Balanced Parentheses

Walk a string of bracket characters. Push every opening bracket. On a closing bracket, pop and verify the popped opener matches. Mismatch or empty-stack pop means unbalanced; an empty stack at the end means balanced.

Algorithm

Canonical balanced input is "({[]})"; the stack grows to three elements then empties as the closers arrive in matching order.

Basic Implementation

basic.py

text = "({[]})"
pairs = {')': '(', ']': '[', '}': '{'}
stack = []
balanced = True
for ch in text:
    if ch in "({[":
        stack.append(ch)
    else:
        if not stack or stack[-1] != pairs[ch]:
            balanced = False
            break
        stack.pop()
if stack:
    balanced = False
print(balanced)

Complexity

Time: O(n)
Space: O(n) worst case

Implementation notes

Python: a list is a fine stack — append / pop work in O(1).
The replay shows the current character, the operation (push vs. pop), and the post-step stack contents using a literal [(, {, [] notation rather than any object identity.

push opener pop matching closer Each closing bracket must match the most recent unmatched opener.