toj 1421
题意:假如存在矩阵A,A[i][0] + A[i][1] + ...... + A[i][n - 1] == SR[i],A[0][j] + A[1][j] + ...... + A[n - 1][j] == SC[j].(0 <= A[i][j] <= 100),输出YES并输出任意一个满足条件的矩阵A,若不存在则输出NO
分析:SR[0] + SR[1] + ...... + SR[n - 1] == SC[0] + SC[1] + ...... + SC[n - 1],建图的重点是把银行和公司之间的边的容量都设为100,作为流的上限.
当图的最大流等于SR的和则找到了满足条件的矩阵.
另外,输出矩阵时,由于建图方法的特殊性,要用栈来倒序输出.
#include <cstdio> #include <cstring> const int MAXN=205;//点数的最大值 const int MAXM=25005;//边数的最大值 const int INF=0x3fffffff; struct Node { int from,to,next; int cap; }edge[MAXM]; int tol; int head[MAXN]; int dep[MAXN]; int gap[MAXN];//gap[x]=y :说明残留网络中dep[i]==x的个数为y int n;//n是总的点的个数,包括源点和汇点 void init() { tol=0; memset(head,-1,sizeof(head)); } void addedge(int u,int v,int w) { edge[tol].from=u; edge[tol].to=v; edge[tol].cap=w; edge[tol].next=head[u]; head[u]=tol++; edge[tol].from=v; edge[tol].to=u; edge[tol].cap=0; edge[tol].next=head[v]; head[v]=tol++; } void BFS(int start,int end) { memset(dep,-1,sizeof(dep)); memset(gap,0,sizeof(gap)); gap[0]=1; int que[MAXN]; int front,rear; front=rear=0; dep[end]=0; que[rear++]=end; while(front!=rear) { int u=que[front++]; if(front==MAXN)front=0; for(int i=head[u];i!=-1;i=edge[i].next) { int v=edge[i].to; if(dep[v]!=-1)continue; que[rear++]=v; if(rear==MAXN)rear=0; dep[v]=dep[u]+1; ++gap[dep[v]]; } } } int SAP(int start,int end) { int res=0; BFS(start,end); int cur[MAXN]; int S[MAXN]; int top=0; memcpy(cur,head,sizeof(head)); int u=start; int i; while(dep[start]<n) { if(u==end) { int temp=INF; int inser; for(i=0;i<top;i++) if(temp>edge[S[i]].cap) { temp=edge[S[i]].cap; inser=i; } for(i=0;i<top;i++) { edge[S[i]].cap-=temp; edge[S[i]^1].cap+=temp; } res+=temp; top=inser; u=edge[S[top]].from; } if(u!=end&&gap[dep[u]-1]==0)//出现断层,无增广路 break; for(i=cur[u];i!=-1;i=edge[i].next) if(edge[i].cap!=0&&dep[u]==dep[edge[i].to]+1) break; if(i!=-1) { cur[u]=i; S[top++]=i; u=edge[i].to; } else { int min=n; for(i=head[u];i!=-1;i=edge[i].next) { if(edge[i].cap==0)continue; if(min>dep[edge[i].to]) { min=dep[edge[i].to]; cur[u]=i; } } --gap[dep[u]]; dep[u]=min+1; ++gap[dep[u]]; if(u!=start)u=edge[S[--top]].from; } } return res; } int main() { int sr,sc,sum; while(~scanf("%d",&n)) { int N = n; n = 2 * n + 2; init(); int s = n - 2,t = n - 1; sum = 0; for(int i = 0;i < N;i++) { scanf("%d",&sr); sum += sr; addedge(s,i,sr); } for(int i = 0;i < N;i++) { scanf("%d",&sc); addedge(N + i,t,sc); } for(int i = 0;i < N;i++) { for(int j = 0;j < N;j++) { addedge(i,N + j,100); } } if(SAP(s,t) == sum) { printf("YES\n"); int stk[105],sn = 0; for(int i = 0;i < N;i++) { for(int j = head[i];edge[j].next != -1;j = edge[j].next) { stk[sn++] = 100 - edge[j].cap; } printf("%d",stk[--sn]); while(sn > 0) { printf(" %d",stk[--sn]); } printf("\n"); } } else printf("NO\n"); } return 0; }