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）

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

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

源代码

// 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……）