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Submission #866289

# Submission time Handle Problem Language Result Execution time Memory
866289 2023-10-25T19:06:59 Z Dec0Dedd Palindromes (APIO14_palindrome) C++14
100 / 100
 265 ms 97980 KB 
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 6e5+1;
const int K = 21;

vector<int> sort_cyclic_shifts(string const& s) {
    int n = s.size();
    const int alphabet = 256;
    vector<int> p(n), c(n), cnt(max(alphabet, n), 0);
    for (int i = 0; i < n; i++)
        cnt[s[i]]++;
    for (int i = 1; i < alphabet; i++)
        cnt[i] += cnt[i-1];
    for (int i = 0; i < n; i++)
        p[--cnt[s[i]]] = i;
    c[p[0]] = 0;
    int classes = 1;
    for (int i = 1; i < n; i++) {
        if (s[p[i]] != s[p[i-1]])
            classes++;
        c[p[i]] = classes - 1;
    }

    vector<int> pn(n), cn(n);
    for (int h = 0; (1 << h) < n; ++h) {
        for (int i = 0; i < n; i++) {
            pn[i] = p[i] - (1 << h);
            if (pn[i] < 0)
                pn[i] += n;
        }
        fill(cnt.begin(), cnt.begin() + classes, 0);
        for (int i = 0; i < n; i++)
            cnt[c[pn[i]]]++;
        for (int i = 1; i < classes; i++)
            cnt[i] += cnt[i-1];
        for (int i = n-1; i >= 0; i--)
            p[--cnt[c[pn[i]]]] = pn[i];
        cn[p[0]] = 0;
        classes = 1;
        for (int i = 1; i < n; i++) {
            pair<int, int> cur = {c[p[i]], c[(p[i] + (1 << h)) % n]};
            pair<int, int> prev = {c[p[i-1]], c[(p[i-1] + (1 << h)) % n]};
            if (cur != prev)
                ++classes;
            cn[p[i]] = classes - 1;
        }
        c.swap(cn);
    }
    return p;
}


vector<int> suffix_array_construction(string s) {
    s += "$";
    vector<int> sorted_shifts = sort_cyclic_shifts(s);
    sorted_shifts.erase(sorted_shifts.begin());
    return sorted_shifts;
}

vector<int> manacher_odd(string s) {
    int n = s.size();
    s = "$" + s + "^";
    vector<int> p(n + 2);
    int l = 1, r = 1;
    for(int i = 1; i <= n; i++) {
        p[i] = max(0, 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 res;
}

vector<int> lcp_construction(string const& s, vector<int> const& p) {
    int n = s.size();
    vector<int> rank(n, 0);
    for (int i = 0; i < n; i++)
        rank[p[i]] = i;

    int k = 0;
    vector<int> lcp(n-1, 0);
    for (int i = 0; i < n; i++) {
        if (rank[i] == n - 1) {
            k = 0;
            continue;
        }
        int j = p[rank[i] + 1];
        while (i + k < n && j + k < n && s[i+k] == s[j+k])
            k++;
        lcp[rank[i]] = k;
        if (k)
            k--;
    }
    return lcp;
}

ll mxr[N], xc[N], vs[N], st[K][N], lg[N];

int que(int l, int r) {
    int i=lg[r-l+1];
    return min(st[i][l], st[i][r-(1<<i)+1]);
}

string s;
int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(NULL);
    cout.tie(NULL);

    cin>>s;

    lg[1]=0;
    for (int i=2; i<N; ++i) lg[i]=lg[i/2]+1;

    int n=s.size();
    vector<int> v=suffix_array_construction(s);

    for (int i=0; i<n; ++i) vs[i+1]=v[i]+1;

    vector<int> lcp=lcp_construction(s, v);

    for (int i=1; i<n; ++i) st[0][i]=lcp[i-1];
    for (int i=1; i<K; ++i) {
        for (int j=1; j+(1<<i)<=n; ++j) {
            st[i][j]=min(st[i-1][j], st[i-1][j+(1<<(i-1))]);
        }
    }

    vector<int> x=manacher(s);
    int sz=x.size();

    for (int i=0; i<sz; ++i) {
        if (i%2 == 1) {
            ll idx=(i+1)/2, l=idx-(x[i]+1)/2+1, r=idx+(x[i]+1)/2-1;
            xc[l]=max(xc[l], r-l+1);
        } else {
            if (i == 0 || x[i] == 1) continue;
            ll idx=i/2, l=idx-x[i]/2+1, r=idx+x[i]/2;
            xc[l]=max(xc[l], r-l+1);
        }
    }

    int val=0, j=0;
    for (int i=1; i<=n; ++i) {
        if (xc[i] >= val-2*(i-j)) val=xc[i], j=i;
        xc[i]=val-2*(i-j);
    }

