2025-钉耙编程-中国大学生算法设计暑期联赛（9）——1006括号匹配（manacher 解决的是最长回文子串问题） · znzryb
## 思路讲解
不难发现，合法字符串必须包含 $()$ 字符。
于是套用manacher就行，注意特判radius=1的奇数长度回文串
```cpp
FOR(i,0,SZ(res)-1){
ll radius=res[i];radius/=2;
if(i&1){
if(radius<2) continue;
ll id1=i/2,id2=i/2+1,l=id1-radius+1,r=id2+radius-1;
// l=max(ban[id1]+1,l);
// r=min(Fban[id2]-1,r);
ll lans=0;
if(Pos[id1]!=-1){
if(Pos[id1]>=l){
lans=max(lans,Pos[id1]-l+1);
}
}
if(Fpos[id2]!=-1){
if(Fpos[id2]<=r){
lans=max(lans,r-Fpos[id2]+1);
}
}
ans+=lans;
}else{
if(radius<2) continue;
ll id=i/2;
ll l=id-radius+1,r=id+radius-1;
// l=max(ban[id]+1,l);
// r=min(Fban[id]-1,r);
ll lans=0;
if(Pos[id]!=-1){
if(Pos[id]>=l){
lans=max(lans,Pos[id]-l+1);
}
}
if(Fpos[id]!=-1){
if(Fpos[id]<=r){
lans=max(lans,r-Fpos[id]+1);
}
}
ans+=min(radius-1,lans);
}
}
```
## AC代码
[https://acm.hdu.edu.cn/contest/view-code?cid=1180&rid=12078](https://acm.hdu.edu.cn/contest/view-code?cid=1180&rid=12078)
::: 源代码
```cpp
// by Gospel_rock
#include <bits/stdc++.h>
#define all(vec) vec.begin(),vec.end()
#define PB push_back
#define EB emplace_back
#define EM emplace
#define FI first
#define SE second
#define pct __builtin_popcountll
#define ctz __builtin_ctzll
#define SZ(a) ((long long) a.size())
#define FOR(i, a, b) for (long long i = (a); i <= (b); ++i)
#define ROF(i, a, b) for (long long i = (a); i >= (b); --i)
#define debug(var) cerr << #var <<":"<<var<<"\n";
#define cend cerr<<"\n-----------\n"
#define lson(var) (var<<1)
#define rson(var) (var<<1|1)
#define fsp(x) fixed<<setprecision(x)
#define minn(vec) *min_element(vec.begin(),vec.end())
#define maxx(vec) *max_element(vec.begin(),vec.end())
using namespace std;
#ifdef LOCAL
template<typename T> void _print(T x) { cerr << x; }
template<typename T> void _print(vector<T> v) { cerr << "[ "; for (T i : v) _print(i), cerr << " "; cerr << "]"; }
template<typename T> void _print(set<T> s) { cerr << "{ "; for (T i : s) _print(i), cerr << " "; cerr << "}"; }
template<typename T, typename U> void _print(pair<T, U> p) { cerr << "{"; _print(p.first); cerr << ", "; _print(p.second); cerr << "}"; }
template<typename T, typename U> void _print(map<T, U> m) { cerr << "{ "; for (auto &p : m) _print(p), cerr << " "; cerr << "}"; }
#endif
using ll = long long;using ull = unsigned long long;
using DB=double;using LD=long double;
using i128 = __int128;
using pdd = pair<DB,DB>;using plb = pair<ll,bool>;
using pll = pair<ll,ll>;using vll=vector<ll>;using vb=vector<bool>;
using tll = tuple<ll,ll,ll>;using vii=vector<int>;
using vpll = vector<pll>;using vtll = vector<tll>;
using vdb = vector<DB>;using vc=vector<char>;
using arr3 = array<ll,3> ;using arr2 = array<ll,2>;
