Problem p00865 (C++)

Buggy submission (status: Runtime Error):
// Header {{{
// includes {{{
#include <algorithm>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <sys/time.h>
#include <unistd.h>
#include <vector>
// }}}
using namespace std;
// consts {{{
static const int INF = 1e9;
static const double PI = acos(-1.0);
static const double EPS = 1e-10;
// }}}
// typedefs {{{
typedef long long int LL;
typedef unsigned long long int ULL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef vector<ULL> VULL;
typedef vector<VULL> VVULL;
typedef vector<double> VD;
typedef vector<VD> VVD;
typedef vector<bool> VB;
typedef vector<VB> VVB;
typedef vector<char> VC;
typedef vector<VC> VVC;
typedef vector<string> VS;
typedef vector<VS> VVS;
typedef pair<int, int> PII;
typedef complex<int> P;
// }}}
// macros & inline functions {{{
// syntax sugars {{{
#define FOR(i, b, e) for (typeof(e) i = (b); i < (e); ++i)
#define FORI(i, b, e) for (typeof(e) i = (b); i <= (e); ++i)
#define REP(i, n) FOR(i, 0, n)
#define REPI(i, n) FORI(i, 0, n)
#define OPOVER(_op, _type) inline bool operator _op(const _type &t) const
// }}}
// conversion {{{
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
// }}}
// array and STL {{{
#define ARRSIZE(a) (sizeof(a) / sizeof(a[0]))
#define ZERO(a, v) (assert(v == 0 || v == -1), memset(a, v, sizeof(a)))
#define F first
#define S second
#define MP(a, b) make_pair(a, b)
#define SIZE(a) ((LL)a.size())
#define PB(e) push_back(e)
#define SORT(v) sort((v).begin(), (v).end())
#define RSORT(v) sort((v).rbegin(), (v).rend())
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define EACH(c, it)                                                            \
  for (typeof((c).begin()) it = (c).begin(); it != (c).end(); ++it)
#define REACH(c, it)                                                           \
  for (typeof((c).rbegin()) it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(s, e) ((s).find(e) != (s).end())
// }}}
// bit manipulation {{{
// singed integers are not for bitwise operations, specifically arithmetic
// shifts ('>>', and maybe not good for '<<' too)
#define IS_UNSIGNED(n) (!numeric_limits<typeof(n)>::is_signed)
#define BIT(n) (assert(IS_UNSIGNED(n)), assert(n < 64), (1ULL << (n)))
#define BITOF(n, m)                                                            \
  (assert(IS_UNSIGNED(n)), assert(m < 64), ((ULL)(n) >> (m)&1))
inline int BITS_COUNT(ULL b) {
  int c = 0;
  while (b != 0) {
    c += (b & 1);
    b >>= 1;
  }
  return c;
}
inline int MSB(ULL b) {
  int c = 0;
  while (b != 0) {
    ++c;
    b >>= 1;
  }
  return c - 1;
}
inline int MAKE_MASK(ULL upper, ULL lower) {
  assert(lower < 64 && upper < 64 && lower <= upper);
  return (BIT(upper) - 1) ^ (BIT(lower) - 1);
}
// }}}
// for readable code {{{
#define EVEN(n) (n % 2 == 0)
#define ODD(n) (!EVEN(n))
// }}}
// debug {{{
#define arrsz(a) (sizeof(a) / sizeof(a[0]))
#define dprt(fmt, ...)                                                         \
  if (opt_debug) {                                                             \
    fprintf(stderr, fmt, ##__VA_ARGS__);                                       \
  }
#define darr(a)                                                                \
  if (opt_debug) {                                                             \
    copy((a), (a) + arrsz(a), ostream_iterator<int>(cerr, " "));               \
    cerr << endl;                                                              \
  }
#define darr_range(a, f, t)                                                    \
  if (opt_debug) {                                                             \
    copy((a) + (f), (a) + (t), ostream_iterator<int>(cerr, " "));              \
    cerr << endl;                                                              \
  }
#define dvec(v)                                                                \
  if (opt_debug) {                                                             \
    copy(ALL(v), ostream_iterator<int>(cerr, " "));                            \
    cerr << endl;                                                              \
  }
#define darr2(a)                                                               \
  if (opt_debug) {                                                             \
    FOR(__i, 0, (arrsz(a))) { darr((a)[__i]); }                                \
  }
#define WAIT()                                                                 \
  if (opt_debug) {                                                             \
    string _wait_;                                                             \
    cerr << "(hit return to continue)" << endl;                                \
    getline(cin, _wait_);                                                      \
  }
#define dump(x)                                                                \
  if (opt_debug) {                                                             \
    cerr << " [L" << __LINE__ << "] " << #x << " = " << (x) << endl;           \
  }
#define dumpl(x)                                                               \
  if (opt_debug) {                                                             \
    cerr << " [L" << __LINE__ << "] " << #x << endl << (x) << endl;            \
  }
#define dumpf()                                                                \
  if (opt_debug) {                                                             \
    cerr << __PRETTY_FUNCTION__ << endl;                                       \
  }
#define where()                                                                \
  if (opt_debug) {                                                             \
    cerr << __FILE__ << ": " << __PRETTY_FUNCTION__ << " [L: " << __LINE__     \
         << "]" << endl;                                                       \
  }
#define show_bits(b, s)                                                        \
  if (opt_debug) {                                                             \
    REP(i, s) {                                                                \
      cerr << BITOF(b, s - 1 - i);                                             \
      if (i % 4 == 3)                                                          \
        cerr << ' ';                                                           \
    }                                                                          \
    cerr << endl;                                                              \
  }

