SH-Quizzes/ACMOJ-2091.cpp

#include <cstdio>
#define unlikely(x) __builtin_expect(!!(x), 0)
struct char_reader {
  FILE *f;
  char *buf, *p1, *p2;
  int size;
  char_reader(FILE *fin, int bufsize = 1 << 16) {
    f = fin;
    size = bufsize;
    p1 = p2 = 0;
    buf = new char[size];
  }
  ~char_reader() { delete[] buf; }
  inline int operator()() {
    return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, size, f), p1 == p2)
               ? EOF
               : *p1++;
  }
};
struct char_writer {
  FILE *f;
  char *buf, *p, *end;
  int size;
  char_writer(FILE *fout, int bufsize = 1 << 16) {
    f = fout;
    size = bufsize;
    buf = new char[size];
    p = buf;
    end = buf + bufsize;
  }
  ~char_writer() {
    fwrite(buf, p - buf, 1, f);
    delete[] buf;
  }
  inline char operator()(char ch) {
    if (unlikely(end == p)) {
      fwrite(buf, end - buf, 1, f);
      p = buf;
    }
    return *p++ = ch;
  }
};
char_reader gch(stdin);
char_writer wch(stdout);
template <typename T>
inline int read(T &t) {
  bool f = false;
  int ch;
  while (ch = gch(), !((ch >= '0' && ch <= '9') || ch == '-')) {
    if (ch == EOF) return 0;
  }
  t = 0;
  if (ch == '-') f = true, ch = gch();
  t = ch ^ 48;
  while (ch = gch(), ch >= '0' && ch <= '9')
    t = (t << 3) + (t << 1) + (ch ^ 48);
  if (f) t = -t;
  return 1;
}
inline int read(char &c) {
  c = 0;
  int ch;
  while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) {
    if (ch == EOF) return 0;
  }
  c = ch;
  return 1;
}
inline int read(char *s) {
  int ch;
  while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) {
    if (ch == EOF) return 0;
  }
  *s++ = ch;
  while (ch = gch(),
         !(ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t') && ch != EOF)
    *s++ = ch;
  *s++ = 0;
  return 1;
}
inline int read(const char *s) { return read((char *)s); }
inline int readline(char *s) {
  int ch;
  while (ch = gch(), (ch == ' ' || ch == '\n' || ch == '\r' || ch == '\t')) {
    if (ch == EOF) return 0;
  }
  *s++ = ch;
  while (ch = gch(), !(ch == '\n' || ch == '\r') && ch != EOF) *s++ = ch;
  *s++ = 0;
  return 1;
}
inline int readline(const char *s) { return readline((char *)s); }
template <typename T>
inline void write(T t) {
  int stk[20], cnt = 0;
  if (t == 0) {
    wch('0');
    return;
  }
  if (t < 0) {
    wch('-');
    t = -t;
  }
  while (t > 0) {
    stk[cnt++] = t % 10;
    t /= 10;
  }
  while (cnt) wch(stk[--cnt] + '0');
}
inline void write(char t) { wch(t); }
inline void write(char *s) {
  while (*s) wch(*s++);
}
inline void write(const char *s) { write((char *)s); }
#if __cplusplus >= 201103L
template <typename T, typename... Args>
inline int read(T &t, Args &...args) {
  return read(t) + read(args...);
}
template <typename T, typename... Args>
inline void write(T t, Args... args) {
  write(t);
  write(args...);
}
#else
template <typename A_t, typename B_t>
inline int read(A_t &a, B_t &b) {
  return read(a) + read(b);
}
template <typename A_t, typename B_t, typename C_t>
inline int read(A_t &a, B_t &b, C_t &c) {
  return read(a) + read(b) + read(c);
}
template <typename A_t, typename B_t, typename C_t, typename D_t>
inline int read(A_t &a, B_t &b, C_t &c, D_t &d) {
  return read(a) + read(b) + read(c) + read(d);
}
template <typename A_t, typename B_t>
inline void write(A_t a, B_t b) {
  write(a);
  write(b);
}
template <typename A_t, typename B_t, typename C_t>
inline void write(A_t a, B_t b, C_t c) {
  write(a);
  write(b);
  write(c);
}
template <typename A_t, typename B_t, typename C_t, typename D_t>
inline void write(A_t a, B_t b, C_t c, D_t d) {
  write(a);
  write(b);
  write(c);
  write(d);
}
#endif
#include <vector>
using namespace std;

typedef long long LL;
const int kMaxN = 1000000 + 10;
const int kMaxS = 1000 + 10;
int n, tot[kMaxS];
LL s[kMaxN], c[kMaxN], f[kMaxN];
vector<int> stk[kMaxS];

inline LL X(int i) { return c[i]; }
inline LL Y(int i) { return f[i - 1] + s[i] * c[i] * c[i] - 2 * s[i] * c[i]; }
inline double Slope(int i, int j) {
  return (Y(i) - Y(j)) / double(X(i) - X(j));
}
inline LL Calc(int i, int j) {
  return f[j - 1] + s[i] * (c[i] - c[j] + 1) * (c[i] - c[j] + 1);
}

int main() {
#ifdef local
  freopen("pro.in", "r", stdin);
#endif
  read(n);
  for (int i = 1; i <= n; ++i) {
    read(s[i]);
    c[i] = ++tot[s[i]];
  }
  for (int i = 1; i <= n; ++i) {
    int t = s[i];
    while (stk[t].size() >= 2 &&
           Slope(stk[t][stk[t].size() - 2], i) >=
               Slope(stk[t][stk[t].size() - 2], stk[t][stk[t].size() - 1]))
      stk[t].pop_back();
    stk[t].push_back(i);
    while (stk[t].size() >= 2 && Calc(i, stk[t][stk[t].size() - 1]) <=
                                     Calc(i, stk[t][stk[t].size() - 2]))
      stk[t].pop_back();
    f[i] = Calc(i, stk[t][stk[t].size() - 1]);
  }
  write(f[n], '\n');
  return 0;
}