speed optimized solution + optional OpenMP

project_euler/Problem 21/sol1.c

@@ -0,0 +1,98 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#ifdef _OPENMP
+#include <omp.h>
+#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;
+}