Language: C++

2#include <iostream>
#include <cstdio>
#include <cassert>
#include <algorithm>
#include <vector>
#include <cmath>
using namespace std;

const int MAX_M = 2000;
const int MAX_N = 2000;

const double EPS = 1e-8;

bool EQ(double a, double b) {
    return abs(a - b) < EPS;
}

double P1[MAX_M + 1][MAX_M + 1]; // P1[m][x] :: アイドル2,3,...,Nがビジュアルアピールをm回中x回だけ行う確率
double SP[MAX_M + 1][MAX_M + 1]; // SP[m][x] :: アイドル2,3,...,Nがビジュアルアピールをm回中x回以上行う確率

int N, M;
vector<int> vi, da, vo;

void initP1() {
    for (int m = 0; m <= MAX_M; m++) for (int x = 0; x <= MAX_M; x++) 
        P1[m][x] = 0;
    P1[0][0] = 1;
    for (int m = 1; m <= MAX_M; m++) {
        for (int x = 0; x <= m; x++) {
            P1[m][x] += P1[m - 1][x] * (2.0 / 3.0);
            if (x >= 1) {
                P1[m][x] += P1[m - 1][x - 1] * (1.0 / 3.0);
            }
        }
    }
}

void initSP() {
    for (int m = 0; m <= MAX_M; m++) for (int x = 0; x <= MAX_M; x++) 
        SP[m][x] = 0;
    for (int m = 0; m <= MAX_M; m++) {
        SP[m][0] = 1;
        for (int x = 1; x <= m; x++) {
            SP[m][x] = SP[m][x - 1] - P1[m][x - 1];
        }
        assert(EQ(SP[m][m], P1[m][m]));
    }
}

void dump() {
    printf("SP:\n");
    for (int i = 0; i <= M; i++) {
        for (int j = 0; j <= i; j++) {
            printf("%3.3f ", SP[i][j]);
        }
        printf("\n");
    }
}

double memo[MAX_M + 1][6][3];
double top(int x, int p, int t, const vector<int>& V) {
    static double dp[MAX_N + 1][5];
    if (memo[x][p][t] > -1e9) return memo[x][p][t];
    int k = V[1];
    int P = x * k;
    for (int i = 0; i <= N; i++) for (int j = 0; j <= 4; j++) dp[i][j] = 0;
    dp[1][1] = 1.0;
    dp[1][4] = 1.0;
    for (int i = 2; i <= N; i++) {
        double X = SP[M][ (P + V[i] - 1) / V[i]];
        dp[i][1] = dp[i - 1][1] * (1.0 - X);
        dp[i][2] = dp[i - 1][2] * (1.0 - X) + dp[i - 1][1] * X;
        dp[i][3] = dp[i - 1][3] * (1.0 - X) + dp[i - 1][2] * X;

        dp[i][4] = dp[i - 1][4] * X;
    }
    return memo[x][p][t] = (dp[N][1] + dp[N][2] + dp[N][3]) * p - dp[N][4] * 1;
}

void solve() {
    double ans = -1e9;
    for (int i = 0; i <= M; i++) for (int j = 0; j <= 6; j++) for (int k = 0; k < 3; k++) memo[i][j][k] = -1e9;
    for (int x = 0; x <= M; x++) {
        for (int y = 0; y <= M - x; y++) {
            int z = M - (x + y);
            // viをx, daをy, voをz回行う
            ans = max(ans, top(x, 5, 0, vi) + top(y, 3, 1, da) + top(z, 2, 2, vo));
        }
    }
    printf("%.8lf\n", ans);
}

int main() {
    cin >> N >> M;
    vi.clear(); da.clear(); vo.clear();
    vi.resize(N + 1); da.resize(N + 1); vo.resize(N + 1);
    for (int i = 1; i <= N; i++) cin >> vi[i] >> da[i] >> vo[i];
    initP1(); initSP();
    solve();
    return 0;
}

