From the fifth chapter of Stephen Prata’s book “C Primer Plus” – a program based on a well-known proverb that illustrates exponential growth.
Background:
The king offered to choose a reward for the hero’s service; the hero asked to put one grain on the first cell on the chessboard, two grains on the second, four on the third, and to double the grains in this way until the board is full. The king was struck by modesty and agreed .. What came of it:
My first version of the program ran into a 32 cell int limit:
#include <stdio.h>
int main (void)
{
const int chess_board = 64;
int square = 1;
double grains = 1.0, grains_sum = 1.0;
const float grain_world_tons = 7.0e7; // yield of wheat in Russia per year in tons
const float grain_mass = 6.5e-8; // how much tons in one grain
float rus_yield = grain_world_tons / grain_mass;
float propotion_of_rus_yield = 1.0 / rus_yield;
printf("Russian yield of wheat (in number or grains): %.1e.\n\nNow lets take a look at chess board:\n",rus_yield);
printf("Square # | Grains | Total grains | Part from Russian yield \n");
while (square<65)
{
printf("%d %.2e %.2e %.2e\n",square, grains, grains_sum,propotion_of_rus_yield);
grains = grains * 2;
square = square + 1;
grains_sum = grains_sum + grains;
propotion_of_rus_yield = grains_sum/rus_yield;
}
getchar();
return 0;
}
Let’s make the output in exponential form and reassign the type of the variable from int to double. Also compare this with the wheat harvest in Russia:
#include <stdio.h>
int main (void)
{
const int chess_board = 64;
int square = 1;
double grains = 1, grains_sum = 1;
const float grain_world_tons = 7.0e7; // yield of wheat in Russia per year in tons
const float grain_mass = 6.5e-8; // how much tons in one grain
float rus_yield = grain_world_tons / grain_mass;
float propotion_of_rus_yield = 1 / rus_yield;
printf("Russian yield of wheat (in number or grains): %.1e.\n\nNow lets take a look at chess board:\n",rus_yield);
printf("Square # | Grains | Total grains | Part from Russian yield \n");
while (square<65)
{
printf("%d %.2e %.2e %.2e\n",square, grains, grains_sum,propotion_of_rus_yield);
grains = grains * 2;
square = square + 1;
grains_sum = grains_sum + grains;
propotion_of_rus_yield = grains_sum/rus_yield;
}
getchar();
return 0;
}
The program came out not the same as in the listing of the book, I had to cram the conversion of tons into grains there, because. I was interested in the numbers of our harvest 🙂 Well, we need to get used to using constants in #define, so that everything is easier to read, variables here and so dofiga. Also, the program had a jamb with the fact that it has to be compared in the cycle not with the constant 64, but with the number 65, otherwise the first grain on the first cell will not be in the cycle; this is solved by printing the first grain on a separate line, like this:
#include <stdio.h>
#define CHESS_BOARD 64
int main (void)
{
int square = 1;
double grains = 1.0, grains_sum = 1.0;
