http://www.lydsy.com/JudgeOnline/problem.php?id=4070
分块建图。
对每个(P_i)分类讨论,(P_i>sqrt N)则直接连边,边数少于(sqrt N)。
对每个横跨长度(leqsqrt N)的边,建一条“滑轨”,当(P_ileqsqrt N)时则把这个点送到滑轨上,可以到任何一个位置下来。一共要建(sqrt N)条滑轨。
最后跑最短路就可以了,uoj上死活过不了hack数据,貌似过了的都没有建图?
时间复杂度(O(nsqrt n)),如果spfa是(O(m))的话。
#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N = 30003;
const int B = 113;
const int Qtot = N * B - 1;
int nxt[N * B * 5], to[N * B * 5], w[N * B * 5];
int point[N * B], cnt = 0, n, m, S[N], P[N];
void ins(int u, int v, int W) {
nxt[++cnt] = point[u]; to[cnt] = v; w[cnt] = W; point[u] = cnt;
}
bool inq[N * B];
int dist[N * B], tot;
queue <int> qu;
int spfa(int s, int t) {
memset(dist, 127, sizeof(int) * (tot + 1));
dist[s] = 0;
int u, v, di; qu.push(s); inq[s] = true;
while (!qu.empty()) {
inq[u = qu.front()] = false; qu.pop();
for (int i = point[u]; i; i = nxt[i]) {
v = to[i];
if ((di = dist[u] + w[i]) < dist[v]) {
dist[v] = di;
if (!inq[v]) {
inq[v] = true;
qu.push(v);
}
}
}
}
return dist[t] == dist[0] ? -1 : dist[t];
}
int main() {
scanf("%d%d", &n, &m);
int Si, Pi; tot = B * n;
int tt = n;
for (int i = 1; i < B; ++i)
for (int j = 1; j <= n; ++j)
ins(++tt, j, 0);
for (int i = 1; i < B; ++i)
for (int j = 1; j <= i; ++j) {
int tmp = j + i, st = i * n;
while (tmp <= n) {
ins(st + tmp - i, st + tmp, 1);
ins(st + tmp, st + tmp - i, 1);
tmp += i;
}
}
for (int i = 1; i <= m; ++i) {
scanf("%d%d", &Si, &Pi);
S[i] = ++Si; P[i] = Pi;
if (Pi >= B) {
for (int tmp = Si + Pi, j = 1; tmp <= n; tmp += Pi, ++j)
ins(Si, tmp, j);
for (int tmp = Si - Pi, j = 1; tmp >= 1; tmp -= Pi, ++j)
ins(Si, tmp, j);
} else
ins(Si, Pi * n + Si, 0);
}
printf("%d
", spfa(S[1], S[2]));
return 0;
}