338 lines
8.9 KiB
C++
338 lines
8.9 KiB
C++
#include <algorithm>
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#include <cstdio>
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#include <cstring>
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#define unlikely(x) __builtin_expect(!!(x), 0)
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struct char_reader {
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FILE *f;
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char *buf, *p1, *p2;
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int size;
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char_reader(FILE *fin, int bufsize = 1 << 16) {
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f = fin;
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size = bufsize;
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p1 = p2 = 0;
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buf = new char[size];
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}
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~char_reader() { delete[] buf; }
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inline int operator()() {
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return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, size, f), p1 == p2)
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? EOF
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: *p1++;
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}
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};
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struct char_writer {
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FILE *f;
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char *buf, *p, *end;
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int size;
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char_writer(FILE *fout, int bufsize = 1 << 16) {
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f = fout;
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size = bufsize;
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buf = new char[size];
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p = buf;
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end = buf + bufsize;
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}
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~char_writer() {
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fwrite(buf, p - buf, 1, f);
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delete[] buf;
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}
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inline char operator()(char ch) {
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if (unlikely(end == p)) {
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fwrite(buf, end - buf, 1, f);
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p = buf;
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}
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return *p++ = ch;
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}
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};
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char_reader gch(stdin);
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char_writer wch(stdout);
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template <typename T>
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inline int read(T &t) {
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bool f = false;
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int ch;
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while (ch = gch(), !((ch >= '0' && ch <= '9') || ch == '-')) {
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if (ch == EOF) return 0;
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}
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t = 0;
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if (ch == '-') f = true, ch = gch();
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t = ch ^ 48;
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while (ch = gch(), ch >= '0' && ch <= '9')
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t = (t << 3) + (t << 1) + (ch ^ 48);
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if (f) t = -t;
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return 1;
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}
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inline int read(char &c) {
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c = 0;
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int ch;
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while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) {
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if (ch == EOF) return 0;
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}
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c = ch;
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return 1;
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}
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inline int read(char *s) {
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int ch;
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while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) {
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if (ch == EOF) return 0;
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}
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*s++ = ch;
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while (ch = gch(),
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!(ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t') && ch != EOF)
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*s++ = ch;
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*s++ = 0;
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return 1;
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}
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inline int read(const char *s) { return read((char *)s); }
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inline int readline(char *s) {
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int ch;
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while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) {
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if (ch == EOF) return 0;
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}
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*s++ = ch;
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while (ch = gch(), !(ch == '\n' || ch == '\r') && ch != EOF) *s++ = ch;
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*s++ = 0;
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return 1;
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}
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inline int readline(const char *s) { return readline((char *)s); }
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template <typename T>
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inline void write(T t) {
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int stk[20], cnt = 0;
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if (t == 0) {
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wch('0');
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return;
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}
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if (t < 0) {
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wch('-');
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t = -t;
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}
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while (t > 0) {
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stk[cnt++] = t % 10;
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t /= 10;
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}
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while (cnt) wch(stk[--cnt] + '0');
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}
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inline void write(char t) { wch(t); }
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inline void write(char *s) {
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while (*s) wch(*s++);
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}
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inline void write(const char *s) { write((char *)s); }
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#if __cplusplus >= 201103L
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template <typename T, typename... Args>
