diff --git a/DIRECTORY.md b/DIRECTORY.md index 4f2a525c..7167850a 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -243,6 +243,17 @@ * [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2015/sol1.c) * Problem 16 * [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2016/sol1.c) + * Problem 20 + * [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2020/sol1.c) + * Problem 19 + * [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2019/sol1.c) + * Problem 21 + * [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2021/sol1.c) + * Problem 22 + * [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2022/sol1.c) + * Problem 23 + * [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2023/sol1.c) + * [Sol2](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2023/sol2.c) ## Searching * [Binary Search](https://github.com/TheAlgorithms/C/blob/master/searching/Binary_Search.c) diff --git a/project_euler/Problem 19/sol1.c b/project_euler/Problem 19/sol1.c new file mode 100644 index 00000000..70fb7f16 --- /dev/null +++ b/project_euler/Problem 19/sol1.c @@ -0,0 +1,120 @@ +#include + +/** + * returns number of days in a month. + * Month is identified by an integer - + * 0 = Jan and 11 = December + * For February, adjust for leap year outside the function. + **/ +char get_month_days(short month) +{ + if (month == 1) /* February has 28 days. Adjust leap year in the loop */ + return 28; + else if (month <= 6) /* odd months till July have 30 days - Jan = 0 (even)*/ + { + if (month & 0x01) + return 30; + else + return 31; + } else if (month >= 7) /* odd months after July have 31 days*/ + { + if (month & 0x01) + return 31; + else + return 30; + } + /* should never reach here! */ + perror("Should never have reached this point!\n"); + return -1; +} + +/** + * return 1 if input year is a leap year + * otherwise, return 0 + **/ +char is_leap_year(short year) +{ + if ((year % 400 == 0) || ((year % 4 == 0) && (year % 100 != 0))) + return 1; + + return 0; +} + +#ifdef DEBUG +const char* day_string(int day) +{ + switch(day) + { + case 0: + return "Sunday"; + case 1: + return "Monday"; + case 2: + return "Tuesday"; + case 3: + return "Wednesday"; + case 4: + return "Thursday"; + case 5: + return "Friday"; + case 6: + return "Saturday"; + default: + return "Shouldnt see this!"; + } +} +#endif + + +int main(int argc, char **argv) +{ + int count_sundays = 0; + const short start_year = 1901; + const short end_year = 2000; + + /** + * Let us identify days i.e., Sunday thru Saturday with integers - 0 thru 6 respectively + * Jan 1 1901 was a Tuesday + **/ + char start_day = 2; + + for (int year = start_year; year <= end_year; year++) + { + char is_leap = is_leap_year(year); + for (char month = 0; month < 12; month ++) + { + /** + * These two for-loops count the start of day for the next month. Hence, + * we have to skip the last December count */ + if (year == end_year && month == 11) + continue; + + int days = get_month_days(month); + + if (is_leap && month == 1) /* for a leap year february, add a day */ + days ++; + + #ifdef DEBUG + if (year == end_year) + { + printf("Year: %d\t Month: %d\t Days: %d\t First of day: %s\n", year, month, days, day_string(start_day)); + } + #endif + + /** Main Algorithm: + * every week has 7 days hence, the start of next day would be modulo 7 + * add to this, the current start date and ensure the result is still + * modulo 7! + **/ + start_day = ((days % 7) + start_day) % 7; + + /* If start-day is a