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;
}