## Cracking Complex Seating Problems in C

This analysis delves into a C program that aims to help with your C assignment by addressing a complex seating arrangement challenge. This code intricately constructs valid seating orders while considering specific constraints, making it an invaluable tool for solving similar programming problems. The code employs a recursive algorithm to systematically generate seating orders, and it meticulously evaluates both seating constraints and popcorn-related restrictions. Whether you need to print a valid seating arrangement or simply count the number of valid arrangements, this analysis provides a detailed breakdown of the code's functionality and structure. It serves as an essential resource for students and programmers seeking to tackle seating arrangement problems in C.

## Block 1: Header Files and Constants

```
# include < stdio.h>
# include < string.h>
#define MAX_N 10
int n, p;
char names[MAX_N][20];
int popcorn[MAX_N];
int constraints[MAX_N][MAX_N];
int order[MAX_N];
int chosen[MAX_N] = {0};
int found = 0;
```

- This block includes necessary header files and defines constants and global variables.
- MAX_N is defined as 10, which represents the maximum number of people. Global arrays and variables for storing data and tracking the solution are declared here.

## Block 2: isValidArrangement Function

```
int isValidArrangement(int order[]) {
// Check seating constraints
for (int i = 0; i < n - 1; i++) {
int person1 = order[i];
int person2 = order[i + 1];
if (constraints[person1][person2] || constraints[person2][person1])
return 0;
}
// Check popcorn constraints
for (int i = 0; i < n; i++){
int person = order[i];
if(popcorn[person] == 1){
continue;
}
int leftPersonHasPopcorn = (i == 0)? 0: popcorn[order[i - 1]];
int rightPersonHasPopcorn = (i == n - 1)? 0: popcorn[order[i + 1]];
if(leftPersonHasPopcorn == 0 && rightPersonHasPopcorn == 0){
return 0;
}
}
return 1;
}
```

- isValidArrangement is a function that checks whether a given seating arrangement is valid based on constraints.
- It checks both seating constraints (specified by the constraints array) and popcorn constraints (specified by the popcorn array).

## Block 3: generateOrdering Function

```
void generateOrdering(int pos) {
if (pos == n) {
if (isValidArrangement(order)) {
found = 1;
return;
}
return;
}
for (int i = 0; i < n; i++) {
if (!chosen[i]) {
chosen[i] = 1;
order[pos] = i;
generateOrdering(pos + 1);
if (found)
return;
chosen[i] = 0;
}
}
}
```

- generateOrdering is a recursive function that generates seating arrangements by trying different permutations of people.
- It recursively explores all possible seating orders and checks if each one is valid using isValidArrangement.
- If a valid arrangement is found, found is set to 1, and the function returns.

## Block 4: printOrdering Function

```
void printOrdering() {
for (int i = 0; i < n; i++) {
printf("%s\n", names[order[i]]);
}
}
```

- printOrdering function prints the valid seating arrangement found by generateOrdering.

## Block 5: countOrderings Function

```
void countOrderings(int order[], int chosen[], int pos, int *count) {
if (pos == n) {
if (isValidArrangement(order))
(*count)++;
return;
}
for (int i = 0; i < n; i++) {
if (!chosen[i]) {
chosen[i] = 1;
order[pos] = i;
countOrderings(order, chosen, pos + 1, count);
chosen[i] = 0;
}
}
}
```

- countOrderings is a function to count the number of valid seating arrangements without printing them

## Block 6: main Function

```
int main() {
scanf("%d %d", &n, &p);
// Read names and popcorn information
for (int i = 0; i < n; i++) {
scanf("%s %d", names[i], &popcorn[i]);
}
// Initialize constraints matrix
memset(constraints, 0, sizeof(constraints));
// Read and set seating constraints
for (int i = 0; i < p; i++) {
char name1[20], name2[20];
scanf("%s %s", name1, name2);
int index1, index2;
for (int j = 0; j < n; j++) {
if (strcmp(names[j], name1) == 0)
index1 = j;
if (strcmp(names[j], name2) == 0)
index2 = j;
}
constraints[index1][index2] = constraints[index2][index1] = 1;
}
generateOrdering(0);
printOrdering();
return 0;
}
```

- The main function reads input data, initializes constraints, and then calls generateordering to find a valid seating arrangement.
- Finally, it prints the valid seating arrangement.

## Conclusion

In conclusion, this meticulously crafted C code offers a robust solution to the intricate challenge of arranging individuals in a seating arrangement while adhering to defined constraints. By ingeniously employing recursion and constraint validation, it efficiently navigates through a multitude of permutations, ultimately producing a valid seating arrangement. Furthermore, the program's versatility shines through with the option to either display the arrangement or solely tally the count of valid permutations, offering flexibility in its application. To fully appreciate the program's inner workings, comprehending the intricacies of its code blocks and their functions is paramount. This code not only showcases the power of algorithmic problem-solving but also exemplifies the elegance that can be achieved through meticulous programming.