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As long as Binbin loves Sangsang
题目连接
- 题意:
给定一个无向图,每个边有两个属性,长度和一个字母‘L‘,’O‘,‘V’,‘E‘中的一个。从1点开始到达n点,每次必须按照L -> O -> V -> E -> ... -> E的顺序,到达终点时候必须经过E边 - 分析:
对于这种对边的限制,比较简单的方法是将一个点拆成若干个点。因为经过’L‘到达点p的状态和经过‘O‘到达点p的状态时不一样的,第一个之后只能经过’O‘边,而第二个只能经过‘V‘边,所以经过不同的边到达同一个点的时候对应的状态应该分开,也就是将点拆分成四个点,分别表示经过四种边到达p点。 - 注意:
图可以有自环,也可以只有一个点
路径必须至少有一个LOVE
路径长度尽可能小,长度若相等,那么LOVE的数量尽可能多
Dijkstra方法:(一个点的时候直接特判,避免不必要的麻烦)
const LL INF = 1e18; const int MAXV = 10000; struct Edge { LL from, to, dist; }; struct HeapNode { LL d, u, num; bool operator < (const HeapNode& rhs) const { return d > rhs.d; } }; struct Dijkstra { int n; //n:点数 m:临时变量 vector<Edge> edges; //存储所有的边 vector<int> G[MAXV];//每个点的所有相邻边序号 bool done[MAXV]; // 是否已永久标号 LL d[MAXV]; // s起点到各个点的距离 LL num[MAXV]; void init(int n) { this->n = n; for(int i = 0; i < n; i++) G[i].clear(); edges.clear(); } void AddEdge(int from, int to, int dist) { G[from].push_back(edges.size()); edges.push_back((Edge) { from, to, dist }); } void dijkstra(int s) { priority_queue<HeapNode> Q; for(int i = 0; i < n; i++) d[i] = INF; CLR(num, 0); d[s] = 0; memset(done, 0, sizeof(done)); Q.push((HeapNode) { 0, s, 0 }); while(!Q.empty()) { HeapNode x = Q.top(); Q.pop(); int u = x.u; if(done[u]) continue; done[u] = true; for(int i = 0; i < G[u].size(); i++) { Edge& e = edges[G[u][i]]; if (d[e.to] == d[u] + e.dist) num[e.to] = max(num[e.to], num[x.u] + 1); if(d[e.to] > d[u] + e.dist) { d[e.to] = d[u] + e.dist; num[e.to] = num[x.u] + 1; Q.push((HeapNode) { d[e.to], e.to, num[e.to] }); } } } } } dij; LL chk[4]; int main() { int T; RI(T); FE(kase, 1, T) { REP(i, 4) chk[i] = INF; int n, m, u, v, d, op; char type; RII(n, m); dij.init(n << 2); REP(i, m) { scanf("%d%d%d %c", &u, &v, &d, &type); u--; v--; if (type == 'L') op = 0; else if (type == 'O') op = 1; else if (type == 'V') op = 2; else op = 3; chk[op] = min(chk[op], (LL)d); dij.AddEdge(u + (op + 3) % 4 * n, v + op * n, d); dij.AddEdge(v + (op + 3) % 4 * n, u + op * n, d); } printf("Case %d: ", kase); if (n == 1) { REP(i, 4) if (chk[i] == INF) { puts("Binbin you disappoint Sangsang again, damn it!"); goto end; } printf("Cute Sangsang, Binbin will come with a donkey after travelling %I64d meters and finding %d LOVE strings at last.\n" , chk[0] + chk[1] + chk[2] + chk[3], 1); end:; } else { dij.dijkstra(3 * n); if (dij.d[4 * n - 1] == INF) puts("Binbin you disappoint Sangsang again, damn it!"); else { printf("Cute Sangsang, Binbin will come with a donkey after travelling %I64d meters and finding %I64d LOVE strings at last.\n" , dij.d[4 * n - 1], dij.num[4 * n - 1] / 4); } } } return 0; }
spfa方法:(一个点也是特判,加点方式与Dijkstra相同)
