std::min_elementで0でない最小値を見つけるための比較関数

min_element内部では

min_element

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

なので，
*firstが0のときにfalse，
*secondが0のときにtrueを返せばOK．

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;
}