[POJ3694]Network（LCA, 割边, 桥）

题目链接：http://poj.org/problem?id=3694

题意：给一张图，每次加一条边，问割边数量。

tarjan先找出所有割边，并且记录每个点的父亲和来自于哪一条边，然后询问的时候从两个点向上找lca，沿途更新割边数量和割边状态即可。

AC代码

/*
━━━━━┒ギリギリ♂ eye！
┓┏┓┏┓┃キリキリ♂ mind！
┛┗┛┗┛┃＼○／
┓┏┓┏┓┃ /
┛┗┛┗┛┃ノ)
┓┏┓┏┓┃
┛┗┛┗┛┃
┓┏┓┏┓┃
┛┗┛┗┛┃
┓┏┓┏┓┃
┛┗┛┗┛┃
┓┏┓┏┓┃
┃┃┃┃┃┃
┻┻┻┻┻┻
*/
#include                     <algorithm>
#include                     <iostream>
#include                     <iomanip>
#include                     <cstring>
#include                     <climits>
#include                     <complex>
#include                     <fstream>
#include                     <cassert>
#include                     <cstdio>
#include                     <bitset>
#include                     <vector>
#include                     <deque>
#include                     <queue>
#include                     <stack>
#include                     <ctime>
#include                     <set>
#include                     <map>
#include                     <cmath>
using namespace             std;
#define fr                     first
#define sc                     second
#define cl                     clear
#define BUG                 puts("here!!!")
#define W(a)                 while(a--)
#define pb(a)                 push_back(a)
#define Rint(a)             scanf("%d", &a)
#define Rll(a)                 scanf("%lld", &a)
#define Rs(a)                 scanf("%s", a)
#define Cin(a)                 cin >> a
#define FRead()             freopen("in", "r", stdin)
#define FWrite()             freopen("out", "w", stdout)
#define Rep(i, len)         for(int i = 0; i < (len); i++)
#define For(i, a, len)         for(int i = (a); i < (len); i++)
#define Cls(a)                 memset((a), 0, sizeof(a))
#define Clr(a, x)             memset((a), (x), sizeof(a))
#define Full(a)             memset((a), 0x7f7f, sizeof(a))
#define lp                    p << 1
#define rp                    p << 1 | 1
#define pi                    3.14159265359
#define RT                    return
typedef    long long             LL;
typedef    long double         LD;
typedef    unsigned long long     ULL;
typedef    pair<int, int>         pii;
typedef    pair<string, int>     psi;
typedef    map<string, int>     msi;
typedef    vector<int>         vi;
typedef    vector<LL>             vl;
typedef    vector<vl>             vvl;
typedef    vector<bool>         vb;

inline bool scan_d(int &num) {
char in;bool IsN=false;
in=getchar();
if(in==EOF) return false;
while(in!='-'&&(in<'0'||in>'9')) in=getchar();
if(in=='-'){ IsN=true;num=0;}
else num=in-'0';
while(in=getchar(),in>='0'&&in<='9'){
num*=10,num+=in-'0';
}
if(IsN) num=-num;
return true;
}

const int maxn = 200010;
const int maxm = 900020;

typedef struct Edge {
int idx, v;
Edge() {}
Edge(int vv, int ii) : v(vv), idx(ii) {}
}Edge;

int n, m, q, cnt, b;
int depth[maxn], fa[maxn], vis[maxn];
int dfn[maxn], low[maxn], pbr[maxm];
vector<Edge> G[maxn];
bool bri[maxm];
void dfs(int u, int p, int d) {
fa[u] = p; depth[u] = d;
Rep(i, G[u].size()) {
int v = G[u][i].v;
if(!vis[v]) {
vis[v] = 1;
dfs(v, u, d+1);
}
}
}

void tarjan(int u, int p, int d, int pe) {
low[u] = dfn[u] = d;
pbr[u] = pe;
Rep(i, G[u].size()) {
int idx = G[u][i].idx;
int v = G[u][i].v;
if(!dfn[v]) {
tarjan(v, u, d+1, idx);
low[u] = min(low[u], low[v]);
if(low[v] > dfn[u]) bri[idx] = 1;
}
else if(v != p) low[u] = min(low[u], dfn[v]);
}
}

