an optimized solution - O(n) complexity

project_euler/Problem 08/sol2.c

@@ -0,0 +1,117 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>     /* for memmove */
+
+int main(int argc, char* argv[])
+{
+    int position = 0, num_bad_chars = 0;
+    int num_digits = 4;
+    char ch;
+    uint8_t num, num_prev;
+    uint8_t *buffer = NULL;
+    int64_t prod = 1, max_prod = 0;
+
+    /* if second command-line argument is given,
+     * use it as the number of digits to compute 
+     * successive product for
+     */
+    if (argc == 2)
+        num_digits = atoi(argv[1]);
+   
+    /* allocate memory to store past values */
+    buffer = calloc(num_digits, sizeof(uint8_t));
+    if(!buffer)
+    {
+        perror("Unable to allocate memory for buffer");
+        return -1;
+    }
+
+    /* open file to read digits from */
+    FILE *fp = fopen("digits.txt", "rt");
+    if (!fp)
+    {
+        perror("Unable to open file");
+        free(buffer);   /* free allocated memory */
+        return -1;
+    }
+
+    /* loop through all digits in the file */
+    do 
+    {
+        /* get character from file */
+        ch = getc(fp);
+
+        /* the ASCII codes of digits is between 0x30 and 0x39. 
+         * any character not in this range implies an invalid character
+         */
+        if (ch < 0x30 || ch > 0x39)
+        {
+            num_bad_chars ++;   /* this is used to get the bad characters in the sequence of 13 characters */
+            continue;
+        } else if (num_bad_chars > 0)
+            num_bad_chars --;
+        
+        num = ch - 0x30;         /* convert character digit to number */
+        num_prev = buffer[0];    /* previous n^th digit */
+
+        /* left shift the buffer -
+         *  using a for loop or a faster memory move
+         */
+        memmove(buffer, buffer+1, num_digits-1);
+        /*
+        for (int i = 1; i < num_digits; i++)
+            buffer[i-1] = buffer[i];
+        */
+
+        buffer[num_digits-1] = num; /* save the latest number in buffer */
+
+        if (num_prev != 0)
+        {
+            /* since product is accumulated, the new product can be obtained by simply 
+             * multiplying the new digit and dividing with the oldest digit
+             */
+            prod /= num_prev;   /* divide first to avoid over-flows */
+            prod *= num;
+        }
+        else
+        {
+            prod = 1;
+            for(int i = 0; i < num_digits; i++)
+            {
+                if(buffer[i] == 0)
+                {
+                    prod = 0;
+                    break;      /* break innermost for-loop */
+                }
+                prod *= buffer[i];
+            }
+        }
+
+        /* check if a new maxima was found */
+        if (prod > max_prod)
+        {
+            max_prod = prod;
+            position = ftell(fp) - num_bad_chars - num_digits - 1;
+        }
+    } while(!feof(fp));      /* loop till end of file is reached */
+    
+    printf("Maximum product: %lld\t Location: %d^th position\n\t", max_prod, position);
+    fseek(fp, position, SEEK_SET);  /* move cursor to identified position in file */
+    /* loop through all digits */
+    for (; num_digits > 0; num_digits--)
+    {
+        char ch = getc(fp);     /* get character */
+        /* skip invalid character */
+        if (ch < 0x30 || ch > 0x39)
+            continue;
+        if (num_digits > 1)
+            printf("%c x ", ch);
+        else
+            printf("%c = %lld\n", ch, max_prod);
+    }
+
+    fclose(fp);     /* close file */
+    free(buffer);   /* free allocated memory */
+
+    return 0;
+}