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english improved

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Meik Hellmund
2026-03-05 20:09:16 +01:00
parent c6609d15f5
commit 733fe8c290
21 changed files with 954 additions and 1042 deletions
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chapters/Erste_Bsp.qmd
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@@ -11,22 +11,22 @@ julia:
using InteractiveUtils
```
# A small Example Program
# A Small Example Program
## What Skills Are Needed for Programming?
- **Thinking in algorithms:**
What steps are required to solve the problem? What data must be stored, what data structures must be created? What cases can occur and must be recognized and handled?
- **Implementation of the algorithm into a program:**
- **Implementing the algorithm in a program:**
What data structures, constructs, functions... does the programming language provide?
- **Formal syntax:**
Humans understand 'broken English'; computers don't understand 'broken C++' or 'broken Julia'. The syntax must be mastered.
- **The "ecosystem" of the language:**
How do I run my code? How do the development environments work? What options does the compiler understand? How do I install additional libraries? How do I read error messages? Where can I get information?
- **The art of debugging:**
Programming beginners are often happy when they have eliminated all syntax errors and the program finally 'runs'. For more complex programs, the work only just begins, as testing and finding and fixing errors in the algorithm must now be done.
- **Sense of the efficiency and complexity of algorithms**
Programming beginners are often happy when they have eliminated all syntax errors and the program finally 'runs'. For more complex programs, the work only just begins, as testing, finding, and fixing errors in the algorithm must now be done.
- **Intuition for the efficiency and complexity of algorithms**
- **Specifics of computer arithmetic**, especially floating point numbers
These cannot all be mastered at once. Be patient with yourself and 'play' with the language.
@@ -81,7 +81,7 @@ for i in 1:999 # loop
s += i # add to accumulator
end # end test
end # end loop
println(" The answer is: $s") # output result
println("The answer is: $s") # output result
```
:::
@@ -118,21 +118,21 @@ How many starting numbers below ten million will arrive at 89?
:::
Programs can be developed [*top-down* and *bottom-up*](https://en.wikipedia.org/wiki/Top-down_and_bottom-up_design).
*Top-down* would probably mean here: "We start with a loop `for i = 1:9999999`." The other way leads over individually testable components and is often more effective. (And with a certain project size, one approaches the goal from both 'top' and 'bottom' simultaneously.)
*Top-down* would probably mean here: "We start with a loop `for i = 1:9999999`." The other approach works through individually testable components and is often more effective. (And with a certain project size, one approaches the goal from both 'top' and 'bottom' simultaneously.)
##### Function No. 1
It should be investigated how numbers behave under repeated calculation of the 'square digit sum' (sum of squares of digits). Therefore, one should write and test a function that calculates this 'square digit sum'.
We want to investigate how numbers behave under repeated calculation of the 'square digit sum' (sum of squares of digits). Therefore, write and test a function that calculates this 'square digit sum'.
:::{.callout-caution icon="false" collapse="true" .titlenormal}
## `q2sum(n)` calculates the sum of the squares of the digits of n in the decimal system:
## `q2sum(n)` calculates the sum of the squares of the digits of n in base 10:
```{julia}
#| output: false
function q2sum(n)
s = 0 # accumulator for the sum
while n > 9 # as long as still multi-digit...
while n > 9 # as long as n is still multi-digit...
q, r = divrem(n, 10) # calculate integer quotient and remainder of division by 10
s += r^2 # add squared digit to accumulator
n = q # continue with the number divided by 10
@@ -143,7 +143,7 @@ end
```
:::
... and let's test it now:
Let's test it now:
```{julia}
for i in [1, 7, 33, 111, 321, 1000, 73201]
j = q2sum(i)
@@ -160,10 +160,10 @@ for i in 1:14
println(n)
end
```
... and we have here hit one of the '89-cycles'.
... and we have now hit one of the '89-cycles'.
#### Function No. 2
##### Function No. 2
We need to test whether repeated application of the function `q2sum()` finally leads to **1** or ends in this **89**-cycle.
@@ -174,11 +174,11 @@ We need to test whether repeated application of the function `q2sum()` finally l
```{julia}
#| output: false
function q2test(n)
while n !=1 && n != 89 # as long as we have not reached 1 or 89....
while n !=1 && n != 89 # as long as we have not reached 1 or 89...
n = q2sum(n) # repeat
end
if n==1 return false end # not an 89-number
return true # 89-number found
if n == 1 return false end # not an 89 cycle
return true # 89 cycle found
end
```
@@ -188,7 +188,7 @@ end
```{julia}
c = 0 # once again an accumulator
for i = 1 : 10_000_000 - 1 # this is how you can separate thousands for better readability in Julia
for i = 1 : 10_000_000 - 1 # this is how you can separate thousands for better readability
if q2test(i) # q2test() returns a boolean, no further test needed
c += 1 # 'if x == true' is redundant, 'if x' is perfectly sufficient
end
@@ -201,7 +201,7 @@ Numbers for which the iterative square digit sum calculation ends at 1 are calle
Here is the complete program again:
:::{.callout-caution icon="false" collapse="true" .titlenormal}
## our solution to Project Euler No 92:
## Our solution to Project Euler No 92:
```{julia}
function q2sum(n)