Submission #46668

#	Time	Username	Problem	Language	Result	Execution time	Memory
46668		minkank	Palindromes (APIO14_palindrome)	C++17	50 / 100	1084 ms	48928 KiB

palindrome

#include <bits/stdc++.h>
#define ll long long
using namespace std;
const ll mod = (ll) 1e9+9;
const ll base = 29;
int lg2[300005];
void prepLg2(int bound){
    for(int i=2;i<=bound;i++)
        lg2[i] = lg2[i>>1] + 1;
}
struct suffixArray{
    vector <int> sa, saRank, tmp;
    vector <vector <int> > lcp;
    int strLen, gap;

    bool saCmp(int x,int y){
        if (saRank[x] != saRank[y])
            return saRank[x] < saRank[y];
        return x+gap < strLen && y+gap < strLen ? saRank[x+gap] < saRank[y+gap] : x > y;
    }

    void build_lcp(string &s){
        int k = 0;
        for(int i = 0; i < strLen; i ++){
            if (saRank[i] != strLen - 1){
                for (int j = sa[saRank[i] + 1]; max(i+k, j+k) < strLen && s[i + k] == s[j + k];)  ++k;
                lcp[saRank[i]][0] = k;
                if (k) k--;
            }
        }
        for(int k = 1; k < 20; k ++){
            for(int i = 0; i < strLen; i ++)
                if (i + (1<<k) < strLen)
                    lcp[i][k] = min(lcp[i][k-1], lcp[i+(1<<(k-1))][k-1]);
                else break;
        }
    }

    int getLcp(int l,int r){
        if (l > r)  swap(l, r);
        if (l == r) return strLen - sa[l];
        int k = lg2[r - l];
        return min(lcp[l][k], lcp[r-(1<<k)][k]);
    }

    void build(string &s, int isIndexFromOne = 0){
        strLen = s.size();
        sa.assign(strLen + 5, 0);
        saRank.assign(strLen + 5, 0);
        tmp.assign(strLen + 5, 0);
        lcp.assign(strLen + 5, vector<int>(20));
        //for(int i = 0; i < strLen; i ++)
        //    lcp[i].assign(20, 0);

        for(int i = 0; i < strLen; i ++)
            sa[i] = i, saRank[i] = s[i];

        for(gap = 1;;gap *= 2){
            sort(sa.begin(), sa.begin() + strLen, [&](int a, int b) {return this->saCmp(a, b);});
            //sort(sa.begin(), sa.begin() + strLen, saCmp);
            for(int i = 0; i < strLen; i ++) tmp[i+1] = tmp[i] + saCmp(sa[i], sa[i+1]);
            for(int i = 0; i < strLen; i ++) saRank[sa[i]] = tmp[i];
            if (tmp[strLen-1] == strLen-1) break;
        }
        build_lcp(s);
    }
};
int n;
string s[2];
suffixArray suff;
ll hashCode[2][300000], pBase[300000];
void prepHash(){
    pBase[0] = 1;
    for(int i=1;i<300000;i++)
        pBase[i] = pBase[i-1] * base % mod;

    hashCode[0][0] = s[0][0] - 'a' + 1;
    hashCode[1][0] = s[1][0] - 'a' + 1;
    for(int i=1;i<n;i++)
        hashCode[0][i] = (hashCode[0][i-1] + pBase[i] * (s[0][i] - 'a')) % mod,
        hashCode[1][i] = (hashCode[1][i-1] + pBase[i] * (s[1][i] - 'a')) % mod;
}
bool checkPalindrome(int l1,int r1){
    int l2 = n-1-r1;
    int r2 = n-1-l1;
    ll val1 = (hashCode[0][r1] - (l1 == 0 ? 0 : hashCode[0][l1-1]) + mod) % mod;
    ll val2 = (hashCode[1][r2] - (l2 == 0 ? 0 : hashCode[1][l2-1]) + mod) % mod;
    val1 = val1 * pBase[max(0, r2 - r1)] % mod;
    val2 = val2 * pBase[max(0, r1 - r2)] % mod;
    return val1 == val2;
}

long long solve(int i, int sz) {
    int id = suff.saRank[i], res = 0;
    int l = 0, r = id;
    while(l < r) {
        int mid = (l + r) >> 1;
        if(suff.getLcp(mid, id) >= sz) r = mid;
        else l = mid + 1;
    }
    res += id - l + 1;
    l = id, r = n - 1;
    while(l < r) {
        int mid = (l + r + 1) >> 1;
        if(suff.getLcp(id, mid) >= sz) l = mid;
        else r = mid - 1;
    }
    res += l - id;
    return 1LL * res * sz;
}

int main(){
    prepLg2(300000);
    iostream::sync_with_stdio(0);
    cin >> s[0];
    n = s[0].size();
    s[1] = s[0];
    reverse(s[1].begin(), s[1].end());
    suff.build(s[0]);
    prepHash();
    int sz0, sz1;
    sz0 = 0, sz1 = 1;
    long long ans = 0;
    for(int i = n - 1; i >= 0; --i) {
        int p0 = i + 2 * sz0 - 1; 
        int p1 = i + 2 * sz1 - 2;
        if(p0 > p1) ans = max(ans, solve(i, p0 - i + 1));
        else ans = max(ans, solve(i, p1 - i + 1));
        if(i == 0) continue;
        sz0++, sz1++;
        while(sz0) {
            p0 = i - 1 + 2 * sz0 - 1;
            if(!checkPalindrome(i - 1, p0)) sz0--;
            else break;
        }
        while(sz1) {
            p1 = i - 1 + 2 * sz1 - 2;
            if(!checkPalindrome(i - 1, p1)) sz1--;
            else break;
        }
    }
    cout << ans;
}

• Subtask 1: 0 / 8
• Subtask 2: 0 / 15
• Subtask 3: 24 / 24
• Subtask 4: 26 / 26
• Subtask 5: 0 / 27