my failures with lambda in c++

test.cpp

#include <algorithm>
#include <functional>
#include <string>
#include <vector>

template<typename A, typename Func> auto map_3(const A& orig, Func f) -> std::vector<decltype(f(begin(A())))> {
  std::vector<decltype(f(begin(A())))> rv;
  rv.resize(orig.size());
  std::transform(begin(orig), end(orig), begin(rv), f);
  return rv;
}

template<typename A, typename Func> auto map_2(const std::vector<A>& orig, Func f) -> std::vector<decltype(f(A()))> {
  std::vector<decltype(f(A()))> rv;
  rv.resize(orig.size());
  std::transform(begin(orig), end(orig), begin(rv), f);
  return rv;
}

template<typename A, typename B, typename C> std::vector<B> map_(const std::vector<A>& orig, C f) {
  std::vector<B> rv;
  rv.resize(orig.size());
  std::transform(begin(orig), end(orig), begin(rv), f);
  return rv;
}

std::vector<int> map(const std::vector<int>& orig, const std::function<int(int)> f) {
  std::vector<int> rv;
  rv.resize(orig.size());
  std::transform(begin(orig), end(orig), begin(rv), f);
  return rv;
}

#if 0
template<typename A, typename B, typename F> B mapXX(const A& orig, const F* f) {
  B rv;
  rv.resize(orig.size());
  std::transform(begin(orig), end(orig), begin(rv), f);
  return rv;
}

template<typename A, typename B> std::vector<B> map_(std::vector<A>& orig, auto f(A) -> B) {
  std::vector<B> rv;
  rv.resize(orig.size());
  std::transform(begin(orig), end(orig), begin(rv), f);
  return rv;
}
#endif

int main(int argc, char **argv) {
  std::vector<int> list;
  list.push_back(10);
  list.push_back(20);
  list.push_back(50);
  
//  std::vector<int> transformed;
//  transformed.resize(list.size());
//  std::transform(begin(list), end(list), begin(transformed), [](int x) -> int { return x + 1; });

//  typedef int (*int2int)(int);
//  int2int f = [](int x) -> int { return x + 1; };
  
  auto transformed = map_2(list, [](int x) -> int { return x + 1; });

  std::for_each(begin(transformed), end(transformed), [](int x) { printf("-> %d\n", x); });
  
  return 0;
}