Stock Buy and Sell (Multiple Transactions)

The problem

Given an array of daily stock prices, compute the maximum profit achievable by making as many buy-sell transactions as you like, but you can only hold one share at a time.

Holding across a multi-day price ascent produces the exact same profit as selling and immediately rebuying every single day the price increases: (p[c] - p[a]) equals (p[b] - p[a]) + (p[c] - p[b]). Capturing every positive consecutive price difference guarantees capturing every upward run without ever tracking valleys and peaks explicitly.

Full solution

Greedy consecutive gains: summing every positive day-to-day difference equals the profit of buying at each valley and selling at each peak, so one O(n) pass with no pointer or boundary logic is the version to write.

def max_profit_multiple(prices: list[int]) -> int:
    # Every upward day is a buy-yesterday/sell-today trade; the gains sum to the same
    # total as holding across the whole run, so just add each positive step.
    profit = 0
    for i in range(1, len(prices)):
        if prices[i] > prices[i - 1]:
            profit += prices[i] - prices[i - 1]
    return profit

function maxProfitMultiple(prices) {
  // Every upward day is a buy-yesterday/sell-today trade; the gains sum to the same
  // total as holding across the whole run, so just add each positive step.
  let profit = 0;
  for (let i = 1; i < prices.length; i++) {
    if (prices[i] > prices[i - 1]) profit += prices[i] - prices[i - 1];
  }
  return profit;
}

The theory behind it

Arrays — the ground this problem stands on. All Arrays problems

What Arrays is

An array is a row of fixed boxes laid side by side in computer memory, like numbered lockers in a hallway. Because each box occupies identical space and sits directly next to its neighbors, jumping to locker zero or locker ten thousand takes the exact same tiny fraction of time. Every box holds an item of the same type, addressed by an offset number called an index.

When to reach for it

Reach for an array when items arrive in a known sequence and need immediate retrieval by position number. Problems asking for running totals, prefix accumulations, cyclic rotations, or in-place rearrangements signal array mechanics. Whenever constraints require constant-time random lookups or contiguous cache scans across fixed collections, a flat sequence is the default container.

How the pattern works

Visualize a tape with zero-indexed slots stretching from start to end. Keep track of write and read cursors when modifying contents without allocating helper buffers. For running computations, maintain an invariant such as having processed all elements left of the current index while pending elements wait to the right. When modifying entries in place, consider scanning backwards from the end so unread data is not overwritten.

What each operation costs

Which roles need this problem

Arrays is a core topic for these 25 roles — if you're targeting one of them, this problem is early in your path, not optional.

Secondary for 3 more roles, including Database Engineer, Bioinformatics Engineer, Networking Engineer.