1. Full length
A valid string uses n open and n close brackets, so length is 2n.
if (path.length === n * 2)Typorithm · medium
Generate Parentheses
▷ Interactive algorithm labgenerate-parenthesesbacktrackingconstraintsopen-close-countschoose-explore-undo
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Full lesson · 8 learning steps Open any exercise for focused practice
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Step 1 of 8 · intro card
Learn Generate Parentheses
Backtracking
Build only valid bracket strings by adding an open while open < n and a close while close < open.
Instead of generating all strings and filtering, the constraints prune invalid branches up front.
You may add an open bracket whenever fewer than n are used, and a close bracket only when it has a matching open.
These two rules guarantee every produced string is already balanced.
Preparing algorithm lab…
01
Open while open < n.
02
Close while close < open.
03
Length 2n means a complete string.
function generateParenthesis(n) {
const result = [];
const path = [];
function backtrack(open, close) {
if (path.length === n * 2) {
result.push(path.join(""));
return;
}
if (open < n) {
path.push("(");
backtrack(open + 1, close);
path.pop();
}
if (close < open) {
path.push(")");
backtrack(open, close + 1);
path.pop();
}
}
backtrack(0, 0);
return result;
}Read the implementation
Connect each part of the code to the concept before you type.
2. Can open
Add an open bracket only while fewer than n have been used.
if (open < n)3. Can close
Add a close bracket only when an unmatched open exists.
if (close < open)4. Undo
Remove the bracket to try the alternative branch.
path.pop()A complete learning loop
01
Understand
Read the concept map and follow the code breakdown.
02
Reconstruct
Type the implementation, repair mistakes and work through every recall exercise.
03
Verify
Use the final check without hints; revisit weak concepts in short practice sessions.