void lca(int u, int v) {
while(depth[u] > depth[v]) {
if(bri[pbr[u]]) {
bri[pbr[u]] = 0; b--;
}
u = fa[u];
}
while(depth[v] > depth[u]) {
if(bri[pbr[v]]) {
bri[pbr[v]] = 0; b--;
}
v = fa[v];
}
while(u != v) {
if(bri[pbr[u]]) {
bri[pbr[u]] = 0; b--;
}
u = fa[u];
if(bri[pbr[v]]) {
bri[pbr[v]] = 0; b--;
}
v = fa[v];
}
}

int main() {
// FRead();
int u, v, _ = 1;
while(~scan_d(n) && ~scan_d(m) && n + m) {
Cls(depth); Cls(vis); Cls(fa); Cls(pbr);
Cls(dfn); Cls(low); Cls(bri); b = 0;
Rep(i, n+5) G[i].cl();
Rep(i, m) {
scan_d(u); scan_d(v);
G[u].pb(Edge(v, cnt++)); G[v].pb(Edge(u, cnt++));
}
dfs(1, 1, 0); tarjan(1, 1, 0, 0);
scan_d(q);
printf("Case %d:\n", _++);
For(i, 1, cnt+1) if(bri[i]) b++;
W(q) {
scan_d(u); scan_d(v);
lca(u, v);
printf("%d\n", b);
}
}
RT 0;
}

第一次TLE了，因为窝把erase的复杂度想象成了O(lgn)…

/*
━━━━━┒ギリギリ♂ eye！
┓┏┓┏┓┃キリキリ♂ mind！
┛┗┛┗┛┃＼○／
┓┏┓┏┓┃ /
┛┗┛┗┛┃ノ)
┓┏┓┏┓┃
┛┗┛┗┛┃
┓┏┓┏┓┃
┛┗┛┗┛┃
┓┏┓┏┓┃
┛┗┛┗┛┃
┓┏┓┏┓┃
┃┃┃┃┃┃
┻┻┻┻┻┻
*/
#include                     <algorithm>
#include                     <iostream>
#include                     <iomanip>
#include                     <cstring>
#include                     <climits>
#include                     <complex>
#include                     <fstream>
#include                     <cassert>
#include                     <cstdio>
#include                     <bitset>
#include                     <vector>
#include                     <deque>
#include                     <queue>
#include                     <stack>
#include                     <ctime>
#include                     <set>
#include                     <map>
#include                     <cmath>
using namespace             std;
#define fr                     first
#define sc                     second
#define cl                     clear
#define BUG                 puts("here!!!")
#define W(a)                 while(a--)
#define pb(a)                 push_back(a)
#define Rint(a)             scanf("%d", &a)
#define Rll(a)                 scanf("%lld", &a)
#define Rs(a)                 scanf("%s", a)
#define Cin(a)                 cin >> a
#define FRead()             freopen("in", "r", stdin)
#define FWrite()             freopen("out", "w", stdout)
#define Rep(i, len)         for(int i = 0; i < (len); i++)
#define For(i, a, len)         for(int i = (a); i < (len); i++)
#define Cls(a)                 memset((a), 0, sizeof(a))
#define Clr(a, x)             memset((a), (x), sizeof(a))
#define Full(a)             memset((a), 0x7f7f, sizeof(a))
#define lp                    p << 1
#define rp                    p << 1 | 1
#define pi                    3.14159265359
#define RT                    return
typedef    long long             LL;
typedef    long double         LD;
typedef    unsigned long long     ULL;
typedef    pair<int, int>         pii;
typedef    pair<string, int>     psi;
typedef    map<string, int>     msi;
typedef    vector<int>         vi;
typedef    vector<LL>             vl;
typedef    vector<vl>             vvl;
typedef    vector<bool>         vb;

inline bool scan_d(int &num) {
char in;bool IsN=false;
in=getchar();
if(in==EOF) return false;
while(in!='-'&&(in<'0'||in>'9')) in=getchar();
if(in=='-'){ IsN=true;num=0;}
else num=in-'0';
while(in=getchar(),in>='0'&&in<='9'){
num*=10,num+=in-'0';
}
if(IsN) num=-num;
return true;
}

