[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 <stdarg.h>
5   #include <math.h>
6   char* readline() {
7   	size_t bufLen = 1024, dataLen = 0;
8   	char* data = malloc(bufLen);
9   	while (1) {
10  		char* cursor = data + dataLen;
11  		char* line = fgets(cursor, bufLen - dataLen, stdin);
12  		if (!line) { break; }
13  		dataLen += strlen(cursor);
14  		if (dataLen < bufLen - 1 || data[dataLen - 1] == '\n') { break; }
15  		size_t new_length = bufLen << 1;
16  		data = realloc(data, new_length);
17  		if (!data) { break; }
18  		bufLen = new_length;
19  	}
20  	if (data[dataLen - 1] == '\n') {
21  		data[dataLen - 1] = '\0';
22  	}
23  	else
24  	{
25  		dataLen++;
26  		data[dataLen - 1] = '\0';
27  	}
28  	data = realloc(data, dataLen);
29  	return data;
30  }
31  int G[1000][1000];
32  int targetX, targetY;
33  void main(int argc, char **argv)
34  {
35  	unsigned int u_w;
36  	int T;
37  	char *str;
38  	char *retStr;
39  	str = readline();
40  	sscanf(str, "%d", &T);
41  	free(str);
42  	u_w = 1;
43  	while (T-- != 0)
44  	{
45  		int R, C, H, V;
46  		int i, j, k, l, m;
47  		char *Waffle[10];
48  		int ChocChipCount[10];
49  		for (i = 0; i < 10; i++)
50  			ChocChipCount[i] = 0;
51  		str = readline();
52  		sscanf(str, "%d %d %d %d", &R, &C, &H, &V);
53  		free(str);
54  		for (i = 0; i < R; i++)
55  		{
56  			Waffle[i] = readline();
57  			for (j = 0; j < C; j++)
58  			{
59  				if (Waffle[i][j] == '@')
60  				{
61  					ChocChipCount[i]++;
62  				}
63  			}
64  		}
65  		retStr = "IMPOSSIBLE";
66  		for (i = 1; (i < R && (strcmp(retStr, "IMPOSSIBLE") == 0)); i++)
67  		{
68  			int topCount, bottomCount;
69  			int topleftCount, toprightCount;
70  			int bottomleftCount, bottomrightCount;
71  			topCount = 0;
72  			bottomCount = 0;
73  			for (j = 0; j < i; j++)
74  				topCount += ChocChipCount[j];
75  			for (j = i; j < R; j++)
76  				bottomCount += ChocChipCount[j];
77  			if (topCount != bottomCount)
78  				continue;
79  			else
80  			{
81  				for (k = 1; k < C; k++)
82  				{
83  					topleftCount = 0;
84  					toprightCount = 0;
85  					for (l = 0; l < i; l++)
86  					{
87  						for (m = 0; m < k; m++)
88  							if (Waffle[l][m] == '@')
89  								topleftCount++;
90  						toprightCount += ChocChipCount[l];
91  					}
92  					toprightCount -= topleftCount;
93  					if (topleftCount == toprightCount)
94  					{
95  						bottomleftCount = 0;
96  						bottomrightCount = 0;
97  						for (l = i; l < R; l++)
98  						{
99  							for (m = 0; m < k; m++)
100  								if (Waffle[l][m] == '@')
101  									bottomleftCount++;
102  							bottomrightCount += ChocChipCount[l];
103  						}
104  						bottomrightCount -= bottomleftCount;
105  						if (bottomleftCount == bottomrightCount)
106  						{
107  							retStr = "POSSIBLE";
108  							break;
109  						}
110  					}
111  				}
112  			}
113  		}
114  		printf("Case #%d: %s", u_w, retStr);
115  		u_w++;
116  	}
117  }
```


**Question**: Does line `81` have control dependence over line `101` in function `main`? If so, provide a trace.

**Output**:


Ground truth answer: yes