// ostreams {{{
// complex
template <typename T> ostream &operator<<(ostream &s, const complex<T> &d) {
  return s << "(" << d.real() << ", " << d.imag() << ")";
}

// pair
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const pair<T1, T2> &d) {
  return s << "(" << d.first << ", " << d.second << ")";
}

// vector
template <typename T> ostream &operator<<(ostream &s, const vector<T> &d) {
  int len = d.size();
  REP(i, len) {
    s << d[i];
    if (i < len - 1)
      s << "\t";
  }
  return s;
}

// 2 dimentional vector
template <typename T>
ostream &operator<<(ostream &s, const vector<vector<T>> &d) {
  int len = d.size();
  REP(i, len) { s << d[i] << endl; }
  return s;
}

// map
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const map<T1, T2> &m) {
  s << "{" << endl;
  for (typeof(m.begin()) itr = m.begin(); itr != m.end(); ++itr) {
    s << "\t" << (*itr).first << " : " << (*itr).second << endl;
  }
  s << "}" << endl;
  return s;
}
// }}}
// }}}
// }}}
// time {{{
inline double now() {
  struct timeval tv;
  gettimeofday(&tv, NULL);
  return (static_cast<double>(tv.tv_sec) +
          static_cast<double>(tv.tv_usec) * 1e-6);
}
// }}}
// string manipulation {{{
inline VS split(string s, char delimiter) {
  VS v;
  string t;
  REP(i, s.length()) {
    if (s[i] == delimiter)
      v.PB(t), t = "";
    else
      t += s[i];
  }
  v.PB(t);
  return v;
}
inline string join(VS s, string j) {
  string t;
  REP(i, s.size()) { t += s[i] + j; }
  return t;
}
// }}}
// geometry {{{
#define Y real()
#define X imag()
// }}}
// 2 dimentional array {{{
P dydx4[4] = {P(-1, 0), P(0, 1), P(1, 0), P(0, -1)};
P dydx8[8] = {P(-1, 0), P(0, 1), P(1, 0),  P(0, -1),
              P(-1, 1), P(1, 1), P(1, -1), P(-1, -1)};
int g_height, g_width;
bool in_field(P p) {
  return (0 <= p.Y && p.Y < g_height) && (0 <= p.X && p.X < g_width);
}
// }}}
// input and output {{{
inline void input(string filename) { freopen(filename.c_str(), "r", stdin); }
inline void output(string filename) { freopen(filename.c_str(), "w", stdout); }
// }}}
// }}}
bool opt_debug = false;

class Fraction {
public:
  int numerator;
  int denominator;
  Fraction(int _numerator, int _denominator) {
    numerator = _numerator;
    denominator = _denominator;
  };

