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Merge branch 'project_euler/problem_23' into project_euler/master2
* project_euler/problem_23: updating DIRECTORY.md move time computation inside loop + comments faster parallleization time computation inside the loop & print loop info added comments sol1 optimized by storing abundant numbers in a condensed array brute-force - compute abundant numbers every time # Conflicts: # DIRECTORY.md
This commit is contained in:
Krishna Vedala
commit
52b83e3ca6
@ -251,6 +251,9 @@
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* [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2021/sol1.c)
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* Problem 22
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* [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2022/sol1.c)
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* Problem 23
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* [Sol1](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2023/sol1.c)
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* [Sol2](https://github.com/TheAlgorithms/C/blob/master/project_euler/Problem%2023/sol2.c)
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## Searching
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* [Binary Search](https://github.com/TheAlgorithms/C/blob/master/searching/Binary_Search.c)
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116
project_euler/Problem 23/sol1.c
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116
project_euler/Problem 23/sol1.c
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#ifdef _OPENMP
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#include <omp.h>
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#endif
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unsigned long MAX_N = 28123;
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/**
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* Returns:
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* -1 if N is deficient
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* 1 if N is abundant
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* 0 if N is perfect
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**/
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char get_perfect_number(unsigned long N)
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{
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unsigned long sum = 1;
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char ret = 0;
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for (unsigned long i = 2; i * i <= N; i++)
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{
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if (N % i == 0)
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{
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sum += i;
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unsigned long tmp = N / i;
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if (tmp != i)
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sum += tmp;
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}
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}
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ret = sum == N ? 0 : (sum > N ? 1 : -1);
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// #ifdef DEBUG
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// printf("%5lu: %5lu : %d\n", N, sum, ret);
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// #endif
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return ret;
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}
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/**
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* Is the given number an abundant number (1) or not (0)
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**/
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unsigned long is_abundant(unsigned long N)
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{
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return get_perfect_number(N) == 1 ? 1 : 0;
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}
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/**
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* Find the next abundant number after N and not including N
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**/
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unsigned long get_next_abundant(unsigned long N)
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{
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unsigned long i;
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for (i = N + 1; !is_abundant(i); i++)
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;
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return i;
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}
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/**
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* check if a given number can be represented as a sum
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* of two abundant numbers.
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* 1 - if yes
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* 0 - if not
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**/
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char is_sum_of_abundant(unsigned long N)
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{
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/** optimized logic:
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* i + j = N where both i and j should be abundant
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* hence we can simply check for j = N - i as we loop through i
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**/
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for (unsigned long i = get_next_abundant(1); i <= (N >> 1); i = get_next_abundant(i))
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if (is_abundant(N - i))
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{
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#ifdef DEBUG
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printf("\t%4lu + %4lu = %4lu\n", i, N - i, N);
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#endif
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return 1;
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}
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return 0;
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}
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int main(int argc, char **argv)
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{
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unsigned long sum = 0;
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if (argc == 2)
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MAX_N = strtoul(argv[1], NULL, 10);
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#ifdef _OPENMP
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printf("Using OpenMP parallleization with %d threads\n", omp_get_max_threads());
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#else
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printf("Not using parallleization!\n");
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#endif
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clock_t dt = 0;
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#ifdef _OPENMP
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#pragma omp parallel for reduction(+ \
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: sum) schedule(runtime)
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#endif
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for (unsigned long i = 1; i <= MAX_N; i++)
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{
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clock_t start_time = clock();
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if (!is_sum_of_abundant(i))
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sum += i;
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clock_t end_time = clock();
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dt += end_time - start_time;
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printf("... %5lu: %8lu\r", i, sum);
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if (i % 100 == 0)
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fflush(stdout);
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}
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printf("Time taken: %.4g ms\n", 1e3 * dt / CLOCKS_PER_SEC);
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printf("Sum of numbers that cannot be represented as sum of two abundant numbers : %lu\n", sum);
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return 0;
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}
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180
project_euler/Problem 23/sol2.c
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180
project_euler/Problem 23/sol2.c
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#include <stdio.h>
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#include <stdlib.h>
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#include <time.h>
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#ifdef _OPENMP
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#include <omp.h>
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#endif
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/**
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* Optimization 1 - compute & store abundant numbers once
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* into a look-up array
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**/
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unsigned long MAX_N = 28123;
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/**
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* This is the global array to be used to store a flag to identify
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* if a particular number is abundant (1) or not (0).
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* Using a whole byte to store a binary info would be redundant.
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* We will use each byte to represent 8 numbers by relying on bits.
