Programs are very useful for the purpose of solving problems. Many
programmers know this potential of programs, and use it to their advantage.
However, all is not so straight-forward in the world of programming and
problem-solving; there are as many ways to go about finding a solution as there
are stars in the sky (perhaps more!).
All in all, the method by which you code a program for finding the solution
to a problem is up to the programmer -- you. That is why it is important to
learn some of the basic ways by which one can arrive at a solution. Only after
you understand these ways, can you move on to more complicated problem-solving.
Before we begin, please note that open and close brackets, i.e.
"[" and "]" respectively, will contain raw code.
Decrementing Function
The first method is the decrementing function. A decrementing function
starts with a non-negative value, which is decreased each time the program
repeats the function's loop. The function will loop so long as the starting
value is non-negative, but once it is equal to or less than 0, it will
terminate.
Example: Find the cubed root of a value, "x", using a decrementing
function.
[ ans * ans * ans = x ], where "ans" is the computer's guess
(which will eventually be the answer), is one way to go about finding
the cube root of a value, "x".
However, a more efficient method would be the decrementing function [
abs(x) - ans^3 ], where "abs(x)" is the absolute value of a value,
"x", and "ans^3" is the computer's guess, cubed.
Remember, a decrementing function terminates when the starting value is
equal to or less than 0; the only way this can happen for our example function
is if the computer's guess is the cubed root of the value "x".
Therefore, the program will terminate when the computer has guessed the correct
answer!
The next post, PY-04, will continue the current series of Solving Problems
in Python. Specifically, Part 2 will cover an even more convenient method of
finding a solution -- exhaustive enumeration!
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