[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   char temp[22][22];
3   int compt(int y, int x)
4   {
5   	if (temp[y][x])
6   	{
7   		temp[y][x] = 0;
8   		return 1 + compt(y-1, x) + compt(y+1, x)
9   		         + compt(y, x-1) + compt(y, x+1);
10  	}
11  	else return 0;
12  }
13  int main(int argc, char **argv)
14  {
15  	unsigned long int no_cases, case_no;
16  	scanf("%lu", &no_cases);
17  	for (case_no = 0; case_no != no_cases; case_no++)
18  	{
19  		int r, c, x, y, s;
20  		int best = 0;
21  		char grid[20][20];
22  		char extras[6] = {};
23  		char quads[16] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1};
24  		scanf("%i%i", &r, &c);
25  		for (y = 0; y != r; y++)
26  		{
27  			while (getchar() != '\n') 
28  				{;} 
29  			int last = 2, this;
30  			for (x = 0; x != c; x++)
31  			{
32  				grid[y][x] = this = getchar() == 'W';
33  				extras[last << 1 | this] = 1;
34  				last = this;
35  			}
36  			temp[y][0] = temp[y][c+1] = 0;
37  		}
38  		for (x = 0; x != c; x++) 
39  			temp[0][x] = temp[r+1][x] = 0;
40  		quads[10] |= extras[2];
41  		quads[5] |= extras[1];
42  		for (y = 1; y != r; y++)
43  			for (x = 1; x != r; x++)
44  				quads[grid[y-1][x-1] << 3 | grid[y-1][x] << 2 | grid[y][x-1] << 1 | grid[y][x]] = 1;
45  		for (y = 1; y != r; y++)
46  			for (x = 0; x != r; x++)
47  			{
48  				int j = grid[y-1][x] << 2 | grid[y][x];
49  				quads[j << 1 | j] = 1;
50  			}
51  		for (int q = 0; q != 16; q++)
52  			if (quads[q])
53  				for (int ydiv = 0; ydiv <= r; ydiv++)
54  					for (int xdiv = 0; xdiv <= c; xdiv++)
55  					{
56  						for (y = 0; y != r; y++)
57  							for (x = 0; x != c; x++)
58  							{
59  								temp[y+1][x+1] = grid[y][x] == (q >> ((y < ydiv) << 1 | (x < xdiv)) & 1);
60  							}
61  						for (y = 0; y != r; y++)
62  							for (x = 0; x != c; x++)
63  							{
64  								s = compt(y + 1, x + 1);
65  								if (s > best) 
66  									best = s;
67  							}
68  					}
69  		printf("Case #%lu: %i\n", case_no + 1, best);
70  	}
71  	return 0;
72  }
```


**Question**: Does line `45` have control dependence over line `48` in function `main`? If so, provide a trace.

**Output**:


Ground truth answer: yes