Find most frequent call path in logs

You are given a sequence of trace log lines for a single-threaded program. Each line is either a function entry or exit:

• Entry: "-> funcName"
• Exit: "<- funcName"

Maintain a call stack as you scan the logs from left to right.

Whenever you see an entry line, push the function onto the stack and form the full call path by joining the stack elements with "->" (including the top). For example, stack [main, handleEvents, handleClickEvent] corresponds to the path:

main->handleEvents->handleClickEvent

Count how many times each full call path occurs (only on entry events). Return the path string with the highest frequency.

Tie-breaking

If multiple paths have the same highest frequency:

1. Prefer the deeper path (the one with more functions).
2. If depth is also tied, prefer the one that appears first while scanning the logs (i.e., the earliest time that path was encountered).

If the input list is empty, return an empty string.

Examples

Example 1 Input:

["-> main",
 "-> handleEvents",
 "-> handleClickEvent",
 "<- handleClickEvent",
 "-> handleClickEvent",
 "<- handleClickEvent",
 "<- handleEvents",
 "<- main"]

Output:

"main->handleEvents->handleClickEvent"

Example 2 Input:

["-> main",
 "-> handleEvents",
 "-> handleKeyEvent",
 "<- handleKeyEvent",
 "-> handleClickEvent",
 "<- handleClickEvent",
 "-> handleClickEvent",
 "<- handleClickEvent",
 "-> handleKeyEvent",
 "<- handleKeyEvent",
 "<- handleEvents",
 "<- main"]

Output:

"main->handleEvents->handleClickEvent"

Example 3 Input:

[]

Output:

""

Constraints

• 0 ≤ len(traces) ≤ 100,000
• Each log line starts with either "-> " or "<- " .
• funcName contains only letters, digits, or underscores.
• Logs are well-formed: every exit matches a previous entry.
• No recursion: the same function will not be re-entered before it returns.
• Max call depth ≤ 1,000.
• Number of distinct paths ≤ number of entry events.