Sunday, increment counter */ + if (start_day == 0) + count_sundays ++; + } + } + + printf("Total number of Sundays that happened on the 1st of a month in the last century: %d\n", count_sundays); + + return 0; +} \ No newline at end of file diff --git a/project_euler/Problem 20/sol1.c b/project_euler/Problem 20/sol1.c new file mode 100644 index 00000000..9464f10a --- /dev/null +++ b/project_euler/Problem 20/sol1.c @@ -0,0 +1,170 @@ +#include +#include +#include + +/** + * store arbitratily large integer values + * as a linked list of digits. + **/ +typedef struct _big_int +{ + char value; /** tens place (single digit) */ + struct _big_int *next_digit; /** hundreds place */ + struct _big_int *prev_digit; /** units place */ +} big_int; + +#ifdef DEBUG +void print_digit(const big_int *my_int) +{ + printf("\tValue : %d\n\tNext : %p\n\tPrev : %p\n", my_int->value, my_int->next_digit, my_int->prev_digit); +} +#endif + +/** + * Function that allocates memory to add another + * digit at the MSB + **/ +big_int *add_digit(big_int *digit, char value) +{ + if (digit == NULL) + { + digit = (big_int *)malloc(sizeof(big_int)); + if (!digit) + { + perror("Unable to allocate memory!"); + return NULL; + } + digit->value = value; + digit->next_digit = NULL; + digit->prev_digit = NULL; + + return digit; + } + + if (digit->next_digit) + { + digit->next_digit->value = value; + return digit->next_digit; + } + + digit->next_digit = (big_int *)malloc(sizeof(big_int)); + if (digit->next_digit == NULL) + { + perror("Unable to allocate memory!"); + return NULL; + } + digit->next_digit->value = value; + digit->next_digit->next_digit = NULL; + digit->next_digit->prev_digit = digit; + return digit->next_digit; +} + +/** + * Function to remove digits preceeding the + * current digit. + **/ +char remove_digits(big_int *digit, int N) +{ + if (digit == NULL) + return 0; + + if (digit->next_digit == NULL) + { + free(digit); + digit = NULL; + return 0; + } + + if (N > 0) + return remove_digits(digit->next_digit, N - 1); + + return remove_digits(digit->next_digit, 0); +} + +int main(int argc, char **argv) +{ + unsigned int N = 5; + big_int *ptr = add_digit(NULL, 1); /* start with 1 */ + const big_int *ptr0 = ptr; /* save the first location */ + unsigned long sum_digits = 0; + unsigned long num_digits = 0; + + if (argc == 2) + N = atoi(argv[1]); + + clock_t start_time = clock(); + + for (unsigned int i = 1; i <= N; i++) + { + int carry = 0; +#ifdef DEBUG + printf("%3d: ", i); +#endif + ptr = (big_int *)ptr0; /* multiply every digit with i */ + while (ptr) + { +#ifdef DEBUG + printf("%p\t", ptr); +#endif + unsigned int tmp = ptr->value * i + carry; + if (tmp >= 10) + { + div_t tmp2 = div(tmp, 10); + carry = tmp2.quot; + tmp = tmp2.rem; + } + else + carry = 0; + + if (carry > 0 && ptr->next_digit == NULL) + add_digit(ptr, 0); + + ptr->value = tmp; + + if (i == N) + /** + * sum digits on the last iteration + * this avoid having another loop over all digits + **/ + sum_digits += tmp; + + if (ptr->next_digit) + /* more digits available */ + ptr = ptr->next_digit; + else + /* no more digits left - reached MSB */ + break; + } +#ifdef DEBUG + printf("\n"); +#endif + } + + clock_t end_time = clock(); + +#ifdef DEBUG + printf("ptr = %p\n", ptr); + printf("%d! = ", N); +#endif + + /** Notice that in the loop above, we make sure that at the end of the loop, + * ptr is pointing to the last digit. Thus we can avoid using another loop. + **/ + // ptr = &my_int; + // /* move ptr