No, selling completes it here. Legal actions depend on holding state and remaining transaction budget.

Draw two rooms per transaction count: free and holding. Every day offers edges—rest, buy, sell. DP keeps the best money reaching each room.

What the function promises: Return maximum profit from integer prices with at most k transactions. Same-day buy after sell is harmless here but never increases profit without fees.

def max_profit(prices, k):
    if k < 0: raise ValueError("Negative k")
    free = [0] + [float("-inf")] * k
    hold = [float("-inf")] * (k+1)
    for price in prices:
        old_free, old_hold = free[:], hold[:]
        for sold in range(k+1):
            hold[sold] = max(old_hold[sold], old_free[sold]-price)
            free[sold] = old_free[sold]
            if sold:
                free[sold] = max(free[sold], old_hold[sold-1]+price)
    return max(free)

assert max_profit([3,2,6,5,0,3], 2) == 7
assert max_profit([], 3) == 0

Work and storage: O(nk) time and O(k) space.

When to recognize it: Legal actions depend on holding state and remaining transaction budget.

Check before applying it: Updating states in-place in the wrong order can use today’s sale to buy again under a different contract.

Add a cooldown/free distinction or carry a recent-sale state; “not holding” is no longer sufficient.