poj2396 Budget 上下界可行流

Budget：http://poj.org/problem?id=2396

题意：

　　给定一个棋盘，给定每一行每一列的和，还有每个点的性质。求一个合理的棋盘数值放置方式。

思路：

　　比较经典的网络流模型，把每一列看成一个点，每一行看成一个点，利用上下界可行流的思路建图就行了，注意这里由于是严格的小于和大于，所以可以利用 x+1, x-1。

还有就是这道题的0 ， 0 说的是对整张图的操作。

#include <algorithm>
#include  <iterator>
#include  <iostream>
#include   <cstring>
#include   <cstdlib>
#include   <iomanip>
#include    <bitset>
#include    <cctype>
#include    <cstdio>
#include    <string>
#include    <vector>
#include     <stack>
#include     <cmath>
#include     <queue>
#include      <list>
#include       <map>
#include       <set>
#include   <cassert>

/*

⊂_ヽ
　 ＼＼ Λ＿Λ  来了老弟
　　 ＼('ㅅ')
　　　 >　⌒ヽ
　　　/ 　 へ＼
　　 /　　/　＼＼
　　 ﾚ　ノ　　 ヽ_つ
　　/　/
　 /　/|
　(　(ヽ
　|　|、＼
　| 丿 ＼ ⌒)
　| |　　) /
'ノ )　　Lﾉ

*/

using namespace std;
#define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "\n";
#define pb push_back
#define pq priority_queue

typedef long long ll;
typedef unsigned long long ull;
//typedef __int128 bll;
typedef pair<ll ,ll > pll;
typedef pair<int ,int > pii;
typedef pair<int,pii> p3;

//priority_queue<int> q;//这是一个大根堆q
//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q
#define fi first
#define se second
//#define endl '\n'

#define boost ios::sync_with_stdio(false);cin.tie(0)
#define rep(a, b, c) for(int a = (b); a <= (c); ++ a)
#define max3(a,b,c) max(max(a,b), c);
#define min3(a,b,c) min(min(a,b), c);

const ll oo = 1ll<<;
const ll mos = 0x7FFFFFFF;  //
const ll nmos = 0x80000000;  //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f; //
const int mod = 1e9+;
const double esp = 1e-;
const double PI=acos(-1.0);
const double PHI=0.61803399;    //黄金分割点
const double tPHI=0.38196601;

template<typename T>
inline T read(T&x){
    x=;int f=;char ch=getchar();
    while (ch<''||ch>'') f|=(ch=='-'),ch=getchar();
    while (ch>=''&&ch<='') x=x*+ch-'',ch=getchar();
    return x=f?-x:x;
}

inline void cmax(int &x,int y){if(x<y)x=y;}
inline void cmax(ll &x,ll y){if(x<y)x=y;}
inline void cmin(int &x,int y){if(x>y)x=y;}
inline void cmin(ll &x,ll y){if(x>y)x=y;}

/*-----------------------showtime----------------------*/

            const int maxn = 1e4+;
            int n,m;
            struct E{
                int v,val,id;
                int nxt;
            }edge[maxn];
            int head[maxn],gtot;
            void addedge(int u,int v,int val, int id){
                edge[gtot].v = v;
                edge[gtot].val = val;
                edge[gtot].nxt = head[u];
                edge[gtot].id = -;
                head[u] = gtot++;

                edge[gtot].v = u;
                edge[gtot].val = ;
                edge[gtot].nxt = head[v];
                edge[gtot].id = id;
                head[v] = gtot++;
            }

            int dis[maxn],cur[maxn],all;
            bool bfs(int s,int t) {
                memset(dis, inf, sizeof(dis));

                for(int i=; i<=all; i++) cur[i] = head[i];
                queue<int>que;  que.push(s);
                dis[s] = ;
                while(!que.empty()){
                    int u = que.front(); que.pop();
                    for(int i=head[u]; ~i; i=edge[i].nxt){
                        int v = edge[i].v,val = edge[i].val;
                        if(val >  && dis[v] > dis[u] + ){
                            dis[v] = dis[u]+ ;
                            que.push(v);
                        }
                    }
                }
                return dis[t] < inf;
            }
            int dfs(int u,int t,int maxflow){
                if(u == t || maxflow == ) return maxflow;
                for(int i=cur[u]; ~i; i=edge[i].nxt){
                    cur[u] = i;
                    int v=edge[i].v,val = edge[i].val;
                    if(val > &&dis[v] == dis[u] + ){
                        int f = dfs(v, t, min(maxflow, val));
                        if(f > ) {
                            edge[i].val -= f;
                            edge[i ^ ].val += f;
                            return f;
                        }
                    }
                }
                return ;
            }
            int dinic(int s,int t){
                int flow = ;
                while(bfs(s, t)){
                    while(int f = dfs(s, t, inf)) flow += f;
                }
                return flow;
            }

