[TEMA] Problema de backtracking - Virgule

Salutare! De ieri ma confrunt cu o problema de backtracking, si anume problema http://www.pbinfo.ro...robleme&id=1502
Am observat ca rezolv cerinta problemei, dar ratez conditiile de optim (in cazul in care exista mai multe posibilitati in care ultimul numar format e minim). Sunt foarte confuz si as vrea sa imi oferiti niste indicatii in rezolvarea problemei. Mai jos este codul meu, va multumesc.

#include <bits/stdc++.h>
using namespace std;
ifstream fin("virgule.in");
ofstream fout("virgule.out");
const int DEBUG = 0;
string initial;
long long lastMin = LLONG_MAX;
int n;
vector<int> ans, finalAns;
inline void debug() {
	if (!DEBUG)
		return;
	for (const int& x: ans)
		fout << x << ' ';
	fout << '\n';
}
inline bool testAns() {
	long long curr = 0, prv = 0;
	int pos = 0, m = ans.size();
	for (int i = 0; i < n; ++i) {
		curr = curr * 10 + (initial[i] - '0');
		if (curr < 0)
			return 0;
		if (pos < m && ans[pos] == i) {
			if (curr <= prv)
				return 0;
			prv = curr;
			curr = 0;
			++pos;
		}
	}
	if (curr <= lastMin) {
		lastMin = curr;
		return 1;
	}
	return 0;
}
void back(int pos, long long last) {
	if (last <= lastMin && pos >= n && testAns()) {
		debug();
		finalAns = ans;
		return;
	}
	long long curr = 0;
	for (int i = pos; i < n; ++i) {
		curr = curr * 10 + (initial[i] - '0');
		if (curr < 0)
			return;
		if (curr > last) {
			if (i != n - 1)
				ans.push_back(i);
			back(i + 1, curr);
			if (ans.size())
				ans.pop_back();
		}
	}
}
int main()
{
	fin >> initial;
	n = initial.size();
	back(0, 0LL);
	int pos = 0, m = finalAns.size();
	for (int i = 0; i < n; ++i) {
		fout << initial[i];
		if (pos < m && finalAns[pos] == i)
			++pos, fout << ',';
	}
	return 0;
}