SH-Quizzes/ACMOJ-1811.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 // if __cplusplus >= 201103L
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 // if __cplusplus >= 201103L
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long   LL;
typedef long double LDB;
const int kMaxn = 1e5 + 5;
int n, a[kMaxn], b[kMaxn];
LL  dp[kMaxn];
int Q[kMaxn], QL = 0, QR = 0;
int main() {
  #ifdef local
  freopen("pro.in", "r", stdin);
  #endif // ifdef local
  read(n);
  for (int i = 1; i <= n; i++) read(a[i]);
  for (int i = 1; i <= n; i++) read(b[i]);
  dp[1]   = 0;
  Q[QR++] = 1;
  for (int i = 2; i <= n; i++) {
    // while (QR - QL >= 2 &&
    //        (dp[Q[QL + 1]] - dp[Q[QL]]) <=
    //        (LL)(-a[i]) * (b[Q[QL + 1]] - b[Q[QL]])) QL++;
    while (QR - QL >= 2 &&
           LDB(dp[Q[QL + 1]] - dp[Q[QL]]) / LDB(b[Q[QL + 1]] - b[Q[QL]]) >=
           -a[i]) QL++;
    int b_j  = b[Q[QL]];
    LL  dp_j = dp[Q[QL]];
    dp[i] = dp_j + (LL)a[i] * b_j;
    // write("dp[",             i,    "] = ", dp[i], '\n');
    // write(char('A' + i - 1), "=(", b[i],   ",",   dp[i], ")\n");
    // while (QR - QL >= 2 &&
    //        (dp[i] - dp[Q[QR - 1]]) * (b[Q[QR - 1]] - b[Q[QR - 2]]) >=
    //        (dp[Q[QR - 1]] - dp[Q[QR - 2]]) * (b[i] - b[Q[QR - 1]]))
    //   QR--;
    while (QR - QL >= 2 &&
           LDB(dp[i] - dp[Q[QR - 1]]) / LDB(b[i] - b[Q[QR - 1]]) >=
           LDB(dp[Q[QR - 1]] - dp[Q[QR - 2]]) / LDB(b[Q[QR - 1]] - b[Q[QR - 2]]))
      QR--;
    Q[QR++] = i;
  }
  write(dp[n], '\n');
  return 0;
}