using CD=complex<double>;
static constexpr ll MAXN=(ll)1e6+10,INF=(ll)1e17+3; // 1e17+3是素数 1e18+9是素数
static constexpr ll mod=(ll)1e9+7; // 998244353;
static constexpr double eps=1e-8;const double pi=acos(-1.0);
ll N,M,Q,X,K,T,lT;
inline void __();
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
// cin>>lT;
// while(lT--)
__();
return 0;
}
/*
*/
// refer cp algorithm
// https://cp-algorithms.com/string/manacher.html
vll manacher_odd(string s){
int n=SZ(s);
s='$'+s+'^';
vll p(n+2);
ll l=0,r=1; // (l,r) 是开区间，其内部是这个回文子串
FOR(i,1,n){
// 保底半径
p[i]=min(r-i,p[l+r-i]);
// 暴力外扩
while (s[i-p[i]]==s[i+p[i]]) { // 因为有哨兵，永不越界
p[i]++;
}
if(i+p[i]>r){
l=i-p[i],r=i+p[i];
}
}
return vll(p.begin()+1,p.end()-1);
}
vll manacher(const string &s){
string t;
for(auto c:s){
t+='#'; // 千万不要 t+='#'+'c'
t+=c;
}
t+='#';
auto res=manacher_odd(t);
return vll(res.begin()+1,res.end()-1);
}
// vector<int> manacher_odd(string s) {
// int n = s.size();
// s = "$" + s + "^";
// vector<int> p(n + 2);
// int l = 0, r = 1;
// for(int i = 1; i <= n; i++) {
// p[i] = min(r - i, p[l + (r - i)]);
// while(s[i - p[i]] == s[i + p[i]]) {
// p[i]++;
// }
// if(i + p[i] > r) {
// l = i - p[i], r = i + p[i];
// }
// }
// return vector<int>(begin(p) + 1, end(p) - 1);
// }
// vector<int> manacher(string s) {
// string t;
// for(auto c: s) {
// t += string("#") + c;
// }
// auto res = manacher_odd(t + "#");
// return vector<int>(begin(res) + 1, end(res) - 1);
// }
inline void __(){
// cin>>N;
string s;
cin>>s;
N=SZ(s);
auto res=manacher(s);
vll Pos(N,-1);
FOR(i,0,N-2){
if(s[i]=='(' && s[i+1]==')'){
Pos[i]=i;
}else{
if(i==0) continue;
Pos[i]=Pos[i-1];
}
}
vll Fpos(N,-1);
ROF(i,N-2,0){
if(s[i-1]=='(' && s[i]==')'){
Fpos[i]=i;
}else{
if(i==N) continue;
Fpos[i]=Fpos[i+1];
}
}
#ifdef LOCAL
_print(Fpos);
_print(Pos);
_print(res);
cend;
#endif
ll ans=0;
FOR(i,0,SZ(res)-1){
ll radius=res[i];radius/=2;
if(i&1){
if(radius<2) continue;
ll id1=i/2,id2=i/2+1,l=id1-radius+1,r=id2+radius-1;
// l=max(ban[id1]+1,l);
// r=min(Fban[id2]-1,r);
ll lans=0;
if(Pos[id1]!=-1){
if(Pos[id1]>=l){
lans=max(lans,Pos[id1]-l+1);
}
}
if(Fpos[id2]!=-1){
if(Fpos[id2]<=r){
lans=max(lans,r-Fpos[id2]+1);
}
}
ans+=lans;
}else{
if(radius<2) continue;
ll id=i/2;
ll l=id-radius+1,r=id+radius-1;
// l=max(ban[id]+1,l);
// r=min(Fban[id]-1,r);
ll lans=0;
if(Pos[id]!=-1){
if(Pos[id]>=l){
lans=max(lans,Pos[id]-l+1);
}
}
if(Fpos[id]!=-1){
if(Fpos[id]<=r){
lans=max(lans,r-Fpos[id]+1);
}
}
ans+=min(radius-1,lans);
#ifdef LOCAL
if(i==2){
debug(r);
debug(Fpos[id]);
debug(r-Fpos[id]+1);
}
#endif
}
#ifdef LOCAL
debug(i);
debug(ans);
#endif
}
cout<<ans<<"\n";
}
/*
*/
```
:::
## 心路历程（WA，TLE，MLE……）
