# bzoj 2406 矩阵

Output

2 2

0 1

2 1

0 1

1

### 题解

s->xi,[ai-mid,ai+mid]
yj->t,[aj-mid,aj+mid]
xi->yj,[L,R]

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <map>
#define N 100010
using namespace std;
const int inf = 0x3f3f3f3f;
int n, m, S, T, s, t, l, r, x, d[N], st[N], cr[N];
struct flows {
struct node {
int to, next, flow;
} e[N];
int tot, st[N], dis[N], cur[N];
void init() {
tot = -1, memset(e, -1, sizeof e),
memset(st, -1, sizeof st);
memset(d, 0, sizeof d);
}
void add(int x, int y, int z) {
e[++tot].to = y;
e[tot].flow = z;
e[tot].next = st[x];
st[x] = tot;
}
void add_edge(int x, int y, int z) {
//      printf("add %d %d %d\n", x, y, z);
}
queue <int> que;
int bfs(int S, int T) {
memcpy(cur, st, sizeof st);
memset(dis, 0, sizeof dis);
while (!que.empty()) que.pop();
que.push(S);
dis[S] = 1;
while(!que.empty()) {
int now = que.front();
que.pop();
for (int i = st[now]; ~i; i = e[i].next)
if (e[i].flow && !dis[e[i].to]) {
dis[e[i].to] = dis[now] + 1;
if (e[i].to == T) return 1;
que.push(e[i].to);
}
}
return 0;
}
int finds(int now, int T, int flow) {
if (now == T)
return flow;
int f;
for (int i = cur[now]; ~i; i = e[i].next) {
cur[now] = i;
if (e[i].flow && dis[e[i].to] == dis[now] + 1 &&
(f = finds(e[i].to, T, min(flow, e[i].flow)))) {
e[i].flow -= f;
e[i^1].flow += f;
return f;
}
}
return 0;
}
int dinic(int S, int T) {
int flow = 0, x;
while(bfs(S, T)) {
while(x = finds(S, T, inf)) {
flow += x;
}
}
return flow;
}
}flow;
bool check(int mid) {
flow.init();
int in = 0, out = 0;
for (int i = 1; i <= n; ++i)
flow.add_edge(s, i, mid * 2),
d[s] -= st[i] - mid, d[i] += st[i] - mid;
for (int i = 1; i <= m; ++i)
flow.add_edge(i + n, t, mid * 2),
d[t] += cr[i] - mid, d[i + n] -= cr[i] - mid;
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= m; ++j)
flow.add_edge(i, j + n, r - l),
d[i] -= l, d[j + n] += l;
for (int i = 1; i <= t; ++i)
if (d[i] > 0)
flow.add_edge(S, i, d[i]), in += d[i];
else if (d[i] < 0)
flow.add_edge(i, T, -d[i]), out -= d[i];
if (in != out) return 0;
int ans = flow.dinic(S, T);
return ans == in;
}
int find() {
int l = 0, r = 2000000, ans;
while (l <= r) {
int mid = l + r >> 1;
if (check(mid))
ans = mid, r = mid - 1;
else
l = mid + 1;
}
return ans;
}
main() {
scanf("%d%d", &n, &m);
s = n + m + 1, t = s + 1, S = t + 1, T = S + 1;
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= m; ++j)
scanf("%d", &x),
st[i] += x, cr[j] += x;
scanf("%d%d", &l, &r);
printf("%d\n", find());
}