std::min_elementで0でない最小値を見つけるための比較関数 ref: http://qiita.com/items/bd65c5473f5ef238d9cd

min.cpp

#include <iostream>
#include <vector>
#include <algorithm>
using std::vector;
using std::cout;
using std::endl;
int main() {
  vector<int> a = {0, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 0};
  auto min = min_element(a.begin(), a.end(), [](int a, int b) {
      return (a == 0) ? false : (b == 0) || a < b;
    });
  cout << *min << endl;
  return 0;
}

min_element

if (comp(*first, *smallest)) {
  smallest = first;
}