ALGORITHM READING NOTE

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.

TYPEAlgorithmCATEGORYClassic ProblemsDEPTHBeginnerTYPICAL COMPLEXITYVaries by implementation / input constraints

SHORT INTERVIEW ANSWER

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.

SIMPLE EXPLANATION

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.

EXECUTION

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.

A small example to keep in mind

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.

READABLE JAVASCRIPT IMPLEMENTATIONJavaScript

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;
}

How to read this code

Do not memorize the syntax. Follow the state that changes on each line and connect it to the invariant described above.

COMPLEXITY

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Do not quote this complexity mechanically.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.

WHEN TO USE IT

Good fit

Use the recognized pattern when its invariant matches the problem constraints.

COMMON MISTAKES

What usually goes wrong

Jumping to code before defining the invariant.
Optimizing before producing a correct baseline.

HOW TO EXPLAIN IT IN AN INTERVIEW

A professional answer shape

Do not sort prices; sorting destroys time order. Track the best historical buy price instead.

Problem→Core idea→Invariant / state→Big-O→Trade-off

QUICK INTERVIEW CHECK

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.

Continue readingProblem patternsEdge casesComplexity trade-offs

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; }