【BZOJ 3445】【Usaco2014 Feb】Roadblock
http://www.lydsy.com/JudgeOnline/problem.php?id=3445
加倍的边一定在最短路上(否则继续走最短路)。
最短路长度是O(n)的,暴力扫最短路上的每条边,再暴力dijkstra,时间复杂度\(O(n^3)\)。
话说堆优dij的复杂度到底多少?\(O((n+m)logn)\)?\(O(nlogn+m)\)?
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N = 253;
int a[N][N], n, m, now, pre[N];
ll dist[N], shortest, t;
bool vis[N];
int main() {
int u, v, e;
memset(a, -1, sizeof(a));
scanf("%d%d", &n, &m);
for (int i = 1; i <= m; ++i) {
scanf("%d%d%d", &u, &v, &e);
a[u][v] = a[v][u] = e;
}
memset(dist, 127, sizeof(ll) * (n + 1));
dist[1] = 0;
for (int i = 1; i <= n; ++i) {
now = -1;
for (int j = 1; j <= n; ++j)
if (!vis[j] && ((dist[j] < dist[now]) || (now == -1)))
now = j;
if (now == -1) break;
for (int j = 1; j <= n; ++j)
if (!vis[j] && a[now][j] != -1 && (t = (dist[now] + a[now][j])) < dist[j]) {
dist[j] = t;
pre[j] = now;
}
vis[now] = true;
}
shortest = dist[n];
int tmp = n; ll ans = shortest;
while (tmp != 1) {
a[pre[tmp]][tmp] <<= 1;
a[tmp][pre[tmp]] <<= 1;
memset(dist, 127, sizeof(ll) * (n + 1));
memset(vis, 0, sizeof(bool) * (n + 1));
dist[1] = 0;
for (int i = 1; i <= n; ++i) {
now = -1;
for (int j = 1; j <= n; ++j)
if (!vis[j] && ((dist[j] < dist[now]) || (now == -1)))
now = j;
if (now == -1) break;
for (int j = 1; j <= n; ++j)
if (!vis[j] && a[now][j] != -1 && (t = (dist[now] + a[now][j])) < dist[j])
dist[j] = t;
vis[now] = true;
}
ans = max(ans, dist[n]);
a[pre[tmp]][tmp] >>= 1;
a[tmp][pre[tmp]] >>= 1;
tmp = pre[tmp];
}
printf("%lld\n", ans - shortest);
return 0;
}
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