ex1.cpp

#include <iostream>
#include <vector>

using namespace std;

int vsum(const vector<int> & v, unsigned start_index);

int main() {
  vector<int> v;
  v.push_back(3);
  v.push_back(1);
  v.push_back(4);
  v.push_back(1);
  v.push_back(5);
  v.push_back(9);

  cout << "Sum: " << vsum(v, 0) << endl;

  return 0;
}

int vsum(const vector<int> & v, unsigned start_index) {
  if (start_index >= v.size())
    return 0;

  return v[start_index] + vsum(v, start_index + 1);
}

ex2.cpp

#include <iostream>

using namespace std;

double pow(double b, int e);

int main() {
  cout << pow(2.0, 4) << endl;
  cout << pow(2.0, -4) << endl;

  return 0;
}

double pow(double b, int e) {
  if (b == 0)
    return 0;

  if (e == 0)
    return 1;

  if (e < 0)
    return 1.0 / pow(b, -e);
  
  return b * pow(b, e - 1);
}

ex3.cpp

#include <iostream>
#include <vector>

using namespace std;

void vprint(const vector<string> & v);
vector<string> permutations(string s);

int main() {
  vprint(permutations("cat"));

  return 0;
}

void vprint(const vector<string> & v) {
  for (unsigned i = 0; i < v.size(); ++i)
    cout << v.at(i) << endl;
}

vector<string> permutations(string s) {
  if (s.size() == 0) {
    vector<string> v;
    v.push_back("");
    return v;
  }

  vector<string> lower_perms = permutations(s.substr(1));

  vector<string> perms;

  for (unsigned i = 0; i < lower_perms.size(); ++i) {
    string perm = lower_perms.at(i);
    for (unsigned i = 0; i < perm.size() + 1; ++i) {
      perms.push_back(perm.substr(0, i) + s.at(0) + perm.substr(i));
    }
  }

  return perms;
}

ex4.cpp

#include <iostream>

using namespace std;

string string_sort(string s);

int main() {
  cout << string_sort("fceatd") << endl;
  
  return 0;
}

string string_sort(string s) {
  if (s.size() == 0 || s.size() == 1)
    return s;

  string lower_sorted = string_sort(s.substr(1));

  unsigned i = 0;
  for (; i < lower_sorted.size(); ++i) {
    if (lower_sorted.at(i) > s.at(0)) 
      break;
  }

  return lower_sorted.substr(0, i) + s.at(0) + lower_sorted.substr(i);
}