BZOJ1579 [Usaco2009 Feb]Revamping Trails 道路升级

各种神作不解释QAQQQ

先是写了个作死的spfa本机过了交上去T了。。。

然后不想写Dijkstra各种自暴自弃。。。

最后改了一下步骤加了个SLF过了。。。

首先一个trivial的想法是$dis[p][t]$表示到了$p$号节点，用了$t$次变0技能，然后可以用$dis[q][t] + e[q][p]$和$dis[q][t - 1] + e[q][p] * 0$来更新

然后点数$O(n * k)$，边数$O(m * k)$，再加上usaco硬卡spfa。。。什么最终鬼畜。。。

其实我们可以这样子想：

先把用了$t$次技能的$dis$先算出来，这就是用$dis[q][t] + e[q][p]$更新

然后计算用了$t + 1$次技能，方法就是先用$dis[q]$更新$dis[p]$表示用了一次技能，再跑一边spfa就好了

 1 /**************************************************************
 2     Problem: 1579
 3     User: rausen
 4     Language: C++
 5     Result: Accepted
 6     Time:4312 ms
 7     Memory:3872 kb
 8 ****************************************************************/
 9
10 #include <cstdio>
11 #include <cstring>
12 #include <algorithm>
13
14 using namespace std;
15 const int N = 1e4 + 5;
16 const int M = 5e4 + 5;
17 const int K = 25;
18 const int inf = 1e9;
19 const int Maxlen = M * 3 * 10;
20
21 struct edge {
22     int next, to, v;
23     edge(int _n = 0, int _t = 0, int _v = 0) : next(_n), to(_t), v(_v) {}
24 } e[M << 1];
25
26 int n, m, k;
27 int first[N], tot;
28 int dis[N], tmp[N], v[N];
29
30 char buf[Maxlen], *c = buf;
31 int Len;
32
33 inline int read();
34
35 inline void Add_Edges(int x, int y, int z) {
36     e[++tot] = edge(first[x], y, z), first[x] = tot;
37     e[++tot] = edge(first[y], x, z), first[y] = tot;
38 }
39
40 #define y e[x].to
41 void spfa(int S) {
42     static int i, x, q[70000], p;
43     static unsigned short l, r;
44     for (i = 1; i <= n; ++i) dis[i] = i == S ? 0 : inf;
45     q[l = r = 0] = S, v[S] = 1;
46     for (i = 1; i <= k + 1; ++i) {
47         while (l != r + 1) {
48             p = q[l++];
49             for (x = first[p]; x; x = e[x].next)
50                 if (dis[p] + e[x].v < dis[y]) {
51                     dis[y] = dis[p] + e[x].v;
52                     if (!v[y]) {
53                         v[y] = 1;
54                         if (dis[y] < dis[q[l]]) q[--l] = y;
55                         else q[++r] = y;
56                     }
57                 }
58             v[p] = 0;
59         }
60         if (i == k + 1) continue;
61         for (p = 1; p <= n; ++p)
62             for (tmp[p] = inf, x = first[p]; x; x = e[x].next)
63                 tmp[p] = min(tmp[p], dis[y]);
64         memcpy(dis, tmp, sizeof(dis));
65         for (p = 1; p <= n; ++p)
66             if (!v[p]) {
67                 v[p] = 1;
68                 if (dis[p] < dis[q[l]]) q[--l] = p;
69                 else q[++r] = p;
70             }
71     }
72 }
73 #undef y
74
75 int main() {
76     Len = fread(c, 1, Maxlen, stdin);
77     buf[Len] = ‘\0‘;
78     int i, x, y, z;
79     n = read(), m = read(), k = read();
80     for (i = 1; i <= m; ++i) {
81         x = read(), y = read(), z = read();
82         Add_Edges(x, y, z);
83     }
84     spfa(1);
85     printf("%d\n", dis[n]);
86     return 0;
87 }
88
89 inline int read() {
90     int x = 0;
91     while (*c < ‘0‘ || ‘9‘ < *c) ++c;
92     while (‘0‘ <= *c && *c <= ‘9‘)
93         x = x * 10 + *c - ‘0‘, ++c;
94     return x;
95 }