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#1111 - Maximum Nesting Depth of Two Valid Parentheses Strings

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String Stack

Problem Description

A string is a valid parentheses string (denoted VPS) if and only if it consists of "(" and ")" characters only, and:

  • It is the empty string, or
  • It can be written as AB (A concatenated with B), where A and B are VPS's, or
  • It can be written as (A), where A is a VPS.

We can similarly define the nesting depth depth(S) of any VPS S as follows:

  • depth("") = 0
  • depth(A + B) = max(depth(A), depth(B)), where A and B are VPS's
  • depth("(" + A + ")") = 1 + depth(A), where A is a VPS.

For example, "", "()()", and "()(()())" are VPS's (with nesting depths 0, 1, and 2), and ")(" and "(()" are not VPS's.

Given a VPS seq, split it into two disjoint subsequences A and B, such that A and B are VPS's (and A.length + B.length = seq.length).

Now choose any such A and B such that max(depth(A), depth(B)) is the minimum possible value.

Return an answer array (of length seq.length) that encodes such a choice of A and B: answer[i] = 0 if seq[i] is part of A, else answer[i] = 1. Note that even though multiple answers may exist, you may return any of them.

Solution

/**
 * @param {string} seq
 * @return {number[]}
 */
var maxDepthAfterSplit = function(seq) {
  const result = new Array(seq.length);
  let depth = 0;

  for (let i = 0; i < seq.length; i++) {
    if (seq[i] === '(') {
      result[i] = depth++ % 2;
    } else {
      result[i] = --depth % 2;
    }
  }

  return result;
};