Best Time to Buy/Sell Stocks
For the one-transaction stock problem, scan once while tracking the minimum price seen so far and the best profit achievable by selling today.
Start with this mental model
For the one-transaction stock problem, scan once while tracking the minimum price seen so far and the best profit achievable by selling today.
How it works, without unnecessary jargon
The buy must occur before the sell, so only past minimums are valid buy candidates.
One pass gives O(n) time and O(1) extra space.
Read the algorithm as a sequence of decisions
Restate constraints and edge cases.
Identify the pattern and invariant.
Walk through a small example before coding.
Read a tiny input by hand and write down the state after every important operation. For Best Time to Buy/Sell Stocks, the goal is to make the invariant visible rather than to memorize code.
function maxProfit(prices) {
let minPrice = Infinity;
let best = 0;
for (const price of prices) {
minPrice = Math.min(minPrice, price);
best = Math.max(best, price - minPrice);
}
return best;
}Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.
Varies by implementation / input constraints
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
Good fit
- Use the recognized pattern when its invariant matches the problem constraints.
What usually goes wrong
- Jumping to code before defining the invariant.
- Optimizing before producing a correct baseline.
A professional answer shape
Do not sort prices; sorting destroys time order. Track the best historical buy price instead.
What problem does Best Time to Buy/Sell Stocks solve?
For the one-transaction stock problem, scan once while tracking the minimum price seen so far and the best profit achievable by selling today.
What should I mention about complexity?
Its typical cost here is Varies by implementation / input constraints, but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
What is the most common mistake?
Jumping to code before defining the invariant.