Language: C++

    #include <iostream>
    #include <algorithm>
    #include <cstdio>
    #define Max(a,b) a>b?a:b
    #define INF 10000000000000000
    using namespace std;
    typedef long long LL;
    const int MAX = 110;
    LL weight[MAX], value[MAX];
    LL W;
    pair<LL, LL> ps[1 << (MAX / 2)];
    int n;
    void slove()
    {
        //枚举前半部分 
        int n2 = n / 2;
        for (int i = 0; i < 1 << n2; i++)//前半部分的枚举总数为 2^(n/2); 
        {
            LL sw = 0, sv = 0;
            //每种结果选取特定的价值和重量(i.e 一共2个东西，就一共四种情况，都不选，选第一个，选第二个，都选) 
            for (int j = 0; j < n2; j++)
            {
                if (i >> j & 1)
                {
                    sw += weight[j];
                    sv += value[j];
                }
            }
            ps[i] = make_pair(sw, sv);//加入到ps数组中 
        }
        //对ps排序 
        sort(ps, ps + (1 << n2));
        //ps 去重 
        int m = 1;
        for (int i = 1; i < 1 << n2; i++)
            if (ps[m - 1].second < ps[i].second)
                ps[m++] = ps[i];
        LL res = 0;//保存结果 
        //枚举后半部分， 并且找到最优解 
        for (int i = 0; i < 1 << (n - n2); i++)//同样枚举的总个数 
        {
            LL sw = 0, sv = 0;
            for (int j = 0; j < n - n2; j++)//和前半部分的一样 
            {
                if (i >> j & 1)
                {
                    sw += weight[n2 + j];
                    sv += value[n2 + j];
                }
            }
            if (sw <= W)//加个判断求解最大价值，只有小于背包容量的时候 
            {
                LL tv = (lower_bound(ps, ps + m, make_pair(W - sw, INF)) - 1)->second;//找到前半部分对应的value 
                res = Max(res, sv + tv); 
            }
        }
        printf("%lld\n", res);
    }
     
    int main()
    {
        while (~scanf("%d %lld", &n, &W))
        {
            for (int i = 0; i < n; i++)
                scanf("%lld %lld", &weight[i], &value[i]);
            slove();
        }
        return 0;
    }

