Language: C++

#include <iostream>
#include <string>
#include <queue>
#include <unordered_map>
#include <algorithm>

using namespace std;

struct Node {
  int start;
  string buf;
  Node(int index, string s): start(index), buf(s) {}
};

int dir[4] = {-1, 1, -4, 4};
unordered_map<string, int> dp;

void solve() {
  dp["01234567"] = 0;
  int step = 0;
  queue<Node> q;
  q.push(Node(0, "01234567"));
  while (!q.empty()) {
    int size = q.size();
    step++;
    while (size-- > 0) {
      Node cur = q.front();
      q.pop();
      for (int i = 0; i < 4; ++i) {
        int next_p = cur.start + dir[i];
        if (next_p >= 0 && next_p < 8
            && !(cur.start == 4 && i == 0)
            && !(cur.start == 3 && i == 1)) {
          string next = cur.buf;
          swap(next[cur.start], next[next_p]);
          if (dp.count(next) == 0) {
            dp[next] = step;
            q.push(Node(next_p, next));
          }
        }
      }
    }
  }
}

int main() {
  solve();
  string input;
  char c;
  while (cin >> c) {
    input.clear();
    input.append(1, c);
    for (int i = 0; i < 7; ++i) {
       cin >> c;
        input.append(c);
     }
     cout << dp[input] << endl;
  }
  return 0;
}

Compiler output:
a.cc: In function 'int main()':
a.cc:55:21: error: no matching function for call to 'std::__cxx11::basic_string<char>::append(char&)'
   55 |         input.append(c);
      |         ~~~~~~~~~~~~^~~
In file included from /usr/include/c++/14/string:54,
                 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/basic_string.h:1480:7: note: candidate: 'std::__cxx11::basic_string<_CharT, _Traits, _Alloc>& std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(const _CharT*) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>]' (near match)
 1480 |       append(const _CharT* __s)
      |       ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1480:7: note:   conversion of argument 1 would be ill-formed:
a.cc:55:22: error: invalid conversion from 'char' to 'const char*' [-fpermissive]
   55 |         input.append(c);
      |                      ^
      |                      |
      |                      char
/usr/include/c++/14/bits/basic_string.h:1529:9: note: candidate: 'template<class _InputIterator, class> std::__cxx11::basic_string<_CharT, _Traits, _Alloc>& std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(_InputIterator, _InputIterator) [with <template-parameter-2-2> = _InputIterator; _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>]'
 1529 |         append(_InputIterator __first, _InputIterator __last)
      |         ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1529:9: note:   candidate expects 2 arguments, 1 provided
/usr/include/c++/14/bits/basic_string.h:1541:9: note: candidate: 'template<class _Tp> std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::_If_sv<_Tp, std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&> std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(const _Tp&) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>]'
 1541 |         append(const _Tp& __svt)
      |         ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1541:9: note:   template argument deduction/substitution failed:
In file included from /usr/include/c++/14/bits/move.h:37,
                 from /usr/include/c++/14/bits/exception_ptr.h:41,
                 from /usr/include/c++/14/exception:166,
                 from /usr/include/c++/14/ios:41:
/usr/include/c++/14/type_traits: In substitution of 'template<bool _Cond, class _Tp> using std::enable_if_t = typename std::enable_if::type [with bool _Cond = false; _Tp = std::__cxx11::basic_string<char>&]':
/usr/include/c++/14/bits/basic_string.h:149:8:   required by substitution of 'template<class _CharT, class _Traits, class _Alloc> template<class _Tp, class _Res> using std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::_If_sv = std::enable_if_t<((bool)std::__and_<std::is_convertible<const _Tp&, std::basic_string_view<_CharT, _Traits> >, std::__not_<std::is_convertible<const _Tp*, const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>*> >, std::__not_<std::is_convertible<const _Tp&, const _CharT*> > >::value), _Res> [with _Tp = char; _Res = std::__cxx11::basic_string<char>&; _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>]'
  149 |         using _If_sv = enable_if_t<
      |               ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1541:9:   required by substitution of 'template<class _Tp> std::__cxx11::basic_string<char>::_If_sv<_Tp, std::__cxx11::basic_string<char>&> std::__cxx11::basic_string<char>::append(const _Tp&) [with _Tp = char]'
 1541 |         append(const _Tp& __svt)
      |         ^~~~~~
a.cc:55:21:   required from here
   55 |         input.append(c);
      |         ~~~~~~~~~~~~^~~
/usr/include/c++/14/type_traits:2711:11: error: no type named 'type' in 'struct std::enable_if<false, std::__cxx11::basic_string<char>&>'
 2711 |     using enable_if_t = typename enable_if<_Cond, _Tp>::type;
      |           ^~~~~~~~~~~
/usr/include/c++/14/bits/basic_string.h:1557:9: note: candidate: 'template<class _Tp> std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::_If_sv<_Tp, std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&> std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(const _Tp&, size_type, size_type) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>]'
 1557 |         append(const _Tp& __svt, size_type __pos, size_type __n = npos)
      |         ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1557:9: note:   candidate expects 2 arguments, 1 provided
/usr/include/c++/14/bits/basic_string.h:1435:7: note: candidate: 'std::__cxx11::basic_string<_CharT, _Traits, _Alloc>& std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>]'
 1435 |       append(const basic_string& __str)
      |       ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1435:34: note:   no known conversion for argument 1 from 'char' to 'const std::__cxx11::basic_string<char>&'
 1435 |       append(const basic_string& __str)
      |              ~~~~~~~~~~~~~~~~~~~~^~~~~
/usr/include/c++/14/bits/basic_string.h:1453:7: note: candidate: 'std::__cxx11::basic_string<_CharT, _Traits, _Alloc>& std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(const std::__cxx11::basic_string<_CharT, _Traits, _Alloc>&, size_type, size_type) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>; size_type = long unsigned int]'
 1453 |       append(const basic_string& __str, size_type __pos, size_type __n = npos)
      |       ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1453:7: note:   candidate expects 3 arguments, 1 provided
/usr/include/c++/14/bits/basic_string.h:1466:7: note: candidate: 'std::__cxx11::basic_string<_CharT, _Traits, _Alloc>& std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(const _CharT*, size_type) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>; size_type = long unsigned int]'
 1466 |       append(const _CharT* __s, size_type __n)
      |       ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1466:7: note:   candidate expects 2 arguments, 1 provided
/usr/include/c++/14/bits/basic_string.h:1498:7: note: candidate: 'std::__cxx11::basic_string<_CharT, _Traits, _Alloc>& std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(size_type, _CharT) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>; size_type = long unsigned int]'
 1498 |       append(size_type __n, _CharT __c)
      |       ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1498:7: note:   candidate expects 2 arguments, 1 provided
/usr/include/c++/14/bits/basic_string.h:1509:7: note: candidate: 'std::__cxx11::basic_string<_CharT, _Traits, _Alloc>& std::__cxx11::basic_string<_CharT, _Traits, _Alloc>::append(std::initializer_list<_Tp>) [with _CharT = char; _Traits = std::char_traits<char>; _Alloc = std::allocator<char>]'
 1509 |       append(initializer_list<_CharT> __l)
      |       ^~~~~~
/usr/include/c++/14/bits/basic_string.h:1509:39: note:   no known conversion for argument 1 from 'char' to 'std::initializer_list<char>'
 1509 |       append(initializer_list<_CharT> __l)
      |              ~~~~~~~~~~~~~~~~~~~~~~~~~^~~