to the MSB digit */ + // while (ptr->next_digit) + // ptr = ptr->next_digit; + do + { + putchar(ptr->value + 0x30); /* convert digit to ASCII char */ + ptr = ptr->prev_digit; + num_digits++; + } while (ptr); /* after coming to units place, there will be no valid ptr */ + + printf("\nTime taken: %.4g millisecond\n", 1e3 * (end_time - start_time) / CLOCKS_PER_SEC); + printf("Digit Sum = %lu\tNumber of digits = %lu\tStorage space = %.3gkb\t \n", + sum_digits, num_digits, num_digits * sizeof(big_int) / 1024.0); + + remove_digits((big_int *)ptr0, -1); + return 0; +} diff --git a/project_euler/Problem 21/sol1.c b/project_euler/Problem 21/sol1.c new file mode 100644 index 00000000..4511426f --- /dev/null +++ b/project_euler/Problem 21/sol1.c @@ -0,0 +1,98 @@ +#include +#include +#include +#ifdef _OPENMP +#include +#endif + +/** + * function to return the sum of proper divisors of N + **/ +unsigned int sum_of_divisors(unsigned int N) +{ + unsigned int sum = 1; /* 1 is always a divisor */ + + /* divisors are symmertically distributed about the square-root */ + for (unsigned int i = 2; (i * i) <= N; i++) + { + if (N % i != 0) + /* i is not a proper divisor */ + continue; + + // #ifdef DEBUG + // printf("%4d, %4d,", i, N / i); + // #endif + + sum += i; + + if (i * i == N) + continue; + + sum += N / i; + } + // #ifdef DEBUG + // printf("\nSum of divisors of %4d: %4d\n", N, sum); + // #endif + return sum; +} + +int main(int argc, char **argv) +{ + unsigned long sum = 0; + unsigned int MAX_N = 500; + if (argc == 2) + MAX_N = atoi(argv[1]); + + /** + * We use an array of flags to check if a number at the index was: + * not-processed = 0 + * is amicable = 1 + * not amicable = -1 + **/ + char *flags = (char *)calloc(MAX_N, sizeof(char)); + + clock_t start_time = clock(); + +#ifdef _OPENMP +#pragma omp for schedule(runtime) +#endif + /* there are no such numbers till 10. Lets search from there on */ + for (unsigned int i = 10; i < MAX_N; i++) + { + if (flags[i] != 0) + /* already processed, skip */ + continue; + + unsigned int b = sum_of_divisors(i); + if (b >= MAX_N) + flags[i] = -1; + else if (flags[b] == -1) + continue; + + unsigned int c = sum_of_divisors(b); + if (c == i && b != i) + { + /* found amicable */ + flags[b] = 1; + flags[i] = 1; + sum += b + i; +#ifdef DEBUG + printf("Amicable: %4d : %4d\n", i, b); +#endif + } + else + { + flags[i] = -1; + if (b < MAX_N) + flags[b] = -1; + } + } + + clock_t end_time = clock(); + + printf("\nTime taken: %.4g millisecond\n", 1e3 * (end_time - start_time) / CLOCKS_PER_SEC); + printf("Sum of all numbers = %lu\n", sum); + + free(flags); + return 0; +} diff --git a/project_euler/Problem 22/names.txt b/project_euler/Problem 22/names.txt new file mode 100644 index 00000000..7b8986bf --- /dev/null +++ b/project_euler/Problem 22/names.txt @@ -0,0 +1 @@ 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\ No newline at end of file diff --git a/project_euler/Problem 22/sol1.c b/project_euler/Problem 22/sol1.c new file mode 100644 index 00000000..37ebea0b --- /dev/null +++ b/project_euler/Problem 22/sol1.c @@ -0,0 +1,138 @@ +#include +#include +#include +#include +#ifdef _OPENMP +#include +#endif + +#define MAX_NAMES 6000 /* Maximum number of names to store */ +#define MAX_NAME_LEN 20 /* Maximum length of each name */ + +/** + * Alphabetical sorting using 'shell sort' algorithm + **/ +void shell_sort(char data[][MAX_NAME_LEN], int LEN) +{ + const int gaps[] = {701, 301, 132, 57, 23, 10, 4, 1}; + const