Stock buy / sell (DP — Kadane / Subarray Sub-pattern)

// Stock states: carry the best profit for each state at the end of each day.
// Shown with a cooldown (after selling you must rest one day).
int maxProfitStates(const vector<int>& prices) {
    long long hold = LLONG_MIN / 2;   // holding a share
    long long sold = LLONG_MIN / 2;   // sold today (tomorrow is cooldown)
    long long rest = 0;               // free, allowed to buy
    for (int p : prices) {
        long long h = hold, s = sold, r = rest;   // yesterday's values
        hold = max(h, r - p);         // keep holding, or buy today
        sold = h + p;                 // sell what we held
        rest = max(r, s);             // stay free, or yesterday's sale cools down
    }
    return (int)max(rest, sold);
}
// One transaction: keep minPrice so far, profit = max(profit, p - minPrice).
// Unlimited, no cooldown: hold = max(hold, free - p); free = max(free, hold + p).