Compiler output:
a.cc:1:2: error: stray '#' in program
    1 | 2#include <iostream>
      |  ^
a.cc:1:1: error: expected unqualified-id before numeric constant
    1 | 2#include <iostream>
      | ^
In file included from /usr/include/c++/14/bits/stl_algobase.h:62,
                 from /usr/include/c++/14/algorithm:60,
                 from a.cc:4:
/usr/include/c++/14/ext/type_traits.h:164:35: error: 'constexpr const bool __gnu_cxx::__is_null_pointer' redeclared as different kind of entity
  164 |   __is_null_pointer(std::nullptr_t)
      |                                   ^
/usr/include/c++/14/ext/type_traits.h:159:5: note: previous declaration 'template<class _Type> constexpr bool __gnu_cxx::__is_null_pointer(_Type)'
  159 |     __is_null_pointer(_Type)
      |     ^~~~~~~~~~~~~~~~~
/usr/include/c++/14/ext/type_traits.h:164:26: error: 'nullptr_t' is not a member of 'std'
  164 |   __is_null_pointer(std::nullptr_t)
      |                          ^~~~~~~~~
In file included from /usr/include/c++/14/bits/stl_pair.h:60,
                 from /usr/include/c++/14/bits/stl_algobase.h:64:
/usr/include/c++/14/type_traits:666:33: error: 'nullptr_t' is not a member of 'std'
  666 |     struct is_null_pointer<std::nullptr_t>
      |                                 ^~~~~~~~~
/usr/include/c++/14/type_traits:666:42: error: template argument 1 is invalid
  666 |     struct is_null_pointer<std::nullptr_t>
      |                                          ^
/usr/include/c++/14/type_traits:670:48: error: template argument 1 is invalid
  670 |     struct is_null_pointer<const std::nullptr_t>
      |                                                ^
/usr/include/c++/14/type_traits:674:51: error: template argument 1 is invalid
  674 |     struct is_null_pointer<volatile std::nullptr_t>
      |                                                   ^
/usr/include/c++/14/type_traits:678:57: error: template argument 1 is invalid
  678 |     struct is_null_pointer<const volatile std::nullptr_t>
      |                                                         ^
/usr/include/c++/14/type_traits:1429:37: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
 1429 |     : public integral_constant<std::size_t, alignof(_Tp)>
      |                                     ^~~~~~
In file included from /usr/include/stdio.h:34,
                 from /usr/include/c++/14/cstdio:42,
                 from a.cc:2:
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/type_traits:1429:57: error: template argument 1 is invalid
 1429 |     : public integral_constant<std::size_t, alignof(_Tp)>
      |                                                         ^
/usr/include/c++/14/type_traits:1429:57: note: invalid template non-type parameter
/usr/include/c++/14/type_traits:1438:37: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
 1438 |     : public integral_constant<std::size_t, 0> { };
      |                                     ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/type_traits:1438:46: error: template argument 1 is invalid
 1438 |     : public integral_constant<std::size_t, 0> { };
      |                                              ^
/usr/include/c++/14/type_traits:1438:46: note: invalid template non-type parameter
/usr/include/c++/14/type_traits:1440:26: error: 'std::size_t' has not been declared
 1440 |   template<typename _Tp, std::size_t _Size>
      |                          ^~~
/usr/include/c++/14/type_traits:1441:21: error: '_Size' was not declared in this scope
 1441 |     struct rank<_Tp[_Size]>
      |                     ^~~~~
/usr/include/c++/14/type_traits:1441:27: error: template argument 1 is invalid
 1441 |     struct rank<_Tp[_Size]>
      |                           ^
/usr/include/c++/14/type_traits:1442:37: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
 1442 |     : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
      |                                     ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/type_traits:1442:65: error: template argument 1 is invalid
 1442 |     : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
      |                                                                 ^
/usr/include/c++/14/type_traits:1442:65: note: invalid template non-type parameter
/usr/include/c++/14/type_traits:1446:37: error: 'size_t' is not a member of 'std'; did you mean 'size_t'?
 1446 |     : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
      |                                     ^~~~~~
/usr/lib/gcc/x86_64-linux-gnu/14/include/stddef.h:214:23: note: 'size_t' declared here
  214 | typedef __SIZE_TYPE__ size_t;
      |                       ^~~~~~
/usr/include/c++/14/type_traits:1446:65: error: template argument 1 is invalid
 1446 |     : public integral_constant<std::size_t, 1 + rank<_Tp>::value> { };
      |                                                                 ^