int gap_len = 8; + int i, j, g; + + for (g = 0; g < gap_len; g++) + { + int gap = gaps[g]; + for (i = gap; i < LEN; i++) + { + char tmp_buffer[MAX_NAME_LEN]; + strcpy(tmp_buffer, data[i]); + + for (j = i; j >= gap && strcmp(data[j - gap], tmp_buffer) > 0; j -= gap) + strcpy(data[j], data[j - gap]); + strcpy(data[j], tmp_buffer); + } + } +#ifdef DEBUG + for (i = 0; i < LEN; i++) + printf("%s\t", data[i]); +#endif +} + +/** + * Alphabetical sorting using 'lazy sort' algorithm + **/ +void lazy_sort(char data[][MAX_NAME_LEN], int LEN) +{ + int i, j; + for (i = 0; i < LEN; i++) + { + for (j = i + 1; j < LEN; j++) + { + if (strcmp(data[i], data[j]) > 0) + { + char tmp_buffer[MAX_NAME_LEN]; + strcpy(tmp_buffer, data[i]); + strcpy(data[i], data[j]); + strcpy(data[j], tmp_buffer); + } + } + } +#ifdef DEBUG + for (i = 0; i < LEN; i++) + printf("%s\t", data[i]); +#endif +} + +int main(int argc, char **argv) +{ + unsigned long COUNT = 0; + char *fname = "names.txt"; + char names[MAX_NAMES][MAX_NAME_LEN]; + short method = 0; /* sorting algorithm to use. 0 = lazy, 1 = shell-sort */ + + if (argc == 2) + method = atoi(argv[1]); + + FILE *fp = fopen(fname, "rt"); + if (!fp) + { + perror("Unable to open file"); + return -1; + } + + /** + * Loops to get total number of rows and columns in the file + **/ + do + { + int ret = fscanf(fp, "\"%[^\",]\",", names[COUNT++]); + if (ret <= 0) + continue; + // printf("%s\t", names[COUNT - 1]); + } while (!feof(fp)); + fclose(fp); + + printf("\nTotal number of names: %lu\n", COUNT); + + if (method == 0) + { + clock_t start_time = clock(); + shell_sort(names, COUNT); + clock_t end_time = clock(); + printf("\nShell sort: %.4g millisecond\n", 1e3 * (end_time - start_time) / CLOCKS_PER_SEC); + } + else if (method == 1) + { + clock_t start_time = clock(); + lazy_sort(names, COUNT); + clock_t end_time = clock(); + printf("\nLazy sort: %.4g millisecond\n", 1e3 * (end_time - start_time) / CLOCKS_PER_SEC); + } + + long sum_score = 0; + clock_t start_time = clock(); +#ifdef _OPENMP +#pragma omp parallel for schedule(runtime) reduction(+ \ + : sum_score) +#endif +#ifdef DEBUG + for (unsigned int i = 935; i < 940; i++) +#else + for (unsigned int i = 0; i < COUNT; i++) +#endif + { + unsigned int score = 0; + /* score the alphabets in i^th name */ + for (int j = 0; names[i][j] != '\0'; j++) + score += names[i][j] - 'A' + 1; /* convert ASCII character to integer score */ + sum_score += score * (i + 1); +#ifdef DEBUG + printf("Name: %s\tScore: %u x %u = %lu\n", names[i], score, i + 1, (unsigned long)score * (i + 1)); +#endif + } + clock_t end_time = clock(); + printf("Scoring time: %.4g millisecond\n", 1e3 * (end_time - start_time) / CLOCKS_PER_SEC); + + printf("Total Score = %lu\n", sum_score); + + return 0; +} diff --git a/project_euler/Problem 23/sol1.c b/project_euler/Problem 23/sol1.c new file mode 100644 index 00000000..e7145946 --- /dev/null +++ b/project_euler/Problem 23/sol1.c @@ -0,0 +1,116 @@ + +#include +#include +#include +#ifdef _OPENMP +#include +#endif + +unsigned long MAX_N = 28123; + +/** + * Returns: + * -1 if N is deficient + * 1 if N is abundant + * 0 if N is perfect + **/ +char get_perfect_number(unsigned long N) +{ + unsigned long sum = 1; + char ret = 0; + + for (unsigned long i = 2; i * i <= N; i++) + { + if (N % i == 0) + { + sum += i; + unsigned long tmp = N / i; + if (tmp != i) + sum += tmp; + } + } + + ret = sum == N ? 0 : (sum > N ? 