题解 P4474 【王者之剑】
Ireliaღ
2019-07-19 09:41:52
教练留的网络流作业,我看见$Saber$就冲进来了,能看到这么一道题月厨深感欣慰。
然后看题。诶?跟方格取数一样的,写一发`ISAP`就切了。
## 建图
- 设$0$为原点,$n \times m + 1$为汇点,把棋盘里的点全部映射到$[1, n \times m]$的节点
- 对于$\forall i \in black$,从$0$向$i$建边,容量为该点数字
- 对于$\forall j \in white$,从$j$向$n \times m + 1$建边,容量为该点数字
- 对于$\forall i \in black$,从$i$向上下左右的白点建边,容量为$\infty$
然后跑最大流,用数字总和减去它即可。
## 代码
指针版`ISAP`,有当前弧优化
```cpp
// luogu-judger-enable-o2
// luogu-judger-enable-o2
#include <iostream>
#include <queue>
#include <cstring>
using namespace std;
const int MAXN = 105;
const int INF = 0x3f3f3f3f;
int m, n;
struct Edge{
int to, val;
Edge *next, *ops;
Edge(int to, int val, Edge *next): to(to), val(val), next(next){}
};
Edge *head[MAXN * MAXN], *cur[MAXN * MAXN];
int ID(int x, int y) {
return (x - 1) * n + y;
}
void AddEdge(int u, int v, int w) {
head[u] = new Edge(v, w, head[u]);
head[v] = new Edge(u, 0, head[v]);
head[u]->ops = head[v]; head[v]->ops = head[u];
}
int dep[MAXN * MAXN], gap[MAXN * MAXN];
int s, t, res;
void Bfs() {
memset(dep, -1, sizeof(dep));
memset(gap, 0, sizeof(gap));
dep[t] = 0; gap[0]++;
queue<int> q; q.push(t);
while (!q.empty()) {
int u = q.front(); q.pop();
for (Edge *e = head[u]; e; e = e->next) {
int v = e->to;
if (dep[v] != -1) continue;
q.push(v);
dep[v] = dep[u] + 1;
gap[dep[v]]++;
}
}
}
int Dfs(int u, int flow) {
if (u == t) {
res += flow;
return flow;
}
int used = 0;
for (Edge *&e = cur[u]; e; e = e->next) {
int v = e->to;
if (e->val && dep[v] == dep[u] - 1) {
int mi = Dfs(v, min(e->val, flow - used));
if (mi) {
e->val -= mi;
e->ops->val += mi;
used += mi;
}
if (used == flow) return used;
}
}
cur[u] = head[u];
gap[dep[u]]--;
if (gap[dep[u]] == 0) dep[s] = n * m + 3;
dep[u]++;
gap[dep[u]]++;
return used;
}
void Work() {
memcpy(cur, head, sizeof(head));
res = 0;
Bfs();
while (dep[s] <= n * m + 2) Dfs(s, INF);
}
int num[MAXN][MAXN];
int main() {
ios :: sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
cin >> m >> n;
s = 0; t = n * m + 1;
int sum = 0;
for (int i = 1; i <= m; i++)
for (int j = 1; j <= n; j++)
cin >> num[i][j], sum += num[i][j];
for (int i = 1; i <= m; i++) {
for (int j = 1; j <= n; j++) {
if ((i + j) % 2 == 1) {
AddEdge(0, ID(i, j), num[i][j]);
if (i > 1) AddEdge(ID(i, j), ID(i - 1, j), INF);
if (i < m) AddEdge(ID(i, j), ID(i + 1, j), INF);
if (j > 1) AddEdge(ID(i, j), ID(i, j - 1), INF);
if (j < n) AddEdge(ID(i, j), ID(i, j + 1), INF);
} else {
AddEdge(ID(i, j), n * m + 1, num[i][j]);
}
}
}
Work();
cout << sum - res << endl;
return 0;
}
```
~~如果做过方格取数的话,直接拷贝进来就A了,注意下数组大小~~