const LL INF = 1e18; const int MAXV = 10000; struct Edge { int from, to, dist; }; struct SPFA { int n; LL d[MAXV]; int num[MAXV]; vector<Edge> edges; vector<int> G[MAXV]; bool inq[MAXV]; void init(int n) { this->n = n; edges.clear(); REP(i, n) G[i].clear(); } void AddEdge(int from, int to, int dist) { G[from].push_back(edges.size()); edges.push_back((Edge) {from, to, dist}); } void spfa(int s) { queue<int> q; CLR(inq, false); CLR(num, 0); REP(i, n) d[i] = INF; d[s] = 0; q.push(s); inq[s] = true; while (!q.empty()) { int u = q.front(); q.pop(); inq[u] = false; REP(i, G[u].size()) { Edge& e = edges[G[u][i]]; if (d[e.to] == d[u] + e.dist && num[u] + 1 > num[e.to]) { num[e.to] = num[u] + 1; if (!inq[e.to]) { q.push(e.to); inq[e.to] = true; } } if(d[e.to] > d[u] + e.dist) { d[e.to] = d[u] + e.dist; num[e.to] = num[u] + 1; if (!inq[e.to]) { q.push(e.to); inq[e.to] = true; } } } } } } spfa; LL chk[4]; int main() { int T; RI(T); FE(kase, 1, T) { REP(i, 4) chk[i] = INF; int n, m, u, v, d, op; char type; RII(n, m); spfa.init(n << 2); REP(i, m) { scanf("%d%d%d %c", &u, &v, &d, &type); u--; v--; if (type == 'L') op = 0; else if (type == 'O') op = 1; else if (type == 'V') op = 2; else op = 3; chk[op] = min(chk[op], (LL)d); spfa.AddEdge(u + (op + 3) % 4 * n, v + op * n, d); spfa.AddEdge(v + (op + 3) % 4 * n, u + op * n, d); } printf("Case %d: ", kase); if (n == 1) { REP(i, 4) if (chk[i] == INF) { puts("Binbin you disappoint Sangsang again, damn it!"); goto end; } printf("Cute Sangsang, Binbin will come with a donkey after travelling %I64d meters and finding %d LOVE strings at last.\n" , chk[0] + chk[1] + chk[2] + chk[3], 1); end:; } else { spfa.spfa(3 * n); if (spfa.d[4 * n - 1] == INF) puts("Binbin you disappoint Sangsang again, damn it!"); else { printf("Cute Sangsang, Binbin will come with a donkey after travelling %I64d meters and finding %d LOVE strings at last.\n" , spfa.d[4 * n - 1], spfa.num[4 * n - 1] / 4); } } } return 0; }
顺便弄一些自己的测试数据,方便查错。
4 4
1 2 1 L
2 1 1 O
1 3 1 V
3 4 1 E
ans:4, 1
4 4
1 2 1 L
2 3 1 O
3 4 1 V
4 1 1 E
ans:no
12 12
1 5 10 L
5 6 10 O
6 7 10 V
7 12 10 E
1 2 1 L
2 3 1 O
3 4 1 V
4 8 1 E
8 9 1 L
9 10 1 O
10 11 1 V
11 12 33 E
ans:40, 2
12 12
1 5 10 L
5 6 10 O
6 7 10 V
7 12 10 E
1 2 1 L
2 3 1 O
3 4 1 V
4 8 1 E
8 9 1 L
9 10 1 O
10 11 1 V
11 12 34 E
ans:40, 1
1 4
1 1 1 L
1 1 1 O
1 1 1 V
1 1 1 E
ans:4, 1
2 8
1 1 2 L
1 1 1 O
1 1 1 V
1 1 1 E
1 2 3 L
2 1 1 O
1 2 1 V
2 1 1 E
ans:5, 1
1 3
1 1 1 L
1 1 1 O
1 1 1 E
ans:no
11 11
1 2 1 L
2 3 1 O
3 4 348 V
4 11 1000 E
1 5 50 L
5 6 50 O
6 7 50 V
7 8 50 E
8 9 50 L
9 10 50 O
10 4 50 V
ans:1350 2
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