Running balance / local rules (Greedy Sub-pattern)

// Circular route: net[i] = gain at i minus cost to go on. Return a start index or -1.
int startOfCircuit(const vector<int>& net) {
    long long total = 0, tank = 0;
    int start = 0;
    for (int i = 0; i < (int)net.size(); i++) {
        total += net[i];
        tank += net[i];
        if (tank < 0) { start = i + 1; tank = 0; }           // no start in start..i can pass i
    }
    return total < 0 ? -1 : start;
}

// Rules on both neighbours: one pass for each side, then take the max.
long long twoPassMin(const vector<int>& r) {                 // Candy
    int n = r.size();
    vector<int> c(n, 1);
    for (int i = 1; i < n; i++) if (r[i] > r[i - 1]) c[i] = c[i - 1] + 1;
    for (int i = n - 2; i >= 0; i--) if (r[i] > r[i + 1]) c[i] = max(c[i], c[i + 1] + 1);
    return accumulate(c.begin(), c.end(), 0LL);
}