  Fraction operator*(const int rhs) {
    return Fraction(this->numerator * rhs, this->denominator);
  };

  Fraction operator+(const Fraction &lhs) {
    // TODO: Use lcm
    assert(this->denominator == lhs.denominator);
    return Fraction(this->numerator + lhs.numerator, this->denominator);
  }
};
std::ostream &operator<<(std::ostream &s, const Fraction &a) {
  if (a.denominator == 1) {
    s << a.numerator;
  } else {
    s << a.numerator << "/" << a.denominator;
  }
  return s;
}

void solve(map<int, int> &count, int sum, int n, int m, int k) {
  if (n == 0) {
    int ans = max(1, sum - k);
    if (!EXIST(count, ans)) {
      count[ans] = 0;
    }
    count[ans]++;
    return;
  }

  REP(i, m) { solve(count, sum + (i + 1), n - 1, m, k); }
}

int main(int argc, char **argv) {
  std::ios_base::sync_with_stdio(false);
  // set options {{{
  int __c;
  while ((__c = getopt(argc, argv, "d")) != -1) {
    switch (__c) {
    case 'd':
      opt_debug = true;
      break;
    default:
      abort();
    }
  }
  // }}}

  input("./inputs/0.txt");
  // output("./outputs/0.txt");

  int n, m, k;
  while (cin >> n >> m >> k, n | m | k) {
    map<int, int> count;
    solve(count, 0, n, m, k);
    Fraction f(0, pow(m, n));
    EACH(count, itr) {
      int ans = (*itr).first, cnt = (*itr).second;
      f = f + Fraction(ans * cnt, pow(m, n));
    }

