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86. Longest Valid Parentheses

hardAsked at Plaid

Find the length of the longest valid parentheses substring. Plaid asks this as a stack-based scanning problem — the same shape they use to find the longest run of properly-paired JSON braces in a corrupted webhook payload.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Source citations

Public interview reports confirming this problem appears in Plaid loops.

  • Glassdoor (2025)— Plaid SWE III hard string.
  • LeetCode Discuss (2026)— Plaid stack-based hard.

Problem

Given a string containing just the characters '(' and ')', return the length of the longest valid (well-formed) parentheses substring.

Constraints

  • 0 <= s.length <= 3 * 10^4
  • s[i] is '(' or ')'.

Examples

Example 1

Input
s = "(()"
Output
2

Example 2

Input
s = ")()())"
Output
4

Example 3

Input
s = ""
Output
0

Approaches

1. Try every substring

Check every (i, j) for validity; track longest.

Time
O(n^3)
Space
O(n)
// Cubic. Don't ship.

Tradeoff: TLE.

2. Stack of indices

Push -1 as a sentinel. Push '(' index. On ')', pop. If stack empty, push current index as new sentinel; else compute length = i - stack.top.

Time
O(n)
Space
O(n)
function longestValidParentheses(s) {
  const stack = [-1];
  let best = 0;
  for (let i = 0; i < s.length; i++) {
    if (s[i] === '(') stack.push(i);
    else {
      stack.pop();
      if (stack.length === 0) stack.push(i);
      else best = Math.max(best, i - stack[stack.length - 1]);
    }
  }
  return best;
}

Tradeoff: Linear. The sentinel -1 (and re-seed on empty pop) is the trick that lets you compute the length as i - stack.top in all cases.

Plaid-specific tips

Plaid grades this on whether the sentinel trick comes naturally. Bonus signal: derive why the sentinel encodes 'the last invalid position.' Connect to webhook-payload repair where finding the longest balanced run is the prefix to the corruption point.

Common mistakes

  • Forgetting the initial -1 sentinel.
  • Not re-seeding the sentinel when the stack becomes empty.
  • Storing characters instead of indices on the stack.

Follow-up questions

An interviewer at Plaid may pivot to one of these next:

  • Return the substring itself.
  • Return all maximal valid substrings.
  • DP variant — equivalent asymptotic.

Solve it now

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Output

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FAQ

Why -1 as the initial sentinel?

It encodes 'the position just before the string,' so when we compute length = i - sentinel, we get the correct length for matches starting at index 0.

Why re-seed on empty pop?

An unmatched ')' invalidates everything before it. We push its index as the new sentinel so subsequent matches measure from there.

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