ACM-ICPC 2018 焦作賽區網路預賽 F. Modular Production Line (K區間覆蓋、最小費用流)
阿新 • • 發佈:2018-12-11
題意:
一個工廠有N個部分,M個部件。每個部件分別需要從Li~Ri部分進行加工,獲得收益Wi。
限制每個部分最多使用K次,並且每個部件最多隻能加工一次,問最大收益。
思路:
因為最多隻有200*2=400個點,但N的範圍為1e5,因此需要先將點離散化,從小到大排序。
之後建立一個源點S,向第一個點連一條流量為K,費用為0的邊。
對於每一對L、R,從L向R+1連一條流量為1,費用為-Wi的邊。
最後對於所有點,從i向i+1連一條流量為INF,費用為0的邊。
之後跑一遍最小費用流再將結果取相反數就可以了。
AC程式碼:
#include<iostream> #include<cstdio> #include<cstring> #include<string> #include<cstdlib> #include<utility> #include<algorithm> #include<utility> #include<queue> #include<vector> #include<set> #include<stack> #include<cmath> #include<map> #include<ctime> #include<functional> #include<bitset> #define P pair<int,int> #define ll long long #define ull unsigned long long #define lson id*2,l,mid #define rson id*2+1,mid+1,r #define ls id*2 #define rs (id*2+1) #define Mod(a,b) a<b?a:a%b+b #define cl0(a) memset(a,0,sizeof(a)) #define cl1(a) memset(a,-1,sizeof(a)) using namespace std; const ll M = 1e9 + 7; const ll INF = 1e9; const int N = 410; const double _e = 10e-6; const int maxn = 5e4 + 10; const int matSize = 9; const int dx[4] = { 0,0,1,-1 }, dy[4] = { 1,-1,0,0 }; const int _dx[8] = { -1,-1,-1,0,0,1,1,1 }, _dy[8] = { -1,0,1,-1,1,-1,0,1 }; struct edge { int to, next, cap, flow, cost; }G[N * 2]; int head[N], tol, pre[N], dis[N], V; bool vis[N]; void init(int n) { V = n; tol = 0; memset(head, -1, sizeof(head)); } void add_edge(int u, int v, int cap, int cost) { G[tol].to = v; G[tol].cap = cap; G[tol].cost = cost; G[tol].flow = 0; G[tol].next = head[u]; head[u] = tol++; G[tol].to = u; G[tol].cap = 0; G[tol].cost = -cost; G[tol].flow = 0; G[tol].next = head[v]; head[v] = tol++; } bool spfa(int s, int t) { queue<int>q; for (int i = 0; i < V; i++) { dis[i] = INF; vis[i] = false; pre[i] = -1; } dis[s] = 0; vis[s] = true; q.push(s); while (!q.empty()) { int u = q.front(); q.pop(); vis[u] = false; for (int i = head[u]; i != -1; i = G[i].next) { int v = G[i].to; if (G[i].cap>G[i].flow&&dis[v]>dis[u] + G[i].cost) { dis[v] = dis[u] + G[i].cost; pre[v] = i; if (!vis[v]) { vis[v] = true; q.push(v); } } } } if (pre[t] == -1) return false; else return true; } int mcmf(int s, int t, int &cost) { int flow = 0; cost = 0; while (spfa(s, t)) { int minn = INF; for (int i = pre[t]; i != -1; i = pre[G[i ^ 1].to]) { if (minn>G[i].cap - G[i].flow) minn = G[i].cap - G[i].flow; } for (int i = pre[t]; i != -1; i = pre[G[i ^ 1].to]) { G[i].flow += minn; G[i ^ 1].flow -= minn; cost += G[i].cost*minn; } flow += minn; } return flow; } struct node { int l, r; int val; }; int x, y, n, m; int k, v; node a[210]; int b[410]; map<int, int> mp; int main() { int t; scanf("%d", &t); while (t--) { scanf("%d%d%d", &n, &k, &m); int cnt = 1; mp.clear(); for (int i = 0; i < m; i++) { scanf("%d%d%d", &a[i].l, &a[i].r, &a[i].val); b[i * 2] = a[i].l; b[i * 2 + 1] = a[i].r; } sort(b, b + m * 2); mp[b[0]] = cnt; for (int i = 1; i < m * 2; i++) { if (b[i] != b[i - 1]) mp[b[i]] = cnt++; } init(cnt + 2); int S = cnt + 1, T = cnt; for (int i = 0; i < m; i++) add_edge(mp[a[i].l] - 1, mp[a[i].r], 1, -a[i].val); add_edge(S, 0, k, 0); for (int i = 0; i < cnt; i++) add_edge(i, i + 1, INF, 0); int ans = 0; mcmf(S, T, ans); printf("%d\n", -ans); } return 0; }