Step by Step solution about How to resolve the algorithm Hofstadter-Conway $10,000 sequence step by step in the C programming language

The provided C code snippet appears to be a program that computes and prints statistical information about a specific mathematical sequence. Here's a detailed breakdown of what the code does:

1. Header Files:

   #include <stdio.h>
   #include <stdlib.h>

   These lines include standard C library header files for input/output operations and dynamic memory allocation.

2. Global Array:

   int a_list[1<<20 + 1];

   A global integer array a_list is declared with a size of 2^20 + 1 elements. It will be used to store values of the mathematical sequence.

3. Function doSqnc:

   int doSqnc(int m)
   {
      ...
   }

   This is the main function that computes and prints the statistical information about the sequence. It takes an integer m as an input parameter, which specifies the length of the sequence to be processed.

4. Initializing Variables:

   int max_df = 0;
   int p2_max = 2;
   int v, n;
   int k1 = 2;
   int lg2 = 1;
   double amax = 0;

   • max_df: This integer variable is used to keep track of the maximum difference between consecutive powers of 2 in the sequence.
   • p2_max: This integer variable is used to store the current power of 2 being compared.
   • v: This integer variable is used to store the current value in the sequence being processed.
   • n: This integer variable represents the current position in the sequence being processed.
   • k1: This integer variable is used to track when n reaches a power of 2.
   • lg2: This integer variable represents the current power of 2 being considered.
   • amax: This double-precision floating-point variable stores the maximum average value of the sequence within a power of 2 range.

5. Initializing the Sequence:

   a_list[0] = -50000;
   a_list[1] = a_list[2] = 1;
   v = a_list[2];

   • The a_list array is initialized with some initial values. These values appear to be arbitrary and are used to start the sequence.

6. Main Sequence Calculation Loop:

   for (n = 3; n <= m; n++) {
      ...
   }

   This loop iterates from position 3 to m in the sequence, calculating the next value in the sequence and storing it in a_list. The sequence appears to be defined recursively as a_n = a_(n - a_(n - 1)) + a_(n - a_(n - 2)).

7. Calculating Maximum Average and Maximum Difference:

   Within the loop, the code calculates amax, which represents the maximum average value of the sequence within the current power of 2 range.

   It also calculates max_df, which tracks the maximum difference between consecutive powers of 2 in the sequence.

8. Printing Results:

   if (0 == (k1 & n)) {
      printf("Maximum between 2^%d and 2^%d was %f\n", lg2, lg2 + 1, amax);
      amax = 0;
      lg2++;
   }

   When n reaches a power of 2, the code prints the maximum average value for the range [2^(lg2), 2^(lg2 + 1)) and resets amax to 0.

9. Function Return:

   Finally, the function doSqnc returns 1 to indicate successful completion.

In summary, this C code calculates and prints statistical information about a specific mathematical sequence, including the maximum average value within a power of 2 range and the maximum difference between consecutive powers of 2 in the sequence. The sequence itself is defined recursively and is initialized with some arbitrary values. The length of the sequence to be processed is specified by the m parameter.

#include <stdio.h>
#include <stdlib.h>

int a_list[1<<20 + 1];

int doSqnc( int m)
{
    int max_df = 0;
    int p2_max = 2;
    int v, n;
    int k1 = 2;
    int lg2 = 1;
    double amax = 0;
    a_list[0] = -50000;
    a_list[1] = a_list[2] = 1;
    v = a_list[2];

    for (n=3; n <= m;  n++) {
        v = a_list[n] = a_list[v] + a_list[n-v];
        if ( amax < v*1.0/n) amax = v*1.0/n;
        if ( 0 == (k1&n)) {
            printf("Maximum between 2^%d and 2^%d was %f\n", lg2,lg2+1, amax);
            amax = 0;
            lg2++;
        }
        k1 = n;
    }
    return 1;
}