[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   int minswaps(char* p, int d, int len);
5   int main()
6   {
7   	int n,i;
8   	scanf("%d",&n);
9   	for(i=0;i<n;i++)
10  	{
11  		int d;
12  		char p[31];
13  		scanf("%d ",&d);
14  		scanf("%s",p);
15  		int r=minswaps(p,d,strlen(p));
16  		if(r==-1)
17  			printf("Case #%d: IMPOSSIBLE\n",i+1 );
18  		else
19  			printf("Case #%d: %d\n",i+1,r );
20  	}
21  }
22  int minswaps(char* p, int d, int len)
23  {
24      if(len==2)
25      {
26          if(p[0]=='S' && p[1]=='C')
27              return(0);
28          if(p[0]=='S'&&p[1]=='S')
29          {
30              if(d<2)
31                  return(-1);
32              else
33                  return(0);
34          }
35          if(p[0]=='C' && p[1]=='S')
36          {
37              if(d<2)
38                  return(1);
39              else
40                  return(0);
41          }
42          return(0);
43      }
44      int i,strength=1,damage=0,temp,k=0,swaps=0,flag=0;
45      int * a=(int*)malloc(sizeof(int)*len);
46      for(i=0;i<len;i++)
47      {
48          if(p[i]=='S')
49          {
50              damage+=strength;
51              a[k++]=strength;
52          }
53          else
54          {
55              strength*=2;
56              a[k++]=strength;
57          }
58      }
59      if(damage<=d)
60          return(0);
61      i=len-1;
62      while(!flag)
63      {
64            flag=1;
65            i=len-1;
66            while(damage-d>0 && i>0)
67            {
68                while(p[i]!='S')
69                    i--;
70                if(p[i-1]=='S')
71                    i--;
72                else
73                {
74                    flag=0;
75                    p[i]='C';
76                    p[i-1]='S';
77                    damage-=a[i];
78                    if(i-1==0)
79                    {
80                        a[i-1]=1;
81                        a[i]=2;
82                    }
83                    else
84                    {
85                      a[i-1]=a[i-2];
86                      a[i]=2*a[i-1];
87                    }
88                    damage+=a[i-1];
89                    swaps++;
90                }
91                if(i==1 && p[i-1]=='S')
92                {
93                  break;
94                }
95            }
96      }
97      free(a);
98      if(damage-d<=0)
99          return(swaps);
100      else
101          return(-1);
102  }
```


**Question**: Does line `46` have control dependence over line `51` in function `minswaps`? If so, provide a trace.

**Output**:


Ground truth answer: yes