1 : -1); + // #ifdef DEBUG + // printf("%5lu: %5lu : %d\n", N, sum, ret); + // #endif + return ret; +} + +/** + * Is the given number an abundant number (1) or not (0) + **/ +unsigned long is_abundant(unsigned long N) +{ + return get_perfect_number(N) == 1 ? 1 : 0; +} + +/** + * Find the next abundant number after N and not including N + **/ +unsigned long get_next_abundant(unsigned long N) +{ + unsigned long i; + for (i = N + 1; !is_abundant(i); i++) + ; + return i; +} + +/** + * check if a given number can be represented as a sum + * of two abundant numbers. + * 1 - if yes + * 0 - if not + **/ +char is_sum_of_abundant(unsigned long N) +{ + /** optimized logic: + * i + j = N where both i and j should be abundant + * hence we can simply check for j = N - i as we loop through i + **/ + for (unsigned long i = get_next_abundant(1); i <= (N >> 1); i = get_next_abundant(i)) + if (is_abundant(N - i)) + { +#ifdef DEBUG + printf("\t%4lu + %4lu = %4lu\n", i, N - i, N); +#endif + return 1; + } + return 0; +} + +int main(int argc, char **argv) +{ + unsigned long sum = 0; + if (argc == 2) + MAX_N = strtoul(argv[1], NULL, 10); + +#ifdef _OPENMP + printf("Using OpenMP parallleization with %d threads\n", omp_get_max_threads()); +#else + printf("Not using parallleization!\n"); +#endif + + clock_t dt = 0; +#ifdef _OPENMP +#pragma omp parallel for reduction(+ \ + : sum) schedule(runtime) +#endif + for (unsigned long i = 1; i <= MAX_N; i++) + { + clock_t start_time = clock(); + if (!is_sum_of_abundant(i)) + sum += i; + clock_t end_time = clock(); + dt += end_time - start_time; + + printf("... %5lu: %8lu\r", i, sum); + if (i % 100 == 0) + fflush(stdout); + } + + printf("Time taken: %.4g ms\n", 1e3 * dt / CLOCKS_PER_SEC); + printf("Sum of numbers that cannot be represented as sum of two abundant numbers : %lu\n", sum); + + return 0; +} diff --git a/project_euler/Problem 23/sol2.c b/project_euler/Problem 23/sol2.c new file mode 100644 index 00000000..9ee09498 --- /dev/null +++ b/project_euler/Problem 23/sol2.c @@ -0,0 +1,180 @@ + +#include +#include +#include +#ifdef _OPENMP +#include +#endif + +/** + * Optimization 1 - compute & store abundant numbers once + * into a look-up array + **/ + +unsigned long MAX_N = 28123; + +/** + * This is the global array to be used to store a flag to identify + * if a particular number is abundant (1) or not (0). + * Using a whole byte to store a binary info would be redundant. + * We will use each byte to represent 8 numbers by relying on bits. + * This saves memory required by 1/8 + **/ +char *abundant_flags = NULL; + +/** + * Returns: + * -1 if N is deficient + * 1 if N is abundant + * 0 if N is perfect + **/ +char get_perfect_number(unsigned long N) +{ + unsigned long sum = 1; + char ret = 0; + + for (unsigned long i = 2; i * i <= N; i++) + { + if (N % i == 0) + { + sum += i; + unsigned long tmp = N / i; + if (tmp != i) + sum += tmp; + } + } + + ret = sum == N ? 0 : (sum > N ? 1 : -1); +#ifdef DEBUG + printf("%5lu: %5lu : %d\n", N, sum, ret); +#endif + return ret; +} + +/** + * Is the given number an abundant number (1) or not (0) + **/ +char is_abundant(unsigned long N) +{ + // return abundant_flags[N >> 3] & (1 << N % 8) ? 1 : 0; + return abundant_flags[N >> 3] & (1 << (N & 7)) ? 