洛谷 P1251 餐巾计划问题(线性规划网络优化)【费用流】

(题外话:心塞...大部分时间都在debug,拆点忘记加N,总边数算错,数据类型标错,字母写错......)

题目链接:https://www.luogu.org/problemnew/show/P1251

洛谷 P1251 餐巾计划问题

洛谷 P1251 餐巾计划问题(线性规划网络优化)【费用流】

洛谷 P1251 餐巾计划问题(线性规划网络优化)【费用流】

输入输出样例

输入样例#1:
3
1 7 5
11 2 2 3 1
输出样例#1:
134

说明

N<=2000

ri<=10000000

p,f,s<=10000

时限4s

题解:拆点再跑费用流呗,第i天拆成Xi(脏的餐巾)和Yi(干净的餐巾)。对于每天情况,建图示例如下(解释详见代码注释):

洛谷 P1251 餐巾计划问题(线性规划网络优化)【费用流】

代码:

 #include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N = ;
const int M = ;
const ll INF = 1e18;
const int INF2 = 1e9;
struct Edge { int to,next,cap,flow,cost; }edge[M];
int head[N],tol;
int pre[N];
ll dis[N];
bool vis[N];
int V;
void init(int n) {
V = n;
tol = ;
memset(head,-,sizeof(head));
}
void addedge(int u,int v,int cap,int cost) {
edge[tol].to = v; edge[tol].cap = cap; edge[tol].cost = cost; edge[tol].flow = ; edge[tol].next = head[u]; head[u] = tol++;
edge[tol].to = u; edge[tol].cap = ; edge[tol].cost = -cost; edge[tol].flow = ; edge[tol].next = head[v]; head[v] = tol++;
}
bool spfa(int s,int t) {
queue<int>q;
for(int i = ;i < V;i++) {
dis[i] = INF;
vis[i] = false;
pre[i] = -;
}
dis[s] = ;
vis[s] = true;
q.push(s);
while(!q.empty()) {
int u = q.front();
q.pop();
vis[u] = false;
for(int i = head[u]; i != -;i = edge[i].next) {
int v = edge[i].to;
if(edge[i].cap > edge[i].flow && dis[v] > dis[u] + edge[i].cost ) {
dis[v] = dis[u] + edge[i].cost;
pre[v] = i;
if(!vis[v]) {
vis[v] = true;
q.push(v);
}
}
}
}
if(pre[t] == -) return false;
else return true;
}
ll minCostMaxflow(int s,int t,ll &cost) {
ll flow = ;
cost = ;
while(spfa(s,t)) {
ll Min = INF;
for(int i = pre[t];i != -;i = pre[edge[i^].to]) {
if(Min > edge[i].cap - edge[i].flow)
Min = edge[i].cap - edge[i].flow;
}
for(int i = pre[t];i != -;i = pre[edge[i^].to]) {
edge[i].flow += Min;
edge[i^].flow -= Min;
cost += edge[i].cost * Min;
}
flow += Min;
}
return flow;
}
int main() {
int n, r, i, j, p, m, f, nn, s;
ll ans = ;
scanf("%d", &n);
init(n*+); int S = n*+, T = n*+; for(i = ; i <= n; ++i) {
scanf("%d", &r);//每天需要餐巾数
addedge(S, i, r, );
addedge(i+n, T, r, );
}
scanf("%d%d%d%d%d", &p, &m, &f, &nn, &s);
for(i = ; i <= n; ++i) {
addedge(S, i+n, INF2, p);//购买新餐巾
if(i+m<=n) addedge(i, i+m+n, INF2, f);//快洗
if(i+nn<=n) addedge(i, i+nn+n, INF2, s);//慢洗
if(i!=n) addedge(i, i+, INF2, );//留到第二天
} minCostMaxflow(S, T, ans);
printf("%lld\n", ans);
return ;
}
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