uva Matrix Decompressing (行列模型)

Matrix Decompressing

题目：

   给出一个矩阵的前i行，前j列的和。要求你求出满足的矩阵。矩阵的数范围在[1,20]。

  一开始就坑在了这里。没读仔细题目。囧。。。

  其实这题的模型就是一个网络流的行列模型，跟poj的那题budge一样建图。不过Poj 的那个建图输入麻烦，而这题是裸的，因为已经告诉你了下界为1，上界为20，囧。。。而且poj那题我至今也不知道为什么我会一直超时。T_T

算法:

   行列模型可以转换成网络流的有源汇上下界网络流求解。而行号和列号分别作为顶点。连结超级源汇点就ok了。跑两边最大流，而每条边上的流量+下界流就是结果了。

#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <cstdio>
#include <cstring>
using namespace std;

const int INF = 1 << 20;
const int MAXN = 400 + 10;
struct Edge{
   int from,to,cap,flow;
   Edge(){};
   Edge(int _from,int _to,int _cap,int _flow)
      :from(_from),to(_to),cap(_cap),flow(_flow){};
};
vector<Edge> edges;
vector<int> G[MAXN];
int cur[MAXN],d[MAXN];
int N,M,src,sink,ss,tt;

//////////////////////////////////////

int ans[MAXN][MAXN];

void init(){
   ss = N + M + 2;   tt = ss + 1;
   src = tt + 1; sink = src + 1;
   for(int i = 0;i <= sink + 1;++i)
     G[i].clear();
   edges.clear();
}

void addEdge(int from,int to,int cap){
   edges.push_back(Edge(from,to,cap,0));
   edges.push_back(Edge(to,from,0,0));
   int sz = edges.size();
   G[from].push_back(sz - 2);
   G[to].push_back(sz - 1);
}

bool BFS(){
   fill(d,d + sink + 2,-1);
   queue<int> Q;
   Q.push(src);
   d[src] = 0;

   while(!Q.empty()){
       int x = Q.front(); Q.pop();
       for(int i = 0;i < (int)G[x].size();++i){
           Edge& e = edges[G[x][i]];
           if(d[e.to] == -1 && e.cap > e.flow){
               d[e.to] = d[x] + 1;
               Q.push(e.to);
           }
       }
   }

   return d[sink] > 0;
}

int DFS(int x,int a){
    if(x == sink || a == 0)
         return a;

    int flow = 0,f;
    for(int& i = cur[x];i < (int)G[x].size();++i){
        Edge& e = edges[G[x][i]];
        if(d[e.to] == d[x] + 1 && (f = DFS(e.to,min(a,e.cap - e.flow))) > 0){
            e.flow += f;
            edges[G[x][i]^1].flow -= f;
            flow += f;
            a -= f;
            if(a == 0) break;
        }
    }
    return flow;
}

int maxflow(){
   int flow = 0;
   while(BFS()){
       memset(cur,0,sizeof(cur));
       flow += DFS(src,INF);
   }
   return flow;
}

int main()
{
   // freopen("Input.txt","r",stdin);

    int T;
    scanf("%d",&T);
    for(int kase = 1;kase <= T;++kase){
        scanf("%d%d",&N,&M);

        init();

        int sum = 0,x;
        for(int i = 1;i <= N;++i){
            scanf("%d",&x);
            addEdge(ss,i,x - sum);
            sum = x;
        }

        sum = 0;
        for(int i = 1;i <= M;++i){
            scanf("%d",&x);
            addEdge(i+N,tt,x - sum);
            sum = x;
        }

        for(int i = 1;i <= N;++i){
            for(int j = 1;j <= M;++j){
              addEdge(i,sink,1);
              addEdge(i,N + j,19);
              addEdge(src,N + j,1);
            }
        }

        addEdge(tt,ss,INF);

       int flow = maxflow();

        src = ss; sink = tt;

        maxflow();
        printf("Matrix %d\n",kase);

        for(int i = 1;i <= N;++i){
            for(int j = 0;j < (int)G[i].size();++j){
                Edge& e = edges[G[i][j]];
                if(e.from > N||e.to <= N||e.to > N+M) continue;
                ans[e.from][e.to - N] = e.flow + 1;
            }
        }

        for(int i = 1;i <= N;++i){
            for(int j = 1;j <= M;++j)
                printf("%d%c",ans[i][j],j == M ? '\n':' ');
        }
    }
    return 0;
}