    ll ans=0;
    for (int i=1; i<=n; ++i) {
        ans=max(ans, xc[vs[i]]);
        int lf=1, rf=i-1, l=i, r=i-1;
        while (lf <= rf) {
            int m=(lf+rf)/2;
            if (que(m, i-1) >= xc[vs[i]]) rf=m-1, l=m;
            else lf=m+1;
        } 
        
        lf=i, rf=n-1;
        while (lf <= rf) {
            int m=(lf+rf)/2;
            if (que(i, m) >= xc[vs[i]]) lf=m+1, r=m;
            else rf=m-1;
        } ++r;

        ans=max(ans, 1ll*(r-l+1)*xc[vs[i]]);
    } cout<<ans<<"\n";
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 12888 KB Output is correct
2 Correct 2 ms 10844 KB Output is correct
3 Correct 3 ms 14940 KB Output is correct
4 Correct 2 ms 8796 KB Output is correct
5 Correct 1 ms 8796 KB Output is correct
6 Correct 2 ms 8796 KB Output is correct
7 Correct 2 ms 10844 KB Output is correct
8 Correct 2 ms 10712 KB Output is correct
9 Correct 2 ms 14940 KB Output is correct
10 Correct 2 ms 14936 KB Output is correct
11 Correct 3 ms 16984 KB Output is correct
12 Correct 2 ms 16988 KB Output is correct
13 Correct 3 ms 19104 KB Output is correct
14 Correct 3 ms 19036 KB Output is correct
15 Correct 3 ms 16988 KB Output is correct
16 Correct 2 ms 16848 KB Output is correct
17 Correct 2 ms 16988 KB Output is correct
18 Correct 3 ms 16988 KB Output is correct
19 Correct 3 ms 21112 KB Output is correct
20 Correct 3 ms 21084 KB Output is correct
21 Correct 3 ms 21084 KB Output is correct
22 Correct 3 ms 21084 KB Output is correct
23 Correct 3 ms 21084 KB Output is correct
24 Correct 3 ms 21084 KB Output is correct
25 Correct 3 ms 21084 KB Output is correct
26 Correct 3 ms 21080 KB Output is correct
27 Correct 3 ms 21084 KB Output is correct
28 Correct 3 ms 21084 KB Output is correct
29 Correct 4 ms 21340 KB Output is correct
30 Correct 3 ms 21084 KB Output is correct
31 Correct 3 ms 21084 KB Output is correct
32 Correct 3 ms 21084 KB Output is correct

Subtask #2
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 27224 KB Output is correct
2 Correct 4 ms 27480 KB Output is correct
3 Correct 4 ms 27228 KB Output is correct
4 Correct 4 ms 27228 KB Output is correct
5 Correct 4 ms 27228 KB Output is correct
6 Correct 4 ms 27228 KB Output is correct
7 Correct 4 ms 27340 KB Output is correct
8 Correct 4 ms 27236 KB Output is correct
9 Correct 4 ms 27232 KB Output is correct
10 Correct 4 ms 27304 KB Output is correct
11 Correct 5 ms 27228 KB Output is correct
12 Correct 4 ms 27428 KB Output is correct

Subtask #3
24.0 / 24.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 35904 KB Output is correct
2 Correct 7 ms 35936 KB Output is correct
3 Correct 8 ms 35904 KB Output is correct
4 Correct 8 ms 35904 KB Output is correct
5 Correct 8 ms 35904 KB Output is correct
6 Correct 8 ms 35976 KB Output is correct
7 Correct 8 ms 35904 KB Output is correct
8 Correct 9 ms 35772 KB Output is correct
9 Correct 8 ms 35904 KB Output is correct
10 Correct 8 ms 35904 KB Output is correct

Subtask #4
26.0 / 26.0

# Verdict Execution time Memory Grader output
1 Correct 52 ms 57524 KB Output is correct
2 Correct 48 ms 57552 KB Output is correct
3 Correct 53 ms 57456 KB Output is correct
4 Correct 51 ms 57552 KB Output is correct
5 Correct 67 ms 57552 KB Output is correct
6 Correct 61 ms 57432 KB Output is correct
7 Correct 55 ms 57548 KB Output is correct
8 Correct 66 ms 57412 KB Output is correct
9 Correct 64 ms 57420 KB Output is correct
10 Correct 62 ms 57448 KB Output is correct

Subtask #5
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 158 ms 97768 KB Output is correct
2 Correct 169 ms 97776 KB Output is correct
3 Correct 147 ms 97776 KB Output is correct
4 Correct 162 ms 97788 KB Output is correct
5 Correct 265 ms 97764 KB Output is correct
6 Correct 183 ms 97816 KB Output is correct
7 Correct 183 ms 97772 KB Output is correct
8 Correct 206 ms 97844 KB Output is correct
9 Correct 202 ms 97980 KB Output is correct
10 Correct 253 ms 97836 KB Output is correct
11 Correct 161 ms 97836 KB Output is correct
12 Correct 208 ms 97696 KB Output is correct