const float grain_world_tons = 7.0e7; // yield of wheat in Russia per year in tons
const float grain_mass = 6.5e-8; // how much tons in one grain
float rus_yield = grain_world_tons / grain_mass;
float propotion_of_rus_yield = 1.0 / rus_yield;
printf("Russian yield of wheat (in number or grains): %.1e.\n\nNow lets take a look at chess board:\n",rus_yield);
printf("Square # | Grains | Total grains | Part from Russian yield \n");
printf("%d %.2e %.2e %.2e\n",square, grains, grains_sum,propotion_of_rus_yield); // printing first grain
while (square<CHESS_BOARD)
{
square = square + 1;
grains = grains * 2;
grains_sum = grains_sum + grains;
propotion_of_rus_yield = grains_sum/rus_yield;
printf("%d %.2e %.2e %.2e\n",square, grains, grains_sum,propotion_of_rus_yield);
}
getchar();
return 0;
}
As a result, we will get:
Russian yield of wheat (in number or grains): 1.1e+15. Now lets take a look at chess board: Square # | Grains | Total grains | Part from Russian yield 1 1.00e+00 1.00e+00 9.29e-16 2 2.00e+00 3.00e+00 2.79e-15 3 4.00e+00 7.00e+00 6.50e-15 4 8.00e+00 1.50e+01 1.39e-14 5 1.60e+01 3.10e+01 2.88e-14 6 3.20e+01 6.30e+01 5.85e-14 7 6.40e+01 1.27e+02 1.18e-13 8 1.28e+02 2.55e+02 2.37e-13 9 2.56e+02 5.11e+02 4.74e-13 10 5.12e+02 1.02e+03 9.50e-13 11 1.02e+03 2.05e+03 1.90e-12 12 2.05e+03 4.10e+03 3.80e-12 13 4.10e+03 8.19e+03 7.61e-12 14 8.19e+03 1.64e+04 1.52e-11 15 1.64e+04 3.28e+04 3.04e-11 16 3.28e+04 6.55e+04 6.09e-11 17 6.55e+04 1.31e+05 1.22e-10 18 1.31e+05 2.62e+05 2.43e-10 19 2.62e+05 5.24e+05 4.87e-10 20 5.24e+05 1.05e+06 9.74e-10 21 1.05e+06 2.10e+06 1.95e-09 22 2.10e+06 4.19e+06 3.89e-09 23 4.19e+06 8.39e+06 7.79e-09 24 8.39e+06 1.68e+07 1.56e-08 25 1.68e+07 3.36e+07 3.12e-08 26 3.36e+07 6.71e+07 6.23e-08 27 6.71e+07 1.34e+08 1.25e-07 28 1.34e+08 2.68e+08 2.49e-07 29 2.68e+08 5.37e+08 4.99e-07 30 5.37e+08 1.07e+09 9.97e-07 31 1.07e+09 2.15e+09 1.99e-06 32 2.15e+09 4.29e+09 3.99e-06 33 4.29e+09 8.59e+09 7.98e-06 34 8.59e+09 1.72e+10 1.60e-05 35 1.72e+10 3.44e+10 3.19e-05 36 3.44e+10 6.87e+10 6.38e-05 37 6.87e+10 1.37e+11 1.28e-04 38 1.37e+11 2.75e+11 2.55e-04 39 2.75e+11 5.50e+11 5.10e-04 40 5.50e+11 1.10e+12 1.02e-03 41 1.10e+12 2.20e+12 2.04e-03 42 2.20e+12 4.40e+12 4.08e-03 43 4.40e+12 8.80e+12 8.17e-03 44 8.80e+12 1.76e+13 1.63e-02 45 1.76e+13 3.52e+13 3.27e-02 46 3.52e+13 7.04e+13 6.53e-02 47 7.04e+13 1.41e+14 1.31e-01 48 1.41e+14 2.81e+14 2.61e-01 49 2.81e+14 5.63e+14 5.23e-01 50 5.63e+14 1.13e+15 1.05e+00 51 1.13e+15 2.25e+15 2.09e+00 52 2.25e+15 4.50e+15 4.18e+00 53 4.50e+15 9.01e+15 8.36e+00 54 9.01e+15 1.80e+16 1.67e+01 55 1.80e+16 3.60e+16 3.35e+01 56 3.60e+16 7.21e+16 6.69e+01 57 7.21e+16 1.44e+17 1.34e+02 58 1.44e+17 2.88e+17 2.68e+02 59 2.88e+17 5.76e+17 5.35e+02 60 5.76e+17 1.15e+18 1.07e+03 61 1.15e+18 2.31e+18 2.14e+03 62 2.31e+18 4.61e+18 4.28e+03 63 4.61e+18 9.22e+18 8.56e+03 64 9.22e+18 1.84e+19 1.71e+04
In total, on the 50th cell, the number of grains on the board was equal to the annual wheat harvest in Russia 🙂
I will be glad to see your comments!