[INSTRUCTIONS]

You are a program-analysis assistant. Your task is to statically analyze the control dependence of a given code snippet. 

## 1. Control Dependence Definition
  Control dependence captures the influence of control-flow decisions on the execution of statements.

  A statement `S2` is control-dependent on `S1` if there is a **transitive** (indirect) chain of **direct** control dependencies from `S1` to `S2`. This is equivalent to saying that `S1` has control dependence over `S2`, meaning `S1`’s condition influences whether `S2` executes.


  **Direct Control Dependence**:
  A statement `S2` is **directly** control-dependent on a statement `S1` if:
  
  1.	`S1` is a conditional control statement (e.g., an `if`, `while`, `for`, `switch`, etc.).
  
  2.	`S1` directly determines whether `S2` executes. That is, `S1` has multiple successor branches, 

  - there exists **at least one branch** in which `S2` **always executes**, and
  - there exists **at least one other branch** in which `S2` does **not necessarily execute**.

    “Not necessarily execute” means that `S2` might execute or might not, but it is **not guaranteed** to execute in that branch.

  `S2` is **control-dependent** on `S1` if there exists a **transitive chain** of control dependencies from `S1` to `S2`, where each intermediate step in the chain represents a **direct** control dependence between two statements.



## 2. Output Format
When asked, “Does line `S1` have control dependence over line `S2`? If so, provide a trace.” You should respond in JSON format as follows:

- If there is a control dependence:

```json
{
  "ControlDependence": true,
  "Trace": [S1, ..., S2]
}
```

- If there is no control dependence:
```json
{
  "ControlDependence": false
}
```

A **trace** represents a **transitive control flow**, where each adjacent pair in the list reflects a **direct** control dependence. The trace must starts with `S1` and ends with `S2`.


    

## 3. Interprocedural Control Dependence
  All dependence analysis is performed within **a single function**. We do not track dependencies across function boundaries. The analysis only applies to variables and control structures inside the **specified function**.


## 4. Example Code Snippet

### Example 1

```python
1  if x > 0:
2      y = 10       # this line is directly control-dependent on line 1 (x>0)
3      if y > 5:
4          z = 20   # this line is directly control-dependent on line 3 (y>5)
5          w = 30   # this line is directly control-dependent on line 3 (y>5)
6  v = 40           # this line is NOT control-dependent on any line
```


**Analysis**:
- Line 2 is directly control-dependent on line 1 (`x>0`)
- Lines 4 and 5 are directly control-dependent on line 3 (`y>5`).
- Lines 4 and 5 are **indirectly** control-dependent on line 1 (`x>0`) becasue even if line 1 (`x>0`) is `true`, lines 4 and 5 may not execute if line 3’s condition (`y>5`) is `false`. However, since control dependence is transitive, lines 4 and 5 are **indirectly** control-dependent on line 1. 
- Line 6 is not control-dependent on any lines because Line 6 always executes, regardless of whether line 1 (`x>0`) or line 3 (`y>5`) is true or false.



#### Example Question 1.1: 
Does line `1` have control dependence over line `5`? If so, provide a trace.

**Output**: 
```json
{
  "ControlDependence": true,
  "Trace": [1, 3, 5]
}
```

#### Example Question 1.2:
Does line `3` have control dependence over line `6`? If so, provide a trace.

**Output**: 
```json
{
  "ControlDependence": false
}
```


### Example 2

```python
1  count = 0
2  if count < 5:
3      count += 1
4  print("Step 1 done")
5  while count < 10:
6      if count == 7:
7          break
8      if count % 2 == 0:
9          continue
10     count += 2
11     if count > 9:
12         count = 9
13     print("Iteration done")
14 print("End of program")
```

#### Example Question 2.1: 
Does line `5` have control dependence over line `13`? If so, provide a trace.

**Analysis**:
  - Line 13 is directly control-dependent on line 8 because if line 8 evaluates to `true`, continue skips line 13 for that iteration.
  - Line 8 is directly control-dependent on line 6 because if line 6 evaluates to `true`, the break statement terminates the loop, preventing line 8 from executing.
  - Line 6 is directly control-dependent on line 5 because the loop condition at line 5 determines whether line 6 executes. If line 5 evaluates to `false`, execution skips the loop entirely.


Since control dependence is transitive, line 5 indirectly controls line 13 through lines 6 and 8. The trace is `5->6->8->13`.

