bank. The $1$ positive integer $p$ of each row indicates that the title can belong to the $p$ class, and then the number of $p$ is the type number to which the question belongs.

Output

Line $i$ Output $ "I:" After the number of type $i$. If there are multiple scenarios that meet the requirements, just output $1$ scenarios.

If the problem is not solved, the output "$No \;\; solution!$ "

Sample Input

3 15
3 3 4
2 1 2
1 3
1 3
1 3
1 3
3 1 2 3
2 2 3
2 1 3
1 2
1 2
2 1 2
2 1 3
2 1 2
1 1
3 1 2 3

Sample Output

1:1 6 8
2:7 9 10
3:2 3 4 5

HINT

$2\;\leq\;k\;\leq\;20,k\;\leq\;n\;\leq\;1000$

Solution

The category $i$ is $x_i$, the title $i$ is $y_i$.

From $s$ to $x_i$, a forward edge with a capacity of $a_i$ is connected,

From $x_i$ to $y_j$, a forward edge with a capacity of $1$ (title $j\in$ category $i$) is connected to the

From $y_i$ to $t$, a forward edge with a capacity of $1$ is connected,

To find the maximum flow.

If the maximum flow $=m$, there is a solution, otherwise there is no solution.

All full-stream edges flowing from the collection $x$ to the collection $y$ are the current scheme.

#include <cmath>#include<ctime>#include<queue>#include<stack>#include<cstdio>#include<vector>#include<cstring>#include<cstdlib>#include<iostream>#include<algorithm>#defineM 25#defineN 1005using namespacestd;structgraph{intnxt,to,f;} E[m*n<<1];intA[m],g[n+m],dep[n+m],n,m,s,t,sum,cnt=1; queue<int>Q;inlinevoidAddedge (intXintYintf) {e[++cnt].nxt=g[x];g[x]=cnt;e[cnt].to=y;e[cnt].f=F;} InlinevoidAdde (intXintYintf) {Addedge (x,y,f); Addedge (Y,x,0);} InlineBOOLBFsintu) {memset (DEP,0,sizeof(DEP)); Q.push (U);d Ep[u]=1;  while(!Q.empty ()) {u=Q.front (); Q.pop ();  for(intI=g[u];i;i=e[i].nxt)if(e[i].f>0&&!Dep[e[i].to])                {Q.push (e[i].to); Dep[e[i].to]=dep[u]+1; }    }    returndep[t];} InlineintDfsintUintf) {    intret=0; if(u==t)returnF;  for(intI=g[u],d;i&&f;i=e[i].nxt)if(e[i].f>0&&dep[e[i].to]>Dep[u]) {D=Dfs (E[i].to,min (F,E[I].F)); RET+=d;f-=d;e[i].f-=d;e[i^1].f+=D; }    returnret;} InlineintDinic () {intret=0;  while(true){        if(!bfs (s))returnret; RET+=DFS (S,M); }}inlinevoidAireen () {scanf ("%d%d",&m,&N); S=m+n+1; t=s+1;  for(intI=1; i<=m;++i) {scanf ("%d",&A[i]); Adde (s,i,a[i]); Sum+=A[i]; }     for(intI=1, j,k;i<=n;++i) {scanf ("%d",&k);  while(k--) {scanf ("%d", &j); Adde (J,i+m,1); } adde (I+m,t,1); }    if(Dinic ()!=sum) puts ("No solution!"); Else{         for(intI=1; i<=m;++i) {printf ("%d:", i);  for(intj=g[i];j;j=e[j].nxt)if(!e[j].f&&! (j&1)) printf ("%d", e[j].to-m); printf ("\ n"); }        }}intMain () {Freopen ("data.in","R", stdin); Freopen ("Data.out","W", stdout);    Aireen ();    Fclose (stdin);    Fclose (stdout); return 0;}

[Network Flow 24 questions] questions of question Bank