[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<stdbool.h>
4   #include<ctype.h>
5   int sol[151];
6   int queryList[150];
7   char solStr[151];
8   int generateQueries(int n)
9   {
10      int beginning = 1, end = n, i = 0;
11      while(beginning <= end)
12      {
13          queryList[i] = beginning;
14          beginning++;
15          i++;
16          if(beginning < end)
17          {
18              queryList[i] = end;
19              end--;
20              i++;
21          }
22      }
23      while(i < 150)
24      {
25          queryList[i] = -1;
26          i++;
27      }
28  }
29  int findFlipBit(int n)
30  {
31      int i = 1;
32      while(i <= n && sol[i] != 2)
33      {
34          if(sol[i] == sol[n-i+1])
35          {
36              return i;
37          }
38          else i++;
39      }
40      return -1;
41  }
42  int findSwapBit(int n)
43  {
44      int i = 1;
45      while(i <= n && sol[i] != 2 && sol[n-i+1] != 2)
46      {
47          if(sol[i] != sol[n-i+1])
48          {
49              return i;
50          }
51          else i++;
52      }
53      return -1;
54  }
55  int query(int i)
56  {
57      int ret;
58      printf("%d\n", i);
59      fflush(stdout);
60      scanf("%d", &ret);
61      if(ret == 'N')
62      {
63          exit(1);
64      }
65      else
66      {
67          return ret;
68      }
69  }
70  void flipSol(int n)
71  {
72      for(int i = 1; i <= n; i++)
73      {
74          if(sol[i] == 1) sol[i] = 0;
75          else if(sol[i] == 0) sol[i] = 1;
76      }
77  }
78  void swapSol(int n)
79  {
80      int beginning = 1, end = n;
81      while (beginning < end)
82      {
83          int aux = sol[beginning];
84          sol[beginning] = sol[end];
85          sol[end] = aux;
86          beginning++;
87          end--;
88      }
89  }
90  void resolve(int n)
91  {
92      for(int i = 1; i <= n; i++)
93      {
94          sol[i] = 2;
95      }
96      generateQueries(n);
97      int queries = 0;
98      int known = 0;
99      int flipBit = -1, swapBit = -1;
100      int flipRes, swapRes, doubleRes;
101      bool flipped = false, swapped = false;
102      while(true)
103      {
104          if(queries % 10 == 0 && queries != 0)
105          {
106              if(flipBit == -1) flipBit = findFlipBit(n);
107              if(flipBit != -1)
108              {
109                  flipRes = query(flipBit);
110                  if(flipRes != sol[flipBit]) flipSol(n);
111                  else flipped = false;
112                  queries++;
113              }
114              else
115              {
116                  query(1);
117                  queries++;
118              }
119              if(swapBit == -1)
120              {
121                  swapBit = findSwapBit(n);
122              }
123              if(swapBit != -1)
124              {
125                  swapRes = query(swapBit);
126                  if(swapRes != sol[swapBit]) swapSol(n);
127                  else swapped = false;
128                  queries++;
129              }
130              else
131              {
132                  query(1);
133                  queries++;
134              }
135          }
136          else
137          {
138              sol[queryList[known]] = query(queryList[known]);
139              known++;
140              queries++;
141              if(queryList[known] == -1)
142              {
143                  for(int i = 1; i < n; i++)
144                  {
145                      printf("%d", sol[i]);
146                  }
147                  printf("%d\n", sol[n]);
148                  fflush(stdout);
149                  char answer  = 10;
150                  while (answer == 10)
151                  {
152                      answer = getchar();
153                  }
154                  if(answer == 'Y')
155                  {
156                      return;
157                  }
158                  else
159                  {
160                      exit(7);
161                  }
162              }
163          }
164      }
165  }
166  int main(void)
167  {
168      int t, n;
169      scanf("%d %d", &t, &n);
170      for(int test = 0; test < t; test++)
171      {
172          resolve(n);
173      }
174      return 0;
175  }
```


**Question**: Does line `16` have control dependence over line `19` in function `generateQueries`? If so, provide a trace.

**Output**:


Ground truth answer: yes