[INSTRUCTIONS]

You are a program-analysis assistant. Perform a **static** data-dependence analysis on a given code snippet, treating each branch or loop condition as potentially taking any outcome, without using semantic or symbolic execution to prune paths.


## 1. Data Dependence Definition

   Data dependence captures the influence of data flow between variables.

   We denote each variable instance as `(var,lineNumber)`, meaning the variable `var` defined or updated at `lineNumber`.

   >  **Direct Data Dependence**
   A variable instance `(varB,lineB)` is **directly** data-dependent on `(varA,lineA)` if `lineA` writes to `varA`. Then, without overwritting the value of `varA`, `lineB` reads `varA` and compute the value of `varB`. In other words, the value of `(varB,lineB)` relies on the value produced at `(varA,lineA)`. In addition, changing the execution order of `(varA,lineA)` and `(varB,lineB)` would alter their results.


   A variable instance `(varB,lineB)` is data-dependent on `(varA,lineA)` if there is a **transitive** (indirect) chain of **direct** data dependencies from `(varA,lineA)` to `(varB,lineB)`. This is equivalent to saying that `(varA,lineA)` has data dependence over `(varB,lineB)`, meaning the value written at `(varA,lineA)` can propagate to `(varB,lineB)` through a sequence of read/write operations.


## 2. Output Format
   When asked "Which variable instances have data dependence over `(targetVar, targetLine)`? List all such variables.", respond:
   ```json
   {
    "DataDependenceSources": [
      ["valA", lineA],
      ["valB", lineB],
      ...
    ]
   }
   ```

  If you believe there is no variables have data dependence over `(targetVar, targetLine)`, respond:
   ```json
   {
    "DataDependenceSources": []
   }
   ```
  

## 3. Intraprocedural Data 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    total = 0
2    value = 1
3    step = value
4    if step > 1:
5        value += 3
6    while total <= 10:
7        total += value
8        difference = total - step
9        step += 1
10   final_result = total * 2
```


#### Example Question 1.1:
Which variable instances have data dependence over `(step,9)`? List all such variables.


**Analysis**:
- Line 9: `step += 1`, meaning `(step,9)` is directly data-dependent on `(step,3)` (or `(step,9)` itself) because step is updated based on its previous value.
- Line 3: `step = value`, meaning `(step,3)` is directly data-dependent on `(value,2)`.
Therefore, there exists a transitive data dependence chain from `(value,2)` to `(step,9)` through `(step,3)`. 


**Output**:
```json
   {
    "DataDependenceSources": [
      ["step", 9],
      ["step", 3],
      ["value", 2],
    ]
   }
```





#### Example Question 1.2 
Which variable instances have data dependence over `(total,7)`? List all such variables.


**Analysis**:
- Line 7: `total += value`, meaning `(total,7)` reads from `total` at line 1 or 7 (itself), and `value` from either `(value,2)` or `(value,5)`.
- Line 5: `value` is updated in `value += 3`, meaning `(value,5)` depends on `(value,2)` (or `(value,5)` itself). However, this update is inside an if statement, which means it may or may not execute depending on runtime conditions.
- Line 2: value is initialized at `(value,2)`.


At this point, whether `(total,7)` depends on `(value,5)` depends on whether line 4 (`if step>1`) is `true`. Since this is a static analysis, all possible paths are considered without analyzing actual reachability. This means line 5 is treated as both possibly executed and possibly not executed.

- If line 4 evaluates to `true`, `(total,7)` depends on `(value,5)`, forming the trace: `(value,2) -> (value,5) -> (total,7)`. 
- If line 4 evaluates to `false`, `(total,7)` directly depends on `(value,2)`, forming the trace: `(value,2) -> (total,7)`



**Output**:
```json
   {
    "DataDependenceSources": [
      ["total", 1],
      ["total", 7],
      ["value", 5],
      ["value", 2]
    ]
   }
```



### Example 2

```python
1    arr = [1, 2, 3]
2    x = 5
3    if x > 2:
4        arr[0] = x   
5    for i in range(3):
6        arr[i] += 1  
7        temp = arr[i]  
8        y = temp + 1  
9    result = arr[-1]
```

#### Example Question 2.1:
Which variable instances have data dependence over `(arr,6)`? List all such variables.



**Analysis**
- Line 6: `arr[i] += 1` modifies `arr[i]`, but i varies during the loop execution.
   - If `i == 0`, `arr[i]` refers to `arr[0]`, which was updated in line 4 (or line 6 itself), establishing a dependence chain `(arr,4)` -> `(arr,6)`.
   - If `i != 0`, `arr[i]` does not refer to `arr[0]`, meaning it depend on `(arr,1)` (or `(arr,6)` itself), not `(arr,4)`.
   - However, since static analysis considers all possible paths without resolving i’s runtime value, we must assume `arr[i]` could be `arr[0]`, leading to a possible dependence.
- Line 4: `arr[0] = x`, meaning `(arr,4)` depends on `(x,2)`.
- Line 2: `x` is initialized at `(x,2)`.




**Output**:
```json
   {
    "DataDependenceSources": [
      ["arr", 6],
      ["arr", 4],
      ["arr", 1],
      ["i", 5],
      ["x", 2]
    ]
   }
```


#### Example Question 2.2:
Which variable instances have data dependence over `(temp,7)`? List all such variables.


**Analysis**:
- Line 7: `temp = arr[i]`, meaning temp depends on `i`, since `i` determines which element of arr is accessed. And `arr[i]` can only refer to `(arr,6)` as they have the same index.
- Line 5: `i` is initialized and iterates over the range 0 to 3.


**Output**:
```json
   {
    "DataDependenceSources": [
      ["arr", 6],
      ["i", 5],
    ]
   }
```

#### Example Question 2.3:
Which variable instances have data dependence over `(result,9)`? List all such variables.

**Analysis**:
- Line 9: `result = arr[-1]`, meaning result depends on `arr[-1]`, which is arr[2], possibly get updated at line 6 (or line 1).
  - If it is from line 6: `arr[i] += 1`, `arr[i]` is modified based on the value of `i`. Line 5: `i` iterates over 0 to 3.
  - If it is from line 1: `arr = [1, 2, 3]`, it is initialized at line 1 without any other data dependencies.

**Output**:
```json
   {
    "DataDependenceSources": [
      ["arr", 6],
      ["arr", 1],
      ["i", 5],
    ]
   }
```

---

[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**: Which variable instances have data dependence over `(stalls_occupancy,44)` in function `fill_bathroom`? List all such variables.

**Output**:


Ground truth answer: yes