1 : 0; /* optimized modulo operation */ +} + +/** + * Find the next abundant number after N and not including N + **/ +unsigned long get_next_abundant(unsigned long N) +{ + unsigned long i; + /* keep checking successive numbers till an abundant number is found */ + for (i = N + 1; !is_abundant(i); ++i) + ; + return i; +} + +/** + * check if a given number can be represented as a sum + * of two abundant numbers. + * 1 - if yes + * 0 - if not + **/ +char is_sum_of_abundant(unsigned long N) +{ + /** optimized logic: + * i + j = N where both i and j should be abundant + * hence we can simply check for j = N - i as we loop through i + **/ + for (unsigned long i = get_next_abundant(1); i <= (N >> 1); i = get_next_abundant(i)) + if (is_abundant(N - i)) + { +#ifdef DEBUG + printf("\t%4lu + %4lu = %4lu\n", i, N - i, N); +#endif + return 1; + } + return 0; +} + +int main(int argc, char **argv) +{ + unsigned long sum = 0; + if (argc == 2) + MAX_N = strtoul(argv[1], NULL, 10); + + /** byte array to store flags to identify abundant numbers + * the flags are identified by bits + **/ + abundant_flags = (char *)calloc(MAX_N >> 3, 1); + if (!abundant_flags) + { + perror("Unable to allocate memoey!"); + return -1; + } + +#ifdef _OPENMP + printf("Using OpenMP parallleization with %d threads\n", omp_get_max_threads()); +#else + printf("Not using parallleization!\n"); +#endif + + clock_t start_time = clock(); + +/* Loop to set abundant flags */ +#ifdef _OPENMP +#pragma omp for schedule(runtime) +#endif + for (unsigned long N = 1; N <= MAX_N; N++) + { + char ret = get_perfect_number(N); + if (ret == 1) + { + // int byte_offset = N % 8, index = N >> 3; + int byte_offset = N & 7, index = N >> 3; +#ifdef _OPENMP +#pragma omp critical +#endif + abundant_flags[index] |= ret << byte_offset; + } + // if (i % 100 == 0) + // printf("... %5lu: %8lu\r", i, sum); + } + + clock_t end_time = clock(); + double t1 = 1e3 * (end_time - start_time) / CLOCKS_PER_SEC; + printf("Time taken to get abundant numbers: %.4g ms\n", t1); + + clock_t t2 = 0; +#ifdef _OPENMP +#pragma omp for schedule(runtime) private(start_time, end_time) +#endif + for (unsigned long i = 1; i < MAX_N; i++) + { + start_time = clock(); + if (!is_sum_of_abundant(i)) +#ifdef _OPENMP +#pragma omp critical +#endif + sum += i; + end_time = clock(); +#ifdef _OPENMP +#pragma omp critical +#endif + t2 += end_time - start_time; + + printf("... %5lu: %8lu\r", i, sum); + if (i % 100 == 0) + fflush(stdout); + } + +#ifdef DEBUG + putchar('\n'); +#endif + double t22 = 1e3 * t2 / CLOCKS_PER_SEC; + printf("Time taken for final sum: %.4g ms\nTotal Time taken: %.4g ms\n", t22, t1 + t22); + printf("Memory used: %lu bytes\n", MAX_N >> 3); + printf("Sum of numbers that cannot be represented as sum of two abundant numbers : %lu\n", sum); + + free(abundant_flags); + + return 0; +} diff --git a/project_euler/Problem 24/sol1 b/project_euler/Problem 24/sol1 new file mode 100755 index 00000000..b67b122c Binary files /dev/null and b/project_euler/Problem 24/sol1 differ diff --git a/project_euler/Problem 25/sol1.c b/project_euler/Problem 25/sol1.c new file mode 100644 index 00000000..b6addd95 --- /dev/null +++ b/project_euler/Problem 25/sol1.c @@ -0,0 +1,109 @@ +#include +#include +#include +#include + +#define MAX_DIGITS 1000 + +/** + * Function to add arbitraty length decimal integers stored in an array. + * a + b = c = new b + **/ +unsigned int add_numbers(uint8_t *a, uint8_t *b, uint8_t *c, int N) +{ + uint8_t carry = 0; + unsigned int i; + + for (i = 0; i < N; i++) + { + // printf("\t%d + %d + %d ", a[i], b[i], carry); + c[i] = carry + a[i] + b[i]; + if (c[i] > 9) /* check for carry */ + { + carry = 1; + c[i] -= 10; + } + else + carry = 0; + // printf("= %d, %d\n", carry, c[i]); + } + + while (carry != 0) + { + // printf("\t\t...adding new digit\n"); + // printf("\t0 + %d + %d ", b[i], carry); + c[i] = carry + c[i]; + if (c[i] > 9) + { + carry = 1; + c[i] -= 10; + } + else + carry = 0; + // printf("= %d, %d\n", carry, c[i]); + i++; + } + return i; +} + +int print_number(uint8_t *number, int N) +{ + int start_pos = N - 1; + + /* skip all initial zeros */ + while (number[start_pos] == 0) + start_pos--; + + for (int i = start_pos; i >= 0; i--) + putchar(number[i] + 0x30); + + return 0; +} + +unsigned int get_digits(uint8_t *number) +{ + unsigned int digits = MAX_DIGITS; + while (number[digits] == 0) + digits--; + return digits; +} + +int main(int argc, char *argv[]) +{ + uint8_t fn[MAX_DIGITS + 1]; /* array to store digits of a large number */ + uint8_t fn1[MAX_DIGITS + 1]; + uint8_t sum[MAX_DIGITS + 1]; + + memset(fn, 0, MAX_DIGITS); + memset(fn1, 0, MAX_DIGITS); + memset(sum, 0, MAX_DIGITS); + + fn[0] = 1; + fn1[1] = 1; + + unsigned int index = 1, digit_count = 1; + + clock_t start_time = clock(); + do + { + digit_count = add_numbers(fn, fn1, sum, digit_count); + // digit_count = get_digits(sum); + + // printf("%5u (%u) (%u) ", index, digit_count, get_digits(sum)); + // print_number(sum, digit_count); + // putchar('\n'); + + if (digit_count == MAX_DIGITS) + break; + memcpy(fn, fn1, MAX_DIGITS); + memcpy(fn1, sum, MAX_DIGITS); + index++; + } while (digit_count < MAX_DIGITS); + clock_t end_time = clock(); + + printf("Time taken: %.4g ms\n", 1e3 * (end_time - start_time) / CLOCKS_PER_SEC); + printf("The nth term for %d digits: %u \n", MAX_DIGITS, index--); + print_number(sum, digit_count); + + return 0; +} diff --git a/sorting/shell_Sort.c b/sorting/shell_Sort.c index c332647d..8ebf6fcc 100644 --- a/sorting/shell_Sort.c +++ b/sorting/shell_Sort.c @@ -2,7 +2,7 @@ #include #include -#define ELEMENT_NR 20 +#define ELEMENT_NR 20000 #define ARRAY_LEN(x) (sizeof(x) / sizeof((x)[0])) const char *notation = "Shell Sort Big O Notation:\ \n--> Best Case: O(n log(n)) \ @@ -37,10 +37,38 @@ void shellSort(int array[], int len) swap(&array[j], &array[j + gap]); } +/** + * Optimized algorithm - takes half the time as other + **/ +void shell_sort2(int array[], int LEN) +{ + const int gaps[] = {701, 301, 132, 57, 23, 10, 4, 1}; + const int gap_len = 8; + int i, j, g; + + for (g = 0; g < gap_len; g++) + { + int gap = gaps[g]; + for (i = gap; i < LEN; i++) + { + int tmp = array[i]; + + for (j = i; j >= gap && (array[j - gap] - tmp) > 0; j -= gap) + array[j] = array[j - gap]; + array[j] = tmp; + } + } +#ifdef DEBUG + for (i = 0; i < LEN; i++) + printf("%s\t", data[i]); +#endif +} + int main(int argc, char *argv[]) { int i; int array[ELEMENT_NR]; + int array2[ELEMENT_NR]; int range = 500; int size; clock_t start, end; @@ -48,7 +76,10 @@ int main(int argc, char *argv[]) srand(time(NULL)); for (i = 0; i < ELEMENT_NR; i++) + { array[i] = rand() % range + 1; + array2[i] = array[i]; + } size = ARRAY_LEN(array); @@ -62,7 +93,19 @@ int main(int argc, char *argv[]) show_data(array, size); printf("%s\n", notation); - printf("Time spent sorting: %f\n", time_spent); + printf("Time spent sorting: %.4g ms\n", time_spent * 1e3); + + printf("--------------------------\n"); + start = clock(); + shell_sort2(array2, size); + end = clock(); + time_spent = (double)(end - start) / CLOCKS_PER_SEC; + + printf("Data Sorted\n"); + show_data(array2, size); + + printf("%s\n", notation); + printf("Time spent sorting: %.4g ms\n", time_spent * 1e3); return 0; }