            int low[][],high[][],du[];
            char op[];
int main(){
            int T;
            scanf("%d", &T);
            while(T--){
                memset(head, -, sizeof(head));
                memset(low, , sizeof(low));
                memset(high, inf, sizeof(high));
                memset(du, , sizeof(du));
                gtot = ;
                scanf("%d%d", &n, &m);
                int s = , t = n+m+, ss = n+m+, tt = n+m+;
                all = tt;
                int s1 = , s2 = ;
                for(int i=; i<=n; i++) {
                    int x;  scanf("%d", &x);
                    addedge(s, i, , -);
                    du[s] -= x;
                    du[i] += x;
                    s1 += x;
                }
                for(int i=; i<=m; i++){
                    int x;  scanf("%d", &x);
                    addedge(n+i, t, , -);
                    du[t] += x;
                    du[n+i] -= x;
                    s2 += x;
                }

                int c;  scanf("%d", &c);
                int flag = ;
                while(c--){
                    int u,v,x;
                    scanf("%d %d %s %d", &u, &v, op, &x);
                    if(u ==  && v == ){
                        for(int i=; i<=n; i++) {
                                for(int j=; j<=m; j++){
                                    if(op[] == '>') low[i][j] = max(low[i][j],x+);
                                    else if(op[] == '<') high[i][j] = min(high[i][j], x-);
                                    else if(op[] == '=')
                                    {
                                        low[i][j] = max(low[i][j], x), high[i][j] = min(high[i][j], x);
                                        if(low[i][j] != x || high[i][j] != x) flag = ;
                                    }
                                }
                        }
                    }
                    else if(u == ) {
                        for(int i=; i<=n; i++) {
                            if(op[] == '>') low[i][v] = max(low[i][v],x+);
                            else if(op[] == '<') high[i][v] = min(high[i][v], x-);
                            else if(op[] == '=')
                            {
                                low[i][v] = max(low[i][v], x), high[i][v] = min(high[i][v], x);
                                if(low[i][v] != x || high[i][v] != x) flag = ;
                            }
                        }
                    }
                    else if(v == ){
                        for(int i=; i<=m; i++) {
                            if(op[] == '>') low[u][i] = max(low[u][i],x+);
                            else if(op[] == '<') high[u][i] = min(high[u][i], x-);
                            else {
                                low[u][i] = max(low[u][i], x), high[u][i] = min(high[u][i], x);
                                if(low[u][i] != x || high[u][i] != x) flag = ;
                            }
                        }
                    }
                    else {
                         if(op[] == '>') low[u][v] = max(low[u][v],x+);
                         else if(op[] == '<') high[u][v] = min(high[u][v], x-);
                         else {
                                low[u][v] = max(low[u][v], x), high[u][v] = min(high[u][v], x);
                                if(low[u][v] != x || high[u][v] != x) flag = ;
                         }
                    }
                }

                for(int i=; i<=n; i++) {
                    for(int j=; j<=m; j++){
                        du[i] -= low[i][j];
                        du[j+n] += low[i][j];
                        addedge(i, n + j, high[i][j] - low[i][j], );
                        if(high[i][j] < low[i][j]) flag = ;
                    }
                }

                int sum = ;
                for(int i=s; i<=t; i++) {
                    if(du[i] > ) addedge(ss, i, du[i], -), sum += du[i];
                    if(du[i] < )addedge(i, tt, -du[i], -);
                }
                if(s1 != s2 || !flag) {
                    puts("IMPOSSIBLE");
                    if(T) puts("");
                    continue;
                }
                int f = dinic(ss, tt);

                if(f + s1==sum) {
                    for(int i=n+;i<=n+m; i++){
                        for(int j=head[i]; ~j; j=edge[j].nxt){
                            int v = edge[j].v,val = edge[j].val;
                            low[v][i-n] += val;
                        }
                    }
                    for(int i=; i<=n; i++){
                        for(int j=; j<=m; j++){
                            if(j < m)printf("%d ", low[i][j]);
                            else printf("%d\n", low[i][j]);
                        }
                    }
                }
                else puts("IMPOSSIBLE");
                if(T) puts("");
            }
            return ;
}
/*
2
2 3
8 10
5 6 7
4
0 2 > 2
2 1 = 3
2 3 > 2
2 3 < 5
2 2
4 5
6 7
1
1 1 > 10
*/