HDU 4888 Redraw Beautiful drawings (solution of network flow seeking matrix)

The paper "Why many network flow problems always have integer solution" http://diaorui.net/archives/189;

Reference: http://www.cnblogs.com/yuiffy/p/3929369.html

Test instructions: The matrix of the n*m, giving each row and each column of the and, to determine whether such a matrix exists, if present, whether the unique, if only, the output solution;

Idea: network flow, maximum flow + judgment ring. Network flow is often used to find polynomial integer solutions.

#include <cstdio>#include<cstring>#include<algorithm>using namespacestd;Const intinf=0x7fffffff;BOOLfound,walked[500010];intT,nr,nc,k,sumr,sumc,ans;intr[500010],c[500010];intan[5005][5005];inthead[500100],h[500010],g[500010];//G[i] is the number of nodes of layer I, h[i] is the number of layers of I pointintd[500010],AUGC;//d record current arc, AUGC for augmented path capacityintCnt,st,ed,flow,n,m;//n points m edge, flow is the maximum streamstructnode{intV,cap,next;}; Node e[500010];voidAddintXintYintz) {E[CNT].V=y; E[cnt].cap=Z; E[cnt].next=Head[x]; HEAD[X]=cnt++; E[CNT].V=x; E[cnt].cap=0; E[cnt].next=Head[y]; Head[y]=cnt++;}BOOLDfsConst int&x,Const int&prex)//Award Ring{    intbiu=-1; WALKED[X]=true;  for(inti=head[x];i!=-1; i=E[i].next) {        if(e[i].v==Prex) {Biu=i;Continue; }        if(e[i].cap>0)        {            if(WALKED[E[I].V])return true; if(Dfs (E[I].V,X))return true; }        if(biu==-1) Head[x]=e[i].next;//There's no ring on this side of the line .        Elsee[biu].next=E[i].next; Biu=i; } Walked[x]=false; return false;}voidAugConst int&AMP;M)//Dicnic{    inti,mini,minh=n-1; intaugco=AUGC; if(m==ed) {//current point is a meeting pointFound=true; Flow+=AUGC;//Increase Traffic        return; }     for(i=d[m];i!=-1; i=e[i].next) {//find the permissible side        if(e[i].cap&&h[e[i].v]+1==H[M])//if the residue is greater than 0 and is a permissible edge        {            if(E[I].CAP&LT;AUGC) Augc=e[i].cap;//if the residue is less than the current augmented path flow, the new wide-path trafficD[m]=i;//set I as the current arc(E[I].V);//Recursive            if(h[st]>=n)return;//returns if the source point layer is greater than n            if(found) Break;//find a meeting point, jump outAugc=augco;//Restore current stream if not found        }    }    if(!found) {         for(i=head[m];i!=-1; i=E[i].next) {            if(e[i].cap&&h[e[i].v]<Minh) {Minh=H[E[I].V]; Mini=i; }} G[h[m]]--; if(!g[h[m]]) h[st]=N; H[M]=minh+1; D[M]=Mini; G[H[M]]++; }Else{//Modify the residual quantityE[I].CAP-=AUGC;//Positive Reductione[i^1].CAP+=AUGC;//Reverse Add    }}voidFarm () {inti,j,x,y,z; memset (Head,-1,sizeof(head)); CNT=0; N=nc+nr+2; St=nc+nr+1;//Source Pointed=nc+nr+2;//meeting Point     for(i=1; i<=nc;i++) Add (St,i,c[i]); //source point to line edge, capacity for the row and     for(i=1; i<=nr;i++) Add (NC+i,ed,r[i]);//column to a meeting point edge, and the capacity for the column and     for(i=1; i<=nc;i++)         for(j=1; j<=nr;j++) Add (i,j+NC,K);//row-to-column edge, capacity Kmemset (H,0,sizeof(h));//number of layers, building a hierarchical mapMemset (G,0,sizeof(g)); g[0]=N; Flow=0;  for(i=1; i<=n;i++) D[i]=head[i];//Current ARC Initialization     while(h[st]<N) {AUGC=inf;//The capacity of the initial augmented path is infinitely largeFound=false;       (ST); //from the source point to start looking for    }    if(FLOW!=SUMR) {//not up to full streamans=0; return; }     for(i=1; i<=nr;i++)    {        intk=1;  for(j=head[nc+i];j!=-1; j=E[j].next) {            if(e[j].v==ed)Continue; An[i][k++]=E[j].cap; intthenext=E[j].next;  while(thenext!=-1&&e[thenext].v==ed) thenext=E[thenext].next; }} memset (walked,false,sizeof(walked));  for(i=nr;i>=1; i--)    {        if(Dfs (i,-1))//the number of rows as the starting position of the ring, if there is a ring, 1~NR must be a bit in the ring{ans=2; return; }} ans=1;}intMain () {intI,j,cas;  while(SCANF ("%d%d%d", &nr,&nc,&k)! =EOF) {SUMR=sumc=0;  for(i=1; i<=nr;i++) {scanf ("%d",&R[i]); SUMR+=R[i]; }         for(i=1; i<=nc;i++) {scanf ("%d",&C[i]); SUMC+=C[i]; } ans=0; if(SUMR==SUMC) farm ();//and different, then no solution        if(ans==0) printf ("impossible\n"); Else if(ans!=1) {printf ("Not unique\n"); }        Else{printf ("unique\n");  for(i=1; i<=nr;i++)           {               if(nc>=1) printf ("%d", AN[I][NC]);  for(j=nc-1; j>=1; j--) {printf ("%d", An[i][j]); }printf ("\ n"); }        }    }    return 0;}

HDU 4888 Redraw Beautiful drawings (solution of network flow seeking matrix)