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inline int read(T &t, Args &...args) {
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return read(t) + read(args...);
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}
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template <typename T, typename... Args>
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inline void write(T t, Args... args) {
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write(t);
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write(args...);
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}
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#else
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template <typename A_t, typename B_t>
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inline int read(A_t &a, B_t &b) {
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return read(a) + read(b);
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}
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template <typename A_t, typename B_t, typename C_t>
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inline int read(A_t &a, B_t &b, C_t &c) {
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return read(a) + read(b) + read(c);
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}
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template <typename A_t, typename B_t, typename C_t, typename D_t>
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inline int read(A_t &a, B_t &b, C_t &c, D_t &d) {
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return read(a) + read(b) + read(c) + read(d);
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}
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template <typename A_t, typename B_t>
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inline void write(A_t a, B_t b) {
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write(a);
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write(b);
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}
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template <typename A_t, typename B_t, typename C_t>
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inline void write(A_t a, B_t b, C_t c) {
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write(a);
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write(b);
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write(c);
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}
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template <typename A_t, typename B_t, typename C_t, typename D_t>
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inline void write(A_t a, B_t b, C_t c, D_t d) {
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write(a);
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write(b);
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write(c);
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write(d);
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}
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#endif
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using namespace std;
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typedef long long LL;
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const int kMaxN = 3e5 + 10;
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const LL kInf = 1e18 + 10;
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int n;
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char s[kMaxN];
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int sa[kMaxN * 2], rk[kMaxN * 2], height[kMaxN];
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LL a[kMaxN];
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namespace __SA_IS {
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int str[kMaxN * 2], sa[kMaxN * 2], typ[kMaxN * 2], c[kMaxN], p[kMaxN * 2],
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sbuc[kMaxN], lbuc[kMaxN], name[kMaxN];
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inline int islms(int *typ, int i) { return !typ[i] && (i == 1 || typ[i - 1]); }
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int cmp(int *s, int *typ, int p, int q) {
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do {
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if (s[p] != s[q]) return 1;
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p++;
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q++;
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} while (!islms(typ, p) && !islms(typ, q));
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return (!islms(typ, p) || !islms(typ, q) || s[p] != s[q]);
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}
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void isort(int *s, int *sa, int *typ, int *c, int n, int m) {
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int i;
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for (lbuc[0] = sbuc[0] = c[0], i = 1; i <= m; i++) {
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lbuc[i] = c[i - 1] + 1;
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sbuc[i] = c[i];
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}
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for (i = 1; i <= n; i++)
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if (sa[i] > 1 && typ[sa[i] - 1]) sa[lbuc[s[sa[i] - 1]]++] = sa[i] - 1;
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for (i = n; i >= 1; i--)
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if (sa[i] > 1 && !typ[sa[i] - 1]) sa[sbuc[s[sa[i] - 1]]--] = sa[i] - 1;
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}
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void build_sa(int *s, int *sa, int *typ, int *c, int *p, int n, int m) {
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int i;
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for (i = 0; i <= m; i++) c[i] = 0;
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for (i = 1; i <= n; i++) c[s[i]]++;
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for (i = 1; i <= m; i++) c[i] += c[i - 1];
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typ[n] = 0;
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for (i = n - 1; i >= 1; i--)
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if (s[i] < s[i + 1])
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typ[i] = 0;
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else if (s[i] > s[i + 1])
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typ[i] = 1;
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else
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typ[i] = typ[i + 1];
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int cnt = 0;
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for (i = 1; i <= n; i++)
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if (!typ[i] && (i == 1 || typ[i - 1])) p[++cnt] = i;
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for (i = 1; i <= n; i++) sa[i] = 0;
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for (i = 0; i <= m; i++) sbuc[i] = c[i];
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for (i = 1; i <= cnt; i++) sa[sbuc[s[p[i]]]--] = p[i];
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isort(s, sa, typ, c, n, m);
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int last = 0, t = -1, x;
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for (i = 1; i <= n; i++) {
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x = sa[i];
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if (!typ[x] && (x == 1 || typ[x - 1])) {
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if (!last || cmp(s, typ, x, last))
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name[x] = ++t;
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else
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name[x] = t;
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last = x;
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}
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}
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for (i = 1; i <= cnt; i++) s[n + i] = name[p[i]];
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if (t < cnt - 1)
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build_sa(s + n, sa + n, typ + n, c + m + 1, p + n, cnt, t);
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else
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for (i = 1; i <= cnt; i++) sa[n + s[n + i] + 1] = i;
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for (i = 0; i <= m; i++) sbuc[i] = c[i];
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for (i = 1; i <= n; i++) sa[i] = 0;
