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

/**************************************************************
    Problem: 1579
    User: rausen
    Language: C++
    Result: Accepted
    Time:4312 ms
    Memory:3872 kb
****************************************************************/
 
#include <cstdio>
#include <cstring>
#include <algorithm>
 
using namespace std;
const int N = 1e4 + 5;
const int M = 5e4 + 5;
const int K = 25;
const int inf = 1e9;
const int Maxlen = M * 3 * 10;
 
struct edge {
    int next, to, v;
    edge(int _n = 0, int _t = 0, int _v = 0) : next(_n), to(_t), v(_v) {}
} e[M << 1];
 
int n, m, k;
int first[N], tot;
int dis[N], tmp[N], v[N];
 
char buf[Maxlen], *c = buf;
int Len;
 
inline int read();
 
inline void Add_Edges(int x, int y, int z) {
    e[++tot] = edge(first[x], y, z), first[x] = tot;
    e[++tot] = edge(first[y], x, z), first[y] = tot;
}
 
#define y e[x].to
void spfa(int S) {
    static int i, x, q[70000], p;
    static unsigned short l, r;
    for (i = 1; i <= n; ++i) dis[i] = i == S ? 0 : inf;
    q[l = r = 0] = S, v[S] = 1;
    for (i = 1; i <= k + 1; ++i) {
        while (l != r + 1) {
            p = q[l++];
            for (x = first[p]; x; x = e[x].next)
                if (dis[p] + e[x].v < dis[y]) {
                    dis[y] = dis[p] + e[x].v;
                    if (!v[y]) {
                        v[y] = 1;
                        if (dis[y] < dis[q[l]]) q[--l] = y;
                        else q[++r] = y;
                    }
                }
            v[p] = 0;
        }
        if (i == k + 1) continue;
        for (p = 1; p <= n; ++p)
            for (tmp[p] = inf, x = first[p]; x; x = e[x].next)
                tmp[p] = min(tmp[p], dis[y]);
        memcpy(dis, tmp, sizeof(dis));
        for (p = 1; p <= n; ++p)
            if (!v[p]) {
                v[p] = 1;
                if (dis[p] < dis[q[l]]) q[--l] = p;
                else q[++r] = p;
            }
    }
}
#undef y
 
int main() {
    Len = fread(c, 1, Maxlen, stdin);
    buf[Len] = '';
    int i, x, y, z;
    n = read(), m = read(), k = read();
    for (i = 1; i <= m; ++i) {
        x = read(), y = read(), z = read();
        Add_Edges(x, y, z);
    }
    spfa(1);
    printf("%d
", dis[n]);
    return 0;
}
 
inline int read() {
    int x = 0;
    while (*c < '0' || '9' < *c) ++c;
    while ('0' <= *c && *c <= '9')
        x = x * 10 + *c - '0', ++c;
    return x;
}