    printf("%.10lf\n", f.numerator / (double)f.denominator);
  }

  return 0;
}

// vim: foldmethod=marker

Fixed submission:
// Header {{{
// includes {{{
#include <algorithm>
#include <cassert>
#include <cctype>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <sys/time.h>
#include <unistd.h>
#include <vector>
// }}}
using namespace std;
// consts {{{
static const int INF = 1e9;
static const double PI = acos(-1.0);
static const double EPS = 1e-10;
// }}}
// typedefs {{{
typedef long long int LL;
typedef unsigned long long int ULL;
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<LL> VLL;
typedef vector<VLL> VVLL;
typedef vector<ULL> VULL;
typedef vector<VULL> VVULL;
typedef vector<double> VD;
typedef vector<VD> VVD;
typedef vector<bool> VB;
typedef vector<VB> VVB;
typedef vector<char> VC;
typedef vector<VC> VVC;
typedef vector<string> VS;
typedef vector<VS> VVS;
typedef pair<int, int> PII;
typedef complex<int> P;
// }}}
// macros & inline functions {{{
// syntax sugars {{{
#define FOR(i, b, e) for (typeof(e) i = (b); i < (e); ++i)
#define FORI(i, b, e) for (typeof(e) i = (b); i <= (e); ++i)
#define REP(i, n) FOR(i, 0, n)
#define REPI(i, n) FORI(i, 0, n)
#define OPOVER(_op, _type) inline bool operator _op(const _type &t) const
// }}}
// conversion {{{
inline int toInt(string s) {
  int v;
  istringstream sin(s);
  sin >> v;
  return v;
}
template <class T> inline string toString(T x) {
  ostringstream sout;
  sout << x;
  return sout.str();
}
// }}}
// array and STL {{{
#define ARRSIZE(a) (sizeof(a) / sizeof(a[0]))
#define ZERO(a, v) (assert(v == 0 || v == -1), memset(a, v, sizeof(a)))
#define F first
#define S second
#define MP(a, b) make_pair(a, b)
#define SIZE(a) ((LL)a.size())
#define PB(e) push_back(e)
#define SORT(v) sort((v).begin(), (v).end())
#define RSORT(v) sort((v).rbegin(), (v).rend())
#define ALL(a) (a).begin(), (a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define EACH(c, it)                                                            \
  for (typeof((c).begin()) it = (c).begin(); it != (c).end(); ++it)
#define REACH(c, it)                                                           \
  for (typeof((c).rbegin()) it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(s, e) ((s).find(e) != (s).end())
// }}}
// bit manipulation {{{
// singed integers are not for bitwise operations, specifically arithmetic
// shifts ('>>', and maybe not good for '<<' too)
#define IS_UNSIGNED(n) (!numeric_limits<typeof(n)>::is_signed)
#define BIT(n) (assert(IS_UNSIGNED(n)), assert(n < 64), (1ULL << (n)))
#define BITOF(n, m)                                                            \
  (assert(IS_UNSIGNED(n)), assert(m < 64), ((ULL)(n) >> (m)&1))
inline int BITS_COUNT(ULL b) {
  int c = 0;
  while (b != 0) {
    c += (b & 1);
    b >>= 1;
  }
  return c;
}
inline int MSB(ULL b) {
  int c = 0;
  while (b != 0) {
    ++c;
    b >>= 1;
  }
  return c - 1;
}
inline int MAKE_MASK(ULL upper, ULL lower) {
  assert(lower < 64 && upper < 64 && lower <= upper);
  return (BIT(upper) - 1) ^ (BIT(lower) - 1);
}
// }}}
// for readable code {{{
#define EVEN(n) (n % 2 == 0)
#define ODD(n) (!EVEN(n))
// }}}
// debug {{{
#define arrsz(a) (sizeof(a) / sizeof(a[0]))
#define dprt(fmt, ...)                                                         \
  if (opt_debug) {                                                             \
    fprintf(stderr, fmt, ##__VA_ARGS__);                                       \
  }
#define darr(a)                                                                \
  if (opt_debug) {                                                             \
    copy((a), (a) + arrsz(a), ostream_iterator<int>(cerr, " "));               \
    cerr << endl;                                                              \
  }
#define darr_range(a, f, t)                                                    \
  if (opt_debug) {                                                             \
    copy((a) + (f), (a) + (t), ostream_iterator<int>(cerr, " "));              \
    cerr << endl;                                                              \
  }
#define dvec(v)                                                                \
  if (opt_debug) {                                                             \
    copy(ALL(v), ostream_iterator<int>(cerr, " "));                            \
    cerr << endl;                                                              \
  }
#define darr2(a)                                                               \
  if (opt_debug) {                                                             \
    FOR(__i, 0, (arrsz(a))) { darr((a)[__i]); }                                \
  }
#define WAIT()                                                                 \
  if (opt_debug) {                                                             \
    string _wait_;                                                             \
    cerr << "(hit return to continue)" << endl;                                \
    getline(cin, _wait_);                                                      \
  }
#define dump(x)                                                                \
  if (opt_debug) {                                                             \
    cerr << " [L" << __LINE__ << "] " << #x << " = " << (x) << endl;           \
  }
#define dumpl(x)                                                               \
  if (opt_debug) {                                                             \
    cerr << " [L" << __LINE__ << "] " << #x << endl << (x) << endl;            \
  }
#define dumpf()                                                                \
  if (opt_debug) {                                                             \
    cerr << __PRETTY_FUNCTION__ << endl;                                       \
  }
#define where()                                                                \
  if (opt_debug) {                                                             \
    cerr << __FILE__ << ": " << __PRETTY_FUNCTION__ << " [L: " << __LINE__     \
         << "]" << endl;                                                       \
  }
#define show_bits(b, s)                                                        \
  if (opt_debug) {                                                             \
    REP(i, s) {                                                                \
      cerr << BITOF(b, s - 1 - i);                                             \
      if (i % 4 == 3)                                                          \
        cerr << ' ';                                                           \
    }                                                                          \
    cerr << endl;                                                              \
  }

// ostreams {{{
// complex
template <typename T> ostream &operator<<(ostream &s, const complex<T> &d) {
  return s << "(" << d.real() << ", " << d.imag() << ")";
}

// pair
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const pair<T1, T2> &d) {
  return s << "(" << d.first << ", " << d.second << ")";
}

