Brief Description

一个回文串的value定义为这个回文串的长度乘以出现次数。给定一个字符串，求\(value_{max}\)。

Algorithm Design

我们使用Manacher暴力算出所有的回文子串，放在SAM里倍增，大力算贡献就好了。

Code

#include <algorithm>
#include <cstdio>
#define ll long long
#include <cstring>
const int maxn = 600010;
int n;
ll ans;
int p[maxn];
char str[maxn];
struct Suffix_Automaton {
int trans[maxn][26], fa[maxn][20], pos[maxn], len[maxn], size[maxn];
int last, root, sz;
int v[maxn], q[maxn], dep[maxn];
void init() {
sz = 0;
last = root = ++sz;
}
void insert(int x, int id) {
int p = last, np = last = ++sz;
len[np] = len[p] + 1;
pos[id] = np;
size[np] = 1;
for (; !trans[p][x]; p = fa[p][0])
trans[p][x] = np;
if (p == 0)
fa[np][0] = root;
else {
int q = trans[p][x];
if (len[q] == len[p] + 1) {
fa[np][0] = q;
} else {
int nq = ++sz;
for (int i = 0; i < 26; i++)
trans[nq][i] = trans[q][i];
fa[nq][0] = fa[q][0];
len[nq] = len[p] + 1;
fa[q][0] = fa[np][0] = nq;
for (; trans[p][x] == q; p = fa[p][0])
trans[p][x] = nq;
}
}
}
void pre() {
for (int i = 1; i <= sz; i++)
v[len[i]]++;
for (int i = 1; i <= n; i++)
v[i] += v[i - 1];
for (int i = sz; i >= 1; i--)
q[v[len[i]]--] = i;
for (int i = sz; i >= 1; i--) {
int t = q[i];
size[fa[t][0]] += size[t];
}
for (int i = 1; i <= sz; i++) {
int t = q[i];
dep[t] = dep[fa[t][0]] + 1;
for (int j = 1; (1 << j) <= dep[t]; j++)
fa[t][i] = fa[fa[t][i - 1]][i - 1];
}
}
void query(int l, int r) {
int ret = pos[r];
for (int i = 19; i >= 0; i--) {
int t = fa[ret][i];
if (len[t] >= r - l + 1)
ret = t;
}
ans = std::max(ans, (ll)size[ret] * (r - l + 1));
}
} sam;
void manacher() {
int mx = 1, id = 1;
for (int i = n; i; i--)
str[i * 2] = '#', str[i * 2 - 1] = str[i];
n <<= 1;
for (int i = 1; i <= n; i++) {
p[i] = std::min(p[id * 2 - i], mx - i);
while (i - p[i] > 0 && str[i - p[i]] == str[i + p[i]]) {
int al = (i - p[i]) / 2 + 1;
int ar = (i + p[i] + 1) / 2;
// printf("%d %d\n", al, ar);
sam.query(al, ar);
p[i]++;
}
if (i + p[i] > mx)
mx = i + p[i], id = i;
}
}
int main() {
#ifndef ONLINE_JUDGE
// freopen("input", "r", stdin);
#endif
scanf("%s", str + 1);
n = strlen(str + 1);
str[0] = '+', str[n + 1] = '-';
sam.init();
for (int i = 1; i <= n; i++) {
sam.insert(str[i] - 'a', i);
}
sam.pre();
manacher();
printf("%lld\n", ans);
}