Matrix Decompressing UVA - 11082 （网络流，输出每条边流量）

题目大意

对于一个R行C列的正整数矩阵（1 <= R, C <= 20），设$A_i$为前i行所有元素之和，$B_i$
为前i列所有元素之和。已知R，C和数组A和B，找一个满足条件的矩阵。矩阵中的元素必须是1~20之间的正整数。

思路

建图方法，设一个超级源点S与超级汇点TO，然后S连每一行容量为这一行的和-1，然后每一列连TO的容量为这一列的和-1，然后每一行连每一列容量为19，然后跑一个最大流

EK算法代码

好处是代码好写，坏处是效率不高

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int inf = 0x3f3f3f3f;
const int maxn = 50;
int c[maxn][maxn];
int f[maxn][maxn];
int a[maxn]; // 当前点到i的可改进量
int p[maxn];
int R, C, n;
int EK(int s, int t) {
    memset(p,0,sizeof(p));
    memset(f,0,sizeof(f));
    int flow = 0;
    for(;;) {
        memset(a, 0, sizeof(a));
        queue<int> Q;
        Q.push(s);
        a[s] = inf;
        while(!Q.empty()) {
            int x = Q.front(); Q.pop();
            for(int to = 0; to < n; to++) {
                if(x == to) continue;
                if(!a[to] &&  c[x][to] > f[x][to]) {
                    p[to] = x;
                    a[to] = min(a[x], c[x][to]-f[x][to]);
                    Q.push(to);
                }
            }
            if(a[t]) break;
        }
        if(!a[t]) break;
        for(int u = t; u != s; u = p[u]) {
            f[p[u]][u]+=a[t];
            f[u][p[u]]-=a[t];
        }
        flow+=a[t];
    }
    return flow;
}
int main() {
    //freopen("/Users/maoxiangsun/MyRepertory/input.txt", "r", stdin);
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    int T;cin>>T;
    int cas = 0;
    while(T--) {
        memset(c, 0, sizeof(c));
        cin>>R>>C;
        cout << "Matrix " << ++cas << endl;
        int tmp = 0;
        for(int i = 1; i <= R; i++) {
            int sum; cin >> sum;
            c[0][i] = sum - tmp - C;
            tmp = sum;
        }
        tmp = 0;
        int TO = R+C+1; n = TO + 1;
        int S = 0;
        for(int i = 1; i <= C; i++) {
            int sum; cin >> sum;
            c[i+R][TO] = sum - tmp - R;
            tmp = sum;
        }
        for(int i = 1; i <= R; i++) {
            for(int j = 1; j <= C; j++) {
                c[i][j+R] = 19;
            }
        }
        EK(S,TO);
        for(int i = 1; i <= R; i++) {
            for(int j = 1; j <= C; j++) {
                cout<<f[i][j+R]+1;  
                if(j==C) cout<<endl;
                else cout<<" ";
            }
        }
        if(T) printf("\n");
    }
    return 0;
}

dinic 算法

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 50;
const int inf = 0x3f3f3f3f;

int R, C;
int ans[22][22];
struct Dinic {
    struct Edge {
        int from, to, cap, flow;
    };
    int s,t;
    vector<Edge> edges;
    vector<int> G[maxn];
    int d[maxn];
    bool vis[maxn];
    int cur[maxn];
    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 tt = (int)edges.size();
        G[from].push_back(tt-2);
        G[to].push_back(tt-1);
    }
    bool BFS() {
        memset(vis, 0, sizeof(vis));
        queue<int>Q;
        Q.push(s);
        d[s] = 0;
        vis[s] = 1;
        while(!Q.empty()) {
            int x = Q.front(); Q.pop();
            for(int i = 0; i < G[x].size(); i++) {
                Edge & e = edges[G[x][i]];
                if(!vis[e.to] && e.cap > e.flow) {
                    vis[e.to] = 1;
                    d[e.to] = d[x] + 1;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }
    int DFS(int x, int a) {
        if(x == t || a == 0) return a;
        int flow = 0, f;
        for(int & i =  cur[x]; i < G[x].size(); i++) {
            Edge& e = edges[G[x][i]];
            if(d[x]+1==d[e.to] && (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 MF(int s, int t) {
        this->s = s; this->t = t;
        int flow = 0;
        while(BFS()) {
            memset(cur, 0, sizeof(cur));
            flow += DFS(s, inf);
        }
        return flow;
    }
    void init() {
        edges.clear();
        for(int i = 0; i <= R+C+2; i++) G[i].clear();
    }
    void getans() {
        for(int i = 1; i <= R; i++) {
            for(int j = 0; j < G[i].size(); j++) {
                int to = edges[G[i][j]].to;
                if(to) ans[i][to-R] = edges[G[i][j]].flow + 1;
            }
        }
    }
}dinic;
int main() {
   // freopen("/Users/maoxiangsun/MyRepertory/input.txt", "r", stdin);
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    int T;cin>>T;
    int cas = 0;
    while(T--) {
        cin>>R>>C;
        dinic.init();
        cout << "Matrix " << ++cas << endl;
        int tmp = 0;
        for(int i = 1; i <= R; i++) {
            int sum; cin >> sum;
            dinic.addEdge(0, i, sum-tmp-C);
            tmp = sum;
        }
        tmp = 0;
        int TO = R+C+1;
        int S = 0;
        for(int i = 1; i <= C; i++) {
            int sum; cin >> sum;
            dinic.addEdge(i+R, TO, sum-tmp-R);
            tmp = sum;
        }
        for(int i = 1; i <= R; i++) {
            for(int j = 1; j <= C; j++) {
                dinic.addEdge(i, j+R, 19);
            }
        }
        dinic.MF(S, TO);
        dinic.getans();
        for(int i = 1; i <= R; i++) {
            for(int j = 1; j <= C; j++) {
                cout<<ans[i][j];
                if(j==C) cout<<endl;
                else cout<<" ";
            }
        }
        if(T) printf("\n");
    }
    return 0;
}