Compiler output:
a.cc:11:23: warning: left shift count >= width of type [-Wshift-count-overflow]
   11 |     pair<LL, LL> ps[1 << (MAX / 2)];
      |                     ~~^~~~~~~~~~~~
In file included from /usr/include/c++/14/bits/stl_algobase.h:71,
                 from /usr/include/c++/14/string:51,
                 from /usr/include/c++/14/bits/locale_classes.h:40,
                 from /usr/include/c++/14/bits/ios_base.h:41,
                 from /usr/include/c++/14/ios:44,
                 from /usr/include/c++/14/ostream:40,
                 from /usr/include/c++/14/iostream:41,
                 from a.cc:1:
/usr/include/c++/14/bits/predefined_ops.h: In instantiation of 'bool __gnu_cxx::__ops::_Iter_less_val::operator()(_Iterator, _Value&) const [with _Iterator = std::pair<long long int, long long int>*; _Value = const std::pair<long long int, long int>]':
/usr/include/c++/14/bits/stl_algobase.h:1504:14:   required from '_ForwardIterator std::__lower_bound(_ForwardIterator, _ForwardIterator, const _Tp&, _Compare) [with _ForwardIterator = pair<long long int, long long int>*; _Tp = pair<long long int, long int>; _Compare = __gnu_cxx::__ops::_Iter_less_val]'
 1504 |           if (__comp(__middle, __val))
      |               ~~~~~~^~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_algobase.h:1539:32:   required from '_ForwardIterator std::lower_bound(_ForwardIterator, _ForwardIterator, const _Tp&) [with _ForwardIterator = pair<long long int, long long int>*; _Tp = pair<long long int, long int>]'
 1539 |       return std::__lower_bound(__first, __last, __val,
      |              ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
 1540 |                                 __gnu_cxx::__ops::__iter_less_val());
      |                                 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a.cc:53:37:   required from here
   53 |                 LL tv = (lower_bound(ps, ps + m, make_pair(W - sw, INF)) - 1)->second;//找到前半部分对应的value
      |                          ~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/bits/predefined_ops.h:69:22: error: no match for 'operator<' (operand types are 'std::pair<long long int, long long int>' and 'const std::pair<long long int, long int>')
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
In file included from /usr/include/c++/14/string:48:
/usr/include/c++/14/bits/stl_iterator.h:1241:5: note: candidate: 'template<class _IteratorL, class _IteratorR, class _Container> bool __gnu_cxx::operator<(const __normal_iterator<_IteratorL, _Container>&, const __normal_iterator<_IteratorR, _Container>&)'
 1241 |     operator<(const __normal_iterator<_IteratorL, _Container>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1241:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const __gnu_cxx::__normal_iterator<_IteratorL, _Container>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1249:5: note: candidate: 'template<class _Iterator, class _Container> bool __gnu_cxx::operator<(const __normal_iterator<_Iterator, _Container>&, const __normal_iterator<_Iterator, _Container>&)'
 1249 |     operator<(const __normal_iterator<_Iterator, _Container>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1249:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const __gnu_cxx::__normal_iterator<_Iterator, _Container>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:448:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator<(const reverse_iterator<_Iterator>&, const reverse_iterator<_Iterator>&)'
  448 |     operator<(const reverse_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:448:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::reverse_iterator<_Iterator>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:493:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator<(const reverse_iterator<_Iterator>&, const reverse_iterator<_IteratorR>&)'
  493 |     operator<(const reverse_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:493:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::reverse_iterator<_Iterator>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1694:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator<(const move_iterator<_IteratorL>&, const move_iterator<_IteratorR>&)'
 1694 |     operator<(const move_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1694:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::move_iterator<_IteratorL>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1760:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator<(const move_iterator<_IteratorL>&, const move_iterator<_IteratorL>&)'
 1760 |     operator<(const move_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1760:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::move_iterator<_IteratorL>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
In file included from /usr/include/c++/14/bits/stl_algobase.h:64:
/usr/include/c++/14/bits/stl_pair.h:1045:5: note: candidate: 'template<class _T1, class _T2> constexpr bool std::operator<(const pair<_T1, _T2>&, const pair<_T1, _T2>&)'
 1045 |     operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_pair.h:1045:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   deduced conflicting types for parameter '_T2' ('long long int' and 'long int')
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
In file included from /usr/include/c++/14/bits/basic_string.h:47,
                 from /usr/include/c++/14/string:54:
/usr/include/c++/14/string_view:673:5: note: candidate: 'template<class _CharT, class _Traits> constexpr bool std::operator<(basic_string_view<_CharT, _Traits>, basic_string_view<_CharT, _Traits>)'
  673 |     operator< (basic_string_view<_CharT, _Traits> __x,
      |     ^~~~~~~~
/usr/include/c++/14/string_view:673:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'std::basic_string_view<_CharT, _Traits>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/string_view:680:5: note: candidate: 'template<class _CharT, class _Traits> constexpr bool std::operator<(basic_string_view<_CharT, _Traits>, __type_identity_t<basic_string_view<_CharT, _Traits> >)'
  680 |     operator< (basic_string_view<_CharT, _Traits> __x,
      |     ^~~~~~~~
/usr/include/c++/14/string_view:680:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'std::basic_string_view<_CharT, _Traits>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/string_view:688:5: note: candidate: 'template<class _CharT, class _Traits> constexpr bool std::operator<(__type_identity_t<basic_string_view<_CharT, _Traits> >, basic_string_view<_CharT, _Traits>)'
  688 |     operator< (__type_identity_t<basic_string_view<_CharT, _Traits>> __x,
      |     ^~~~~~~~
/usr/include/c++/14/string_view:688:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long int>' is not derived from 'std::basic_string_view<_CharT, _Traits>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/basic_string.h:3874:5: note: candidate: 'template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const __cxx11::basic_string<_CharT, _Traits, _Allocator>&, const __cxx11::basic_string<_CharT, _Traits, _Allocator>&)'
 3874 |     operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/basic_string.h:3874:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::__cxx11::basic_string<_CharT, _Traits, _Allocator>'
   69 |       { return *__it < __val; }
      |                ~~~~~~^~~~~~~
/usr/include/c++/14/bits/basic_string.h:3888:5: note: candidate: 'template<class _CharT, class _Traits, class _Alloc> bool std::operator<(const __cxx11::basic_string<_CharT, _Traits, _Allocator>&, const _CharT*)'
 3888 |     operator<(const basic_string<_CharT, _Traits, _Alloc>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/basic_string.h:3888:5: note:   template argument deduction/substitution failed:
/usr/include/c++/14/bits/predefined_ops.h:69:22: note:   'std::pair<long long int, long long int>' is not derived from 'const std::__cxx11::basic_string<_CharT, _Traits, _Allocator>'