exclusive-time-of-functions

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Algorithms

On a single-threaded CPU, we execute a program containing <code>n</code> functions. Each function has a unique ID between <code>0</code> and <code>n-1</code>.

Function calls are stored in a <a href="https://en.wikipedia.org/wiki/Call_stack">call stack</a>: when a function call starts, its ID is pushed onto the stack, and when a function call ends, its ID is popped off the stack. The function whose ID is at the top of the stack is the current function being executed. Each time a function starts or ends, we write a log with the ID, whether it started or ended, and the timestamp.

You are given a list <code>logs</code>, where <code>logs[i]</code> represents the <code>ith</code> log message formatted as a string <code>&quot;{function_id}:{&quot;start&quot; | &quot;end&quot;}:{timestamp}&quot;</code>. For example, <code>&quot;0:start:3&quot;</code> means a function call with function ID <code>0</code> started at the beginning of timestamp <code>3</code>, and <code>&quot;1:end:2&quot;</code> means a function call with function ID <code>1</code> ended at the end of timestamp <code>2</code>. Note that a function can be called multiple times, possibly recursively.

A function&#39;s exclusive time is the sum of execution times for all function calls in the program. For example, if a function is called twice, one call executing for <code>2</code> time units and another call executing for <code>1</code> time unit, the exclusive time is <code>2 + 1 = 3</code>.

Return the exclusive time of each function in an array, where the value at the <code>ith</code> index represents the exclusive time for the function with ID <code>i</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2019/04/05/diag1b.png" style="width: 550px; height: 239px;" />
<pre>
Input: n = 2, logs = [&quot;0:start:0&quot;,&quot;1:start:2&quot;,&quot;1:end:5&quot;,&quot;0:end:6&quot;]
Output: [3,4]
Explanation:
Function 0 starts at the beginning of time 0, then it executes 2 for units of time and reaches the end of time 1.
Function 1 starts at the beginning of time 2, executes for 4 units of time, and ends at the end of time 5.
Function 0 resumes execution at the beginning of time 6 and executes for 1 unit of time.
So function 0 spends 2 + 1 = 3 units of total time executing, and function 1 spends 4 units of total time executing.
</pre>

Example 2:

<pre>
Input: n = 1, logs = [&quot;0:start:0&quot;,&quot;0:start:2&quot;,&quot;0:end:5&quot;,&quot;0:start:6&quot;,&quot;0:end:6&quot;,&quot;0:end:7&quot;]
Output: [8]
Explanation:
Function 0 starts at the beginning of time 0, executes for 2 units of time, and recursively calls itself.
Function 0 (recursive call) starts at the beginning of time 2 and executes for 4 units of time.
Function 0 (initial call) resumes execution then immediately calls itself again.
Function 0 (2nd recursive call) starts at the beginning of time 6 and executes for 1 unit of time.
Function 0 (initial call) resumes execution at the beginning of time 7 and executes for 1 unit of time.
So function 0 spends 2 + 4 + 1 + 1 = 8 units of total time executing.
</pre>

Example 3:

<pre>
Input: n = 2, logs = [&quot;0:start:0&quot;,&quot;0:start:2&quot;,&quot;0:end:5&quot;,&quot;1:start:6&quot;,&quot;1:end:6&quot;,&quot;0:end:7&quot;]
Output: [7,1]
Explanation:
Function 0 starts at the beginning of time 0, executes for 2 units of time, and recursively calls itself.
Function 0 (recursive call) starts at the beginning of time 2 and executes for 4 units of time.
Function 0 (initial call) resumes execution then immediately calls function 1.
Function 1 starts at the beginning of time 6, executes 1 unit of time, and ends at the end of time 6.
Function 0 resumes execution at the beginning of time 6 and executes for 2 units of time.
So function 0 spends 2 + 4 + 1 = 7 units of total time executing, and function 1 spends 1 unit of total time executing.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>2 &lt;= logs.length &lt;= 500</code></li>
	<li><code>0 &lt;= function_id &lt; n</code></li>
	<li><code>0 &lt;= timestamp &lt;= 109</code></li>
	<li>No two start events will happen at the same timestamp.</li>
	<li>No two end events will happen at the same timestamp.</li>
	<li>Each function has an <code>&quot;end&quot;</code> log for each <code>&quot;start&quot;</code> log.</li>
</ul>