0408EasyStringStackBracket Sequences

Deepest Bracket Layer

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Trains the technique from

LeetCode 1614Maximum Nesting Depth of the Parentheses

This is an original problem, written from a brief that listed the technique, the difficulty, the topics, the function shape and the input bounds — none of that problem's wording, examples, hints or editorials. The link is there so you can map your practice onto the standard set.

Same function shape, different story and different numbers.

A control panel writes each logged formula as a string line built from the digits 0 to 9 and the characters +, -, *, /, ( and ).

The brackets in line always pair up: reading left to right, a ) never appears before its partner, and every ( is closed before the line ends. The panel makes no promise about the arithmetic itself, so apart from the brackets a line may read oddly.

Every bracket pair in line sits inside some number of other bracket pairs. Call one more than that number the pair's layer, so a pair nested inside nothing is on layer 1.

Return the largest layer reached by any bracket pair in line, and 0 when line has no brackets at all.

Examples

Example 1

Input: line = "7+((5-2)*3)"
Output: 2

The outer pair wrapping `(5-2)*3` sits inside nothing, so it is on layer 1, and the pair around `5-2` sits inside it on layer 2.

Example 2

Input: line = "4*5-6"
Output: 0

No brackets appear anywhere in the line.

Example 3

Input: line = "((9))+(8)"
Output: 2

The pair around `9` sits inside one other pair, putting it on layer 2. The pair around `8` sits inside nothing, so it is only on layer 1.

Example 4

Input: line = "(2+(3)*(4+(5)))"
Output: 3

The pair around `5` sits inside the pair around `4+(5)`, which sits inside the outermost pair, so that innermost pair is on layer 3. The pair around `3` reaches only layer 2.

Example 5

Input: line = "(6)"
Output: 1

One pair, sitting inside nothing, so its layer is 1.

Constraints

1 <= line.length <= 100
line consists of digits 0-9 and the characters '+', '-', '*', '/', '(' and ')'.
The brackets of line are guaranteed to pair up correctly.

The signature

The editor is preloaded with this. It matches the parent problem's shape, so a solution that works here transfers to a judge unchanged.

Python

def max_depth(line: str) -> int:

Java

public int maxDepth(String line)

The intended approach

Time O(n)Space O(1)

A pair's layer is exactly how many brackets are still open at the moment its `(` is read, so there is no need to remember which bracket is which. Carry a single counter that rises on `(` and falls on `)`, and keep the highest value the counter ever shows right after a rise.

Pythonentry point: max_depth

def max_depth(line):
    # Time O(n): one pass over the characters. Space O(1): two counters, and
    # no stack is retained since only the running open count matters.
    deepest = 0
    open_now = 0
    for ch in line:
        if ch == '(':
            open_now += 1
            if open_now > deepest:
                deepest = open_now
        elif ch == ')':
            open_now -= 1
    return deepest

The obvious version

For every position in the line, recount the opening brackets minus the closing brackets in the whole prefix ending there, and keep the largest count seen.

This is not filler. It was written independently of the fast solution and the two were run against thousands of random inputs to confirm they agree — which is how the answer above is known to be right. Read it when the intended approach feels like a rabbit pulled out of a hat.

Python

def bf_max_depth(line):
    deepest = 0
    for i in range(len(line)):
        balance = 0
        for j in range(i + 1):
            if line[j] == '(':
                balance += 1
            elif line[j] == ')':
                balance -= 1
        if balance > deepest:
            deepest = balance
    return deepest

How this problem was checked

Reference solution executed against 12 test cases — 12 passed
5 worked examples confirmed by running the code
0 eight-word sequences shared with the parent problem's text
Agrees with an independent brute-force implementation on random inputs
Test set proven to catch deliberately broken solutions
Reviewed by a separate quality pass
Function arity matches the parent problem's

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