【BZOJ4514】【SDOI2016】数字配对_数字配对 c++-优快云博客

本文介绍了一种基于最小费用最大流算法的实现方案，包括关键的数据结构定义、SPFA算法的应用以及如何寻找增广路径等内容。通过具体的代码示例展示了如何解决一类特殊的网络流问题。

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【题目链接】

点击打开链接

【思路要点】

补档博客，无题解。

【代码】

#include<bits/stdc++.h>
using namespace std;
#define MAXN	505
#define INF	1e18
#define MAXQ	1000005
template <typename T> void read(T &x) {
	x = 0; int f = 1;
	char c = getchar();
	for (; !isdigit(c); c = getchar()) if (c == '-') f = -f;
	for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
	x *= f;
}
struct edge {int dest, flow; long long cost; unsigned home; };
int n, s, t, flow;
long long cost, len;
long long dist[MAXN], c[MAXN];
int path[MAXN], value[MAXN], cnt[MAXN];
unsigned home[MAXN];
vector <edge> a[MAXN];
vector <int> b[MAXN];
bool visited[MAXN], colour[MAXN], unsolved;
void flow_path() {
	int p = t, ans = 1e9;
	while (p != s) {
		ans = min(ans, a[path[p]][home[p]].flow);
		p = path[p];
	}
	if (cost + ans * len < 0) {
		unsolved = false;
		ans = cost / (-len);
	}
	flow += ans, cost += ans * len;
	p = t;
	while (p != s) {
		a[path[p]][home[p]].flow -= ans;
		a[p][a[path[p]][home[p]].home].flow += ans;
		p = path[p];
	}
}
bool spfa() {
	static int q[MAXQ];
	static bool inq[MAXN];
	int l = 0, r = 0;
	q[0] = s, inq[s] = true, dist[s] = 0;
	while (l <= r) {
		int tmp = q[l++];
		inq[tmp] = false;
		for (unsigned i = 0; i < a[tmp].size(); i++)
			if (a[tmp][i].flow != 0 && dist[a[tmp][i].dest] < dist[tmp] + a[tmp][i].cost) {
				dist[a[tmp][i].dest] = dist[tmp] + a[tmp][i].cost;
				path[a[tmp][i].dest] = tmp;
				home[a[tmp][i].dest] = i;
				if (!inq[a[tmp][i].dest]) {
					inq[a[tmp][i].dest] = true;
					q[++r] = a[tmp][i].dest;
				}
			}
	}
	len = dist[t];
	for (int i = 0; i <= r; i++)
		dist[q[i]] = -INF;
	return len != -INF;
}
void addedge(int s, int t, int flow, long long cost) {
	a[s].push_back((edge) {t, flow, cost, a[t].size()});
	a[t].push_back((edge) {s, 0, -cost, a[s].size() - 1});
}
bool prime(int value) {
	if (value == 1) return false;
	int tmp = sqrt(value);
	for (int i = 2; i <= tmp; i++)
		if (value % i == 0) return false;
	return true;
}
void work(int pos) {
	visited[pos] = true;
	for (unsigned i = 0; i < b[pos].size(); i++)
		if (!visited[b[pos][i]]) {
			colour[b[pos][i]] = !colour[pos];
			work(b[pos][i]);
		}
}
int main() {
	read(n);
	for (int i = 1; i <= n; i++)
		read(value[i]);
	for (int i = 1; i <= n; i++)
		read(cnt[i]);
	for (int i = 1; i <= n; i++)
		read(c[i]);
	for (int i = 1; i <= n; i++)
	for (int j = 1; j <= n; j++)
		if (value[i] % value[j] == 0 && prime(value[i] / value[j])) {
			b[i].push_back(j);
			b[j].push_back(i);
		}
	for (int i = 1; i <= n; i++)
		if (!visited[i]) work(i);
	s = 0, t = n + 1;
	for (int i = 1; i <= n; i++)
		if (colour[i]) {
			addedge(s, i, cnt[i], 0);
			for (unsigned j = 0; j < b[i].size(); j++)
				addedge(i, b[i][j], 1e9, c[i] * c[b[i][j]]);
		} else addedge(i, t, cnt[i], 0);
	for (int i = 0; i <= n + 1; i++)
		dist[i] = -INF;
	unsolved = true;
	while (unsolved && spfa())
		flow_path();
	cout << flow << endl;
	return 0;
}