P1453 城市环路

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#include<cstdio>
#include<cstring>
#include<queue>
using namespace std;
#define re register
const int MAXn = 1e5;
const int MAXm = MAXn;
const int INF = 0x3f3f3f3f;

template <class T>
inline void read(T &a) {
register char c;while (c = getchar(), c < '0' || c > '9');register T x(c - '0');while (c = getchar(), c >= '0' && c <= '9') {x = (x << 1) + (x << 3) + (c ^ 48);}a = x;
}

int head[MAXn + 10], cntnex, nex[MAXm * 2 + 10], to[MAXm * 2 + 10];
void Insert(int u, int v) {
nex[++cntnex] = head[u];
head[u] = cntnex;
to[cntnex] = v;
}

double k;
int n, a[MAXn + 10], deg[MAXn + 10];

queue<int> q;
bool vis[MAXn + 10];
int cntring, ring[MAXn + 10];
void EvaRing() {
for (re int i = 1; i <= n; ++i) {
if (deg[i] == 1) {
q.push(i);
}
}
int cur;
while (!q.empty()) {
cur = q.front(); q.pop();
vis[cur] = 1;
for (re int i = head[cur]; i; i = nex[i]) {
if (!vis[to[i]]) {
--deg[to[i]];
if (deg[to[i]] == 1) {
q.push(to[i]);
}
}
}
}
for (re int i = 1; i <= n; ++i) {
if (deg[i] == 2) {
vis[i] = 1;
ring[++cntring] = i;
break;
}
}
bool ok = 1;
while (ok) {
ok = 0;
for (re int i = head[ring[cntring]]; i; i = nex[i]) {
if (vis[to[i]] || deg[to[i]] == 1) continue;
vis[to[i]] = 1;
ring[++cntring] = to[i];
ok = 1;
break;
}
}
}

int d[MAXn + 10][2];
void dp(int cur) {
vis[cur] = 1;
for (re int i = head[cur]; i; i = nex[i]) {
if (vis[to[i]] || deg[to[i]] == 2) continue;
dp(to[i]);
d[cur][0] += max(d[to[i]][1], d[to[i]][0]);
d[cur][1] += d[to[i]][0];
}
d[cur][1] += a[cur];
}
void Dp() {
memset(vis, 0, sizeof(vis));
for (re int i = 1; i <= cntring; ++i) {
dp(ring[i]);
}
}

int f[MAXn + 10][2][2];
int Dp2() {
f[1][0][0] = d[ring[1]][0];
f[1][1][1] = d[ring[1]][1];
f[1][0][1] = f[1][1][0] = -INF;
for (re int i = 2; i <= cntring; ++i) {
f[i][0][0] = max(f[i - 1][0][0], f[i - 1][0][1]) + d[ring[i]][0];
f[i][0][1] = f[i - 1][0][0] + d[ring[i]][1];
f[i][1][0] = max(f[i - 1][1][0], f[i - 1][1][1]) + d[ring[i]][0];
f[i][1][1] = f[i - 1][1][0] + d[ring[i]][1];
}
return max(max(f[cntring][0][0], f[cntring][0][1]), f[cntring][1][0]);
}

int main() {
read(n);
for (re int i = 1; i <= n; ++i) {
read(a[i]);
}
for (re int i = 1, u, v; i <= n; ++i) {
read(u), read(v);
++u; ++v;
++deg[u]; ++deg[v];
Insert(u, v); Insert(v, u);
}
scanf("%lf", &k);
EvaRing();
Dp();
printf("%.1lf\n", (double)Dp2() * k);
}

基环树求环长度和环上每个节点前的边的长度:

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int cntinring, ring[MAXnd + 10], ringdis;
int ndwei[MAXnd + 10];
void EvaRing(int cur, int fromedge, int begin) {
for (int i = head[cur]; i; i = nex[i]) {
if (iscut[i] || i == (fromedge ^ 1)) continue;
ring[++cntinring] = to[i];
ringdis += wei[i];
ndwei[to[i]] = wei[i];
if (to[i] != begin) EvaRing(to[i], i, begin);
if (cur == begin) break;
}
}