// vector
template <typename T> ostream &operator<<(ostream &s, const vector<T> &d) {
  int len = d.size();
  REP(i, len) {
    s << d[i];
    if (i < len - 1)
      s << "\t";
  }
  return s;
}

// 2 dimentional vector
template <typename T>
ostream &operator<<(ostream &s, const vector<vector<T>> &d) {
  int len = d.size();
  REP(i, len) { s << d[i] << endl; }
  return s;
}

// map
template <typename T1, typename T2>
ostream &operator<<(ostream &s, const map<T1, T2> &m) {
  s << "{" << endl;
  for (typeof(m.begin()) itr = m.begin(); itr != m.end(); ++itr) {
    s << "\t" << (*itr).first << " : " << (*itr).second << endl;
  }
  s << "}" << endl;
  return s;
}
// }}}
// }}}
// }}}
// time {{{
inline double now() {
  struct timeval tv;
  gettimeofday(&tv, NULL);
  return (static_cast<double>(tv.tv_sec) +
          static_cast<double>(tv.tv_usec) * 1e-6);
}
// }}}
// string manipulation {{{
inline VS split(string s, char delimiter) {
  VS v;
  string t;
  REP(i, s.length()) {
    if (s[i] == delimiter)
      v.PB(t), t = "";
    else
      t += s[i];
  }
  v.PB(t);
  return v;
}
inline string join(VS s, string j) {
  string t;
  REP(i, s.size()) { t += s[i] + j; }
  return t;
}
// }}}
// geometry {{{
#define Y real()
#define X imag()
// }}}
// 2 dimentional array {{{
P dydx4[4] = {P(-1, 0), P(0, 1), P(1, 0), P(0, -1)};
P dydx8[8] = {P(-1, 0), P(0, 1), P(1, 0),  P(0, -1),
              P(-1, 1), P(1, 1), P(1, -1), P(-1, -1)};
int g_height, g_width;
bool in_field(P p) {
  return (0 <= p.Y && p.Y < g_height) && (0 <= p.X && p.X < g_width);
}
// }}}
// input and output {{{
inline void input(string filename) { freopen(filename.c_str(), "r", stdin); }
inline void output(string filename) { freopen(filename.c_str(), "w", stdout); }
// }}}
// }}}
bool opt_debug = false;

class Fraction {
public:
  int numerator;
  int denominator;
  Fraction(int _numerator, int _denominator) {
    numerator = _numerator;
    denominator = _denominator;
  };

  Fraction operator*(const int rhs) {
    return Fraction(this->numerator * rhs, this->denominator);
  };

  Fraction operator+(const Fraction &lhs) {
    // TODO: Use lcm
    assert(this->denominator == lhs.denominator);
    return Fraction(this->numerator + lhs.numerator, this->denominator);
  }
};
std::ostream &operator<<(std::ostream &s, const Fraction &a) {
  if (a.denominator == 1) {
    s << a.numerator;
  } else {
    s << a.numerator << "/" << a.denominator;
  }
  return s;
}

void solve(map<int, int> &count, int sum, int n, int m, int k) {
  if (n == 0) {
    int ans = max(1, sum - k);
    if (!EXIST(count, ans)) {
      count[ans] = 0;
    }
    count[ans]++;
    return;
  }

  REP(i, m) { solve(count, sum + (i + 1), n - 1, m, k); }
}

int main(int argc, char **argv) {
  std::ios_base::sync_with_stdio(false);
  // set options {{{
  int __c;
  while ((__c = getopt(argc, argv, "d")) != -1) {
    switch (__c) {
    case 'd':
      opt_debug = true;
      break;
    default:
      abort();
    }
  }
  // }}}

  // input("./inputs/0.txt");
  // output("./outputs/0.txt");

  int n, m, k;
  while (cin >> n >> m >> k, n | m | k) {
    map<int, int> count;
    solve(count, 0, n, m, k);
    Fraction f(0, pow(m, n));
    EACH(count, itr) {
      int ans = (*itr).first, cnt = (*itr).second;
      f = f + Fraction(ans * cnt, pow(m, n));
    }

    printf("%.10lf\n", f.numerator / (double)f.denominator);
  }

  return 0;
}

// vim: foldmethod=marker