[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   typedef struct{
4     int fmax;
5     int flow;
6     int n[2];
7   }TEdge;
8   typedef struct{
9     int num;
10    int e[1200];
11  }TVertex;
12  TEdge e[1200];
13  TVertex v[120];
14  #define MIN(x,y) ((x)<(y)?(x):(y))
15  int V,E;
16  int et[120];
17  int route(int s, int ed,int c){
18    int res=0,r=-1,m=0,i=0;
19    r=-1;
20    et[s]=1;
21    for(i=0;i<v[s].num;i++){
22      if(e[v[s].e[i]].n[0]==s){
23        if(et[e[v[s].e[i]].n[1]]==0){
24          if(e[v[s].e[i]].fmax-e[v[s].e[i]].flow>0){
25            m=MIN(c,e[v[s].e[i]].fmax-e[v[s].e[i]].flow);
26            if(e[v[s].e[i]].n[1]==ed){
27              r=m;
28              e[v[s].e[i]].flow+=r;
29              res+=r;
30              if(res>=c){
31                et[s]=0;
32                return res;
33              }
34              c-=r;
35            }else{
36              r=route(e[v[s].e[i]].n[1],ed,m);
37              if(r>0){
38                e[v[s].e[i]].flow+=r;
39                res+=r;
40                if(res>=c){
41                  et[s]=0;
42                  return res;
43                }
44                c-=r;
45              }
46            }
47          }
48        }
49      }else{
50        if(et[e[v[s].e[i]].n[0]]==0){
51          if(e[v[s].e[i]].flow>0){
52            m=MIN(c,e[v[s].e[i]].flow);
53            r=route(e[v[s].e[i]].n[0],ed,m);
54            if(r>0){
55              e[v[s].e[i]].flow-=r;
56              res+=r;
57              if(res>=c){
58                et[s]=0;
59                return res;
60              }
61              c-=r;
62            }
63          }
64        }
65      }
66    }
67    et[s]=0;
68    return res;
69  }
70  int main(){
71    int i;
72    int res,cmax;
73    scanf("%d %d",&V,&E);
74    for(i=0;i<V;i++){
75      v[i].num=0;
76    }
77    cmax=0;
78    for(i=0;i<E;i++){
79      int a,b,c;
80      scanf("%d %d %d",&a,&b,&c);
81      e[i].n[0]=a;
82      e[i].n[1]=b;
83      v[a].e[v[a].num++]=i;
84      v[b].e[v[b].num++]=i;
85      e[i].fmax=c;
86      e[i].flow=0;
87      if(b==V-1){
88        v[a].e[v[a].num-1]=v[a].e[0];
89        v[a].e[0]=i;
90        cmax+=c;
91      }
92    }
93    res=0;
94    for(i=0;i<100;i++){
95      et[i]=0;
96    }
97    for(i=0;i<3;i++){
98      int x;
99      x=route(0,V-1,cmax);
100      if(x<=0){
101        printf("%d\n",res);
102        return 0;
103      }
104      res+=x;
105    }
106    printf("er\n");
107    return 0;
108  }
```


**Question**: Does line `87` have control dependence over line `90` in function `main`? If so, provide a trace.

**Output**:


Ground truth answer: yes