**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [5, 6, 8, 13]
}
```

#### Example Question 2.2: 
Does line `8` have control dependence over line `10`? If so, provide a trace.


**Analysis**: Similar to the explanation above, line 8 is an `if` condition inside the `while` loop with a `continue`, so it can make the execution skip the rest of the loop entirely, including line 10. Therefore, line 10 directly control-dependent on 8.



**Output**:
```json
{
  "ControlDependence": true,
  "Trace": [8, 10]
}
```

#### Example Question 2.3: 
Does line `5` have control dependence over line `14`? If so, provide a trace.

**Analysis**: Line 5 doesn't affect whether line 14 is reached. Line 14 is outside the while loop (lines 5 -- 13) and will be executed regardless of the condition. 

**Output**:
```json
{
  "ControlDependence": false
}
```


#### Example Question 2.4: 
Does line `2` have control dependence over line `12`? If so, provide a trace.

**Analysis**: Line 2 doesn't affect whether line 12 is reached. The condition in line 2 only controls whether line 3 is executed. Line 12 is in while loop (line 5 -- 13) and will or will not be executed regardless of the condition in line 2. 

**Output**:
```json
{
  "ControlDependence": false
}
```

---

[YOUR TURN]

Below is **your target snippet**. 

```C
1   #include <stdio.h>
2   #include <stdlib.h>
3   #include <string.h>
4   #include <math.h>
5   #define MIN(a,b) (((a)<(b))?(a):(b))
6   #define MAX(a,b) (((a)>(b))?(a):(b))
7   void fill_bathroom(int n_case, int stalls, int users){
8       int *stalls_occupancy = (int*)malloc(stalls * sizeof(int));
9       memset(stalls_occupancy, 0, stalls * sizeof(int));
10      int *ls = (int*)malloc(stalls * sizeof(int));
11      int *rs = (int*)malloc(stalls * sizeof(int));
12      int max_crit1 = 0;
13      int max_crit2 = 0;
14      for(int i = 0; i < stalls; i++)
15      {
16          ls[i] = i;
17          rs[i] = stalls - i - 1;
18      }
19      for(int i = 0; i < users; i++)
20      {
21          int pos = 0;
22          max_crit1 = 0;
23          max_crit2 = 0;
24          for(int j = 0; j < stalls; j++)
25          {
26              if(stalls_occupancy[j] == 0)
27              {
28                  int crit1 = MIN(ls[j], rs[j]);
29                  int crit2 = MAX(ls[j], rs[j]);
30                  if(crit1 >= max_crit1 && crit2 > max_crit2)
31                  {
32                      pos = j;
33                      max_crit1 = crit1;
34                      max_crit2 = crit2;
35                  }
36                  else if (crit1 > max_crit1)
37                  {
38                      pos = j;
39                      max_crit1 = crit1;
40                      max_crit2 = crit2;
41                  }
42              }
43          }
44          stalls_occupancy[pos] = 1;
45          int reset_counter = 0;
46          for(int i = pos + 1; i < stalls; i++)
47          {
48              if(stalls_occupancy[i] == 0)
49              {
50                  ls[i] = reset_counter;
51                  reset_counter++;
52              }
53              else
54              {
55                  ls[i] = reset_counter;
56                  reset_counter++;
57                  break;
58              }
59          }
60          reset_counter = 0;
61          for(int i = pos - 1; i >= 0; i--)
62          {
63              if(stalls_occupancy[i] == 0)
64              {
65                  rs[i] = reset_counter;
66                  reset_counter++;
67              }
68              else
69              {
70                  rs[i] = reset_counter;
71                  reset_counter++;
72                  break;
73              }
74          }
75      }
76      free(stalls_occupancy);
77      free(ls);
78      free(rs);
79      printf("Case #%d: %d %d\n", n_case + 1, max_crit2, max_crit1);
80  }
81  int main() {
82      int T = 0;
83      scanf("%d", &T);
84      for(int i = 0; i < T; i++)
85      {
86          int stalls = 0, users = 0;
87          scanf("%d %d", &stalls, &users);
88          fill_bathroom(i, stalls, users);
89      }
90      return 0;
91  }
```


**Question**: Does line `30` have control dependence over line `51` in function `fill_bathroom`? If so, provide a trace.

**Output**:


Ground truth answer: no