/usr/include/c++/14/type_traits:1446:65: note: invalid template non-type parameter
/usr/include/c++/14/type_traits:2086:26: error: 'std::size_t' has not been declared
 2086 |   template<typename _Tp, std::size_t _Size>
      |                          ^~~
/usr/include/c++/14/type_traits:2087:30: error: '_Size' was not declared in this scope
 2087 |     struct remove_extent<_Tp[_Size]>
      |                              ^~~~~
/usr/include/c++/14/type_traits:2087:36: error: template argument 1 is invalid
 2087 |     struct remove_extent<_Tp[_Size]>
      |                                    ^
/usr/include/c++/14/type_traits:2099:26: error: 'std::size_t' has not been declared
 2099 |   template<typename _Tp, std::size_t _Size>
      |                          ^~~
/usr/include/c++/14/type_traits:2100:35: error: '_Size' was not declared in this scope
 2100 |     struct remove_all_extents<_Tp[_Size]>
      |                                   ^~~~~
/usr/include/c++/14/type_traits:2100:41: error: template argument 1 is invalid
 2100 |     struct remove_all_extents<_Tp[_Size]>
      |                                         ^
/usr/include/c++/14/type_traits:2171:12: error: 'std::size_t' has not been declared
 2171 |   template<std::size_t _Len>
      |            ^~~
/usr/include/c++/14/type_traits:2176:30: error: '_Len' was not declared in this scope
 2176 |         unsigned char __data[_Len];
      |                              ^~~~
/usr/include/c++/14/type_traits:2194:12: error: 'std::size_t' has not been declared
 2194 |   template<std::size_t _Len, std::size_t _Align =
      |            ^~~
/usr/include/c++/14/type_traits:2194:30: error: 'std::size_t' has not been declared
 2194 |   template<std::size_t _Len, std::size_t _Align =
      |                              ^~~
/usr/include/c++/14/type_traits:2195:55: error: '_Len' was not declared in this scope
 2195 |            __alignof__(typename __aligned_storage_msa<_Len>::__type)>
      |                                                       ^~~~
/usr/include/c++/14/type_traits:2195:59: error: template argument 1 is invalid
 2195 |            __alignof__(typename __aligned_storage_msa<_Len>::__type)>
      |                                                           ^
/usr/include/c++/14/type_traits:2202:30: error: '_Len' was not declared in this scope
 2202 |         unsigned char __data[_Len];
      |                              ^~~~
/usr/include/c++/14/type_traits:2203:44: error: '_Align' was not declared in this scope
 2203 |         struct __attribute__((__aligned__((_Align)))) { } __align;
      |                                            ^~~~~~
In file included from /usr/include/c++/14/bits/stl_algobase.h:65:
/usr/include/c++/14/bits/stl_iterator_base_types.h:125:67: error: 'ptrdiff_t' does not name a type
  125 |   template<typename _Category, typename _Tp, typename _Distance = ptrdiff_t,
      |                                                                   ^~~~~~~~~
/usr/include/c++/14/bits/stl_iterator_base_types.h:1:1: note: 'ptrdiff_t' is defined in header '<cstddef>'; this is probably fixable by adding '#include <cstddef>'
  +++ |+#include <cstddef>
    1 | // Types used in iterator implementation -*- C++ -*-
/usr/include/c++/14/bits/stl_iterator_base_types.h:214:15: error: 'ptrdiff_t' does not name a type
  214 |       typedef ptrdiff_t                   difference_type;
      |               ^~~~~~~~~
/usr/include/c++/14/bits/stl_iterator_base_types.h:214:15: note: 'ptrdiff_t' is defined in header '<cstddef>'; this is probably fixable by adding '#include <cstddef>'
/usr/include/c++/14/bits/stl_iterator_base_types.h:225:15: error: 'ptrdiff_t' does not name a type
  225 |       typedef ptrdiff_t                   difference_type;
      |               ^~~~~~~~~
/usr/include/c++/14/bits/stl_iterator_base_types.h:225:15: note: 'ptrdiff_t' is defined in header '<cstddef>'; this is probably fixable by adding '#include <cstddef>'
In file included from /usr/include/c++/14/bits/stl_algobase.h:66:
/usr/include/c++/14/bits/stl_iterator_base_funcs.h:112:5: error: 'ptrdiff_t' does not name a type
  112 |     ptrdiff_t
      |     ^~~~~~~~~
/usr/include/c++/14/bits/stl_iterator_base_funcs.h:66:1: note: 'ptrdiff_t' is defined in header '<cstddef>'; this is probably fixable by adding '#include <cstddef>'
   65 | #include <debug/assertions.h>
  +++ |+#include <cstddef>
   66 | #include <bits/stl_iterator_base_types.h>
/usr/include/c++/14/bits/stl_iterator_base_funcs.h:118:5: error: 'ptrdiff_t' does not name a type
  118 |     ptrdiff_t
      |     ^~~~~~~~~
/usr/include/c++/14/bits/stl_iterator_base_funcs.h:118:5: note: 'ptrdiff_t' is defined in header '<cstddef>'; this is probably fixable by adding '#include <cstddef>'
In file included from /usr/include/c++/14/bits/stl_iterator.h:67,
                 from /usr/include/c++/14/bits/stl_algobase.h:67:
/usr/inc