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for (i = cnt; i >= 1; i--) sa[sbuc[s[p[sa[n + i]]]]--] = p[sa[n + i]];
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isort(s, sa, typ, c, n, m);
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}
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} // namespace __SA_IS
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void SA_IS(char *s, int n, int *sa, int *rk) {
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using namespace __SA_IS;
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for (int i = 1; i <= n; i++) str[i] = s[i];
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str[++n] = 0;
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build_sa(str, sa, typ, c, p, n, 256);
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n--;
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for (int i = 1; i <= n; i++) sa[i] = sa[i + 1];
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for (int i = 1; i <= n; i++) rk[sa[i]] = i;
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}
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void computeHeight(char *s, int n, int *sa, int *rk, int *height) {
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int k = 0;
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for (int i = 1; i <= n; i++) {
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if (rk[i] == 1) {
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height[rk[i]] = 0;
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continue;
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}
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if (k > 0) {
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k--;
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}
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int j = sa[rk[i] - 1];
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while (i + k <= n && j + k <= n && s[i + k] == s[j + k]) {
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k++;
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}
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height[rk[i]] = k;
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}
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}
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LL exact_method[kMaxN], exact_yammy[kMaxN];
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struct H_Struct {
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int height_index, height_value;
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H_Struct() {}
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H_Struct(int __h_i, int __h_v) : height_index(__h_i), height_value(__h_v) {}
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};
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bool operator<(const H_Struct &A, const H_Struct &B) {
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return A.height_value > B.height_value;
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}
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H_Struct merge_pair[kMaxN];
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int fa[kMaxN], min_a[kMaxN], max_a[kMaxN], subtree_size[kMaxN];
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LL subtree_max_yammy[kMaxN];
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inline int ff(int u) {
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int v = u, x;
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while (u != fa[u]) u = fa[u];
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while (v != u) {
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x = fa[v];
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fa[v] = u;
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v = x;
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}
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return u;
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}
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int main() {
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#ifdef local
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freopen("pro.in", "r", stdin);
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#endif
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read(n);
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read(s + 1);
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for (int i = 1; i <= n; i++) read(a[i]);
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SA_IS(s, n, sa, rk);
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computeHeight(s, n, sa, rk, height);
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for (int i = 2; i <= n; i++) merge_pair[i - 1] = H_Struct(i, height[i]);
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sort(merge_pair + 1, merge_pair + 1 + n - 1);
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for (int i = 1; i <= n; i++) {
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fa[i] = i;
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max_a[i] = min_a[i] = a[i];
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subtree_size[i] = 1;
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subtree_max_yammy[i] = -kInf;
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exact_yammy[i] = -kInf;
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}
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for (int i = 1; i <= n - 1; i++) {
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int x = sa[merge_pair[i].height_index];
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int y = sa[merge_pair[i].height_index - 1];
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int ht = merge_pair[i].height_value;
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// printf("%d and %d\n", x, y);
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x = ff(x);
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y = ff(y);
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fa[y] = x;
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exact_method[ht] += (LL)subtree_size[x] * (LL)subtree_size[y];
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// 可以归纳证明当多个height相同时,这个递推方式也是正确的
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subtree_size[x] += subtree_size[y];
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subtree_max_yammy[x] = max(subtree_max_yammy[x], subtree_max_yammy[y]);
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// printf("smy %d %lld\n", x, subtree_max_yammy[x]);
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subtree_max_yammy[x] =
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max(subtree_max_yammy[x],
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max(min_a[x] * (LL)min_a[y], max_a[x] * (LL)max_a[y]));
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// printf("smy %d %lld\n", x, subtree_max_yammy[x]);
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subtree_max_yammy[x] =
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max(subtree_max_yammy[x],
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max(max_a[x] * (LL)min_a[y], min_a[x] * (LL)max_a[y]));
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// printf("smy %d %lld\n", x, subtree_max_yammy[x]);
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min_a[x] = min(min_a[x], min_a[y]);
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max_a[x] = max(max_a[x], max_a[y]);
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// printf("mm %d %d\n", x, max_a[x]);
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// printf("mi %d %d\n", x, min_a[x]);
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exact_yammy[ht] = max(exact_yammy[ht], subtree_max_yammy[x]);
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// 这里很显然
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}
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for (int i = n - 2; i >= 0; i--) {
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exact_method[i] += exact_method[i + 1];
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exact_yammy[i] = max(exact_yammy[i], exact_yammy[i + 1]);
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}
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for (int i = 0; i <= n - 1; i++)
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printf("%lld %lld\n", exact_method[i],
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exact_method[i] != 0 ? exact_yammy[i] : 0);
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return 0;
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} |