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* This saves memory required by 1/8
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**/
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char *abundant_flags = NULL;
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/**
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* Returns:
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* -1 if N is deficient
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* 1 if N is abundant
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* 0 if N is perfect
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**/
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char get_perfect_number(unsigned long N)
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{
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unsigned long sum = 1;
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char ret = 0;
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for (unsigned long i = 2; i * i <= N; i++)
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{
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if (N % i == 0)
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{
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sum += i;
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unsigned long tmp = N / i;
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if (tmp != i)
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sum += tmp;
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}
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}
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ret = sum == N ? 0 : (sum > N ? 1 : -1);
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#ifdef DEBUG
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printf("%5lu: %5lu : %d\n", N, sum, ret);
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#endif
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return ret;
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}
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/**
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* Is the given number an abundant number (1) or not (0)
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**/
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char is_abundant(unsigned long N)
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{
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// return abundant_flags[N >> 3] & (1 << N % 8) ? 1 : 0;
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return abundant_flags[N >> 3] & (1 << (N & 7)) ? 1 : 0; /* optimized modulo operation */
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}
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/**
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* Find the next abundant number after N and not including N
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**/
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unsigned long get_next_abundant(unsigned long N)
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{
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unsigned long i;
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/* keep checking successive numbers till an abundant number is found */
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for (i = N + 1; !is_abundant(i); ++i)
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;
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return i;
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}
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/**
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* check if a given number can be represented as a sum
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* of two abundant numbers.
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* 1 - if yes
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* 0 - if not
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**/
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char is_sum_of_abundant(unsigned long N)
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{
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/** optimized logic:
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* i + j = N where both i and j should be abundant
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* hence we can simply check for j = N - i as we loop through i
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**/
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for (unsigned long i = get_next_abundant(1); i <= (N >> 1); i = get_next_abundant(i))
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if (is_abundant(N - i))
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{
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#ifdef DEBUG
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printf("\t%4lu + %4lu = %4lu\n", i, N - i, N);
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#endif
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return 1;
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}
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return 0;
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}
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int main(int argc, char **argv)
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{
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unsigned long sum = 0;
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if (argc == 2)
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MAX_N = strtoul(argv[1], NULL, 10);
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/** byte array to store flags to identify abundant numbers
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* the flags are identified by bits
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**/
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abundant_flags = (char *)calloc(MAX_N >> 3, 1);
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if (!abundant_flags)
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{
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perror("Unable to allocate memoey!");
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return -1;
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}
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#ifdef _OPENMP
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printf("Using OpenMP parallleization with %d threads\n", omp_get_max_threads());
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#else
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printf("Not using parallleization!\n");
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#endif
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clock_t start_time = clock();
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/* Loop to set abundant flags */
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#ifdef _OPENMP
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#pragma omp for schedule(runtime)
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#endif
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for (unsigned long N = 1; N <= MAX_N; N++)
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{
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char ret = get_perfect_number(N);
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if (ret == 1)
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{
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// int byte_offset = N % 8, index = N >> 3;
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int byte_offset = N & 7, index = N >> 3;
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#ifdef _OPENMP
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#pragma omp critical
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#endif
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abundant_flags[index] |= ret << byte_offset;
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}
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// if (i % 100 == 0)
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// printf("... %5lu: %8lu\r", i, sum);
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}
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clock_t end_time = clock();
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double t1 = 1e3 * (end_time - start_time) / CLOCKS_PER_SEC;
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printf("Time taken to get abundant numbers: %.4g ms\n", t1);
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clock_t t2 = 0;
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#ifdef _OPENMP
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#pragma omp for schedule(runtime) private(start_time, end_time)
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#endif
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for (unsigned long i = 1; i < MAX_N; i++)
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{
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start_time = clock();
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if (!is_sum_of_abundant(i))
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#ifdef _OPENMP
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#pragma omp critical
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#endif
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sum += i;
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end_time = clock();
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#ifdef _OPENMP
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#pragma omp critical
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#endif
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t2 += end_time - start_time;
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printf("... %5lu: %8lu\r", i, sum);
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if (i % 100 == 0)
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fflush(stdout);
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}
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#ifdef DEBUG
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putchar('\n');
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#endif
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double t22 = 1e3 * t2 / CLOCKS_PER_SEC;
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printf("Time taken for final sum: %.4g ms\nTotal Time taken: %.4g ms\n", t22, t1 + t22);
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printf("Memory used: %lu bytes\n", MAX_N >> 3);
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printf("Sum of numbers that cannot be represented as sum of two abundant numbers : %lu\n", sum);
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free(abundant_flags);
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return 0;
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}
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