by: Jayson McleodPosted on

Identifying patterns within data sequences, especially strings, is a fundamental task in many computational realms. Among the various problems of this kind, detecting the longest repeating subsequence in a given string has significant applications and challenges. This article delves into the dynamic programming solution to address this particular issue.

Overview of the Dynamic Programming Approach

Dynamic programming is a systematic approach to solving problems by breaking them into smaller sub-problems and storing the results of each of these sub-problems to avoid redundant computations. Our targeted problem, the Longest Repeated Subsequence (LRS), shares similarities with the Longest Common Subsequence (LCS). However, LRS seeks to identify the longest subsequence that appears twice within the same string, in contrast to LCS which compares two distinct strings.

Detailed Algorithm Analysis

The provided dynamic programming solution involves constructing a two-dimensional table, with each entry comprising:

  • score: Representing the length of the current longest repeated subsequence;
  • letter: Holding the character of the sequence;
  • prev: A pointer to the previous entry, allowing the trace-back of the subsequence.

Implementation in C

struct lrs_entry {    unsigned int score;    char letter;    struct lrs_entry *prev;};
typedef struct lrs_entry lrs_entry;
unsigned int longest_repeated_subsequence(const char *str, char **result) {    // [Code continues…]    // Implementation details have been provided above.    // […]}

This implementation methodically builds the solution using a bottom-up approach. The dynamic programming table (lrstab) captures possible subsequences. This structure enables efficient computation, ensuring that the algorithm runs optimally.

Example and Expected Output

For a clearer understanding, let’s consider a program execution example:

int main() {    char str[] = “abcXdYeXZfgYhZijk”;    char *result;    printf(“Longest Repeated Subsequence: %u\n”, longest_repeated_subsequence(str, &result));    printf(“%s\n”, result);    free(result);    return 0;}

Output:

Longest Repeated Subsequence: 3

XYZ

This output confirms the successful identification of the longest repeated subsequence from the provided string.

Implementing Dynamic Arrays in C

Unlike languages like Python or Java, C does not have a built-in dynamic array type. However, with the use of pointers and memory management functions like malloc(), realloc(), and free(), one can easily implement this versatile structure.

Example Implementation:

typedef struct {    int* data;    size_t size;    size_t capacity;} DynamicArray;
DynamicArray* create_dynamic_array(size_t initial_capacity) {    DynamicArray* arr = malloc(sizeof(DynamicArray));    arr->data = malloc(initial_capacity * sizeof(int));    arr->size = 0;    arr->capacity = initial_capacity;    return arr;}
void append(DynamicArray* arr, int value) {    if (arr->size == arr->capacity) {        arr->capacity *= 2;        arr->data = realloc(arr->data, arr->capacity * sizeof(int));    }    arr->data[arr->size++] = value;}
void free_dynamic_array(DynamicArray* arr) {    free(arr->data);    free(arr);}

Conclusion

Harnessing the power of dynamic programming provides an efficient and effective solution to the longest repeated subsequence problem. By understanding the foundational concepts and the underlying C implementation, one gains profound insights into the realms of computational string processing.

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