#include <cassert>
#include <string>
#include <vector>

namespace {

template <typename T>
void pop_and_push(std::vector<T> &src, std::vector<T> &dst) {
  assert(src.size());
  dst.push_back(src.back());
  src.pop_back();
}

int priority(char op) {
  switch (op) {
  case '(':
  case ')':
    return 0;
  case '+':
  case '-':
    return 1;
  case '*':
  case '/':
    return 2;
  case '^':
    return 3;
  default:
    assert(false);
  }
}

enum assoc_t { LEFT, RIGHT, NONE };

assoc_t associativity(char op) {
  assert(!std::isdigit(op));

  switch (op) {
  case '(':
  case ')':
    return assoc_t::NONE;
  case '^':
    return assoc_t::RIGHT;
  default:
    return assoc_t::LEFT;
  }
}

bool pop_operator(std::vector<char> &op_stack, char o1) {
  if (op_stack.empty()) {
    return false;
  }

  char o2 = op_stack.back();
  if (o2 == '(') {
    return false;
  }

  int o1_priority = priority(o1);
  int o2_priority = priority(o2);

  return o2_priority > o1_priority ||
         (o2_priority == o1_priority && associativity(o1) == assoc_t::LEFT);
}

} // namespace

std::string to_postfix(std::string infix) {
  std::vector<char> output_queue;
  std::vector<char> operator_stack;

  for (char token : infix) {
    if (std::isdigit(token)) {
      output_queue.push_back(token);
    } else if (token == '(') {
      operator_stack.push_back(token);
    } else if (token == ')') {
      while (operator_stack.back() != '(') {
        assert(operator_stack.size());
        pop_and_push(operator_stack, output_queue);
      }

      assert(operator_stack.back() == '(');
      operator_stack.pop_back();
    } else {
      while (pop_operator(operator_stack, token)) {
        pop_and_push(operator_stack, output_queue);
      }
      operator_stack.push_back(token);
    }
  }

  while (operator_stack.size()) {
    assert(operator_stack.back() != '(');
    pop_and_push(operator_stack, output_queue);
  }

  return std::string(output_queue.begin(), output_queue.end());
}

int main() {
  assert(to_postfix("2+7*5") == "275*+");
  assert(to_postfix("3*3/(7+1)") == "33*71+/");
  assert(to_postfix("5+(6-2)*9+3^(7-1)") == "562-9*+371-^+");
  assert(to_postfix("(5-4-1)+9/5/2-7/1/7") == "54-1-95/2/+71/7/-");
  assert(to_postfix("1^2^3") == "123^^");

  return 0;
}