const int maxn = 100010;
const int maxm = 300020;
typedef struct Bridge {
int u, v;
Bridge() {}
Bridge(int uu, int vv) : u(uu), v(vv) { if(u > v) swap(u, v); }
bool operator<(Bridge y) {
if(u == y.u) return v < y.v;
return u < y.u;
}
}Bridge;

int n, m, q;
int ufs[maxn];
int depth[maxn], fa[maxn], vis[maxn];
int dfn[maxn], low[maxn];
vi G[maxn];
vector<Bridge> b;
vector<Bridge>::iterator it;

int find(int x) {
return x == ufs[x] ? x : ufs[x] = find(ufs[x]);
}

void unite(int x, int y) {
x = find(x);
y = find(y);
if(x != y) ufs[y] = x;
}

void dfs(int u, int p, int d) {
fa[u] = p; depth[u] = d;
Rep(i, G[u].size()) {
int v = G[u][i];
if(!vis[v]) {
vis[v] = 1;
dfs(v, u, d+1);
}
}
}

void tarjan(int u, int p, int d) {
low[u] = dfn[u] = d;
Rep(i, G[u].size()) {
int v = G[u][i];
if(!dfn[v]) {
tarjan(v, u, d+1);
low[u] = min(low[u], low[v]);
if(low[v] > dfn[u]) b.pb(Bridge(u, v));
}
else if(v != p) low[u] = min(low[u], dfn[v]);
}
}

bool cmp(Bridge x, Bridge y) {
if(x.u == y.u) return x.v < y.v;
return x.u < y.u;
}

int bs(Bridge x) {
int lo = 0, hi = b.size();
while(lo <= hi) {
int mi = (lo + hi) >> 1;
if(b[mi].u == x.u && b[mi].v == x.v) return mi;
if(cmp(x, b[mi]) > 0) hi = mi - 1;
else lo = mi + 1;
}
if(b[lo].u == x.u && b[lo].v == x.v) return lo;
if(b[hi].u == x.u && b[hi].v == x.v) return hi;
return -1;
}

void lca(int u, int v) {
while(depth[u] > depth[v]) {
Bridge tmp = Bridge(u, fa[u]);
it = lower_bound(b.begin(), b.end(), tmp);
if(it != b.end() && it->u == tmp.u && it->v == tmp.v) b.erase(it);
u = fa[u];
}
while(depth[v] > depth[u]) {
Bridge tmp = Bridge(v, fa[v]);
it = lower_bound(b.begin(), b.end(), tmp);
if(it != b.end() && it->u == tmp.u && it->v == tmp.v) b.erase(it);
v = fa[v];
}
while(u != v) {
Bridge tmp = Bridge(u, fa[u]);
it = lower_bound(b.begin(), b.end(), tmp);
if(it != b.end() && it->u == tmp.u && it->v == tmp.v) b.erase(it);
tmp = Bridge(v, fa[v]);
it = lower_bound(b.begin(), b.end(), tmp);
if(it != b.end() && it->u == tmp.u && it->v == tmp.v) b.erase(it);
u = fa[u];
v = fa[v];
}
}

int main() {
// FRead();
int u, v, _ = 1;
while(~scan_d(n) && ~scan_d(m) && n + m) {
Cls(depth); Cls(vis); Cls(fa);
Cls(dfn); Cls(low); b.cl();
Rep(i, n+5) G[i].cl(), ufs[i] = i;
Rep(i, m) {
scan_d(u); scan_d(v);
G[u].pb(v); G[v].pb(u);
}
dfs(1, 1, 0); tarjan(1, 1, 0);
sort(b.begin(), b.end(), cmp);
scan_d(q);
printf("Case %d:\n", _++);
W(q) {
scan_d(u); scan_d(v);
Bridge tmp = Bridge(u, v);
it = lower_bound(b.begin(), b.end(), tmp);
if(it != b.end() && it->u == tmp.u && it->v == tmp.v) {
b.erase(it);
printf("%d\n", b.size());
continue;
}
else {
lca(u, v);
printf("%d\n", b.size());
}
}
}
RT 0;
}