Loop(while, for, do...while)
===
Intro
---
**Loop** is a tool for special purpose, it allows program operating similar instructions repeatly. ex. Counting, Array Traversal, List some information
And in general, we have 3 kinds of loop: **while loop**, **for loop** and **do...while**
```c=
// Counting
// it will print from 0~(n-1)
for(int i=0;i<n;i++){
printf("%d ", i);
}
```
"while" Loop
---
**while** loop is most basic loop, and it usually which contains 3 parts:
1. **Shell**
2. **Checking Statement**
3. **Instructions**.
```c=
while(2.Check){ // 1.Shell
...
...
Instrunction
Instrunction // 3.Instructions
Instrunction
...
...
} //1.Shell
```
And **while loop** works by 3 steps
1. Check the statement
-> if **true**, continue next step
-> if **false**, break the while loop
2. Do instructions
3. Go back step 1
### Practice:
#### Collatz conjecture:
There is a number **n**, and the rule is:
if n is **even**, divide it by 2
if n is **odd**, time it by 3 and plus 1
n finally go back to 1
So, there is a example.
Input a number **n**,
and please ouput the outcomes of **n** at every step and the step(s) where **n** will go back to **1** according to the rule of **Collatz conjecture**.
ex.
input:
10
ouput:
5 16 8 4 2 1
6
```c=
#include<stdio.h>
int main(){
int n, count = 0;
scanf("%d", &n);
while(/*Statement*/){
if(/*Statement*/) n /= 2;
else n = (3 * n + 1);
printf("%d ", n);
count++;
}
printf("\n");
printf("%d\n", count);
}
```
:::success
Hint:
**while loop** is usually used for **UNKNOWN** steps operations.
:::
"for" Loop
---
**for loop** is a kind of loop based on the **while loop**, in other words, **for loop** can also be implemented by **while loop**.
**for loop** contains 5 parts:
1. Shell
2. Initial Declaration
3. Checking Statement
4. Instructions
5. Operation after Intrucitons
```c=
for(2.Init;3.Check;4.Oper){ // 1.Shell
...
...
Instrunction
Instrunction // 5.Instructions
Instrunction
...
...
} // 1.Shell
```
And **for loop** works by 3 steps
1. Initial Declaration
2. Check the statement
-> if **true**, continue next step
-> if **false**, break the while loop
3. Do instructions
4. Do operation
5. go back step 2
:::success
Hint:
**for loop** is used more often than other 2 types of loop, because its convenience for **iterations**, **traversal** and so on.
We usually use letter 'i' to be the iteration variable in the for loop, meaning "Iterations", and it became a kind of common sense...
So, something you will see very common in **programs** or **projects** is like:
```c=
for(int i=0;i<n;i++){
...blablabla
}
```
:::
### Practice
There is a program,
1. Please trace the following code step by step.
2. Please implement same function by using **while loop**
3. Analyze what will happen if we remove "i+=2"
```c=
#include<stdio.h>
int main(){
int x = 100;
for(int i=0;i<10;i+=2, x-=10){
printf("x: %d\n", x);
}
return 0;
}
```
"do...while" Loop
---
**do...while** is a kind of variation of **while**, and it is used least among 3 types of **loop**, the only difference between them is that **do...while** checking the statement after instructions.
Therefore, Instructions in **do...while** will be executed at least once, however, those in **while** may not.
ps. You can test by yourself if you are curious.
ex.
```c=
// Using do...while
int i = 0;
do {
System.out.println("This will be printed at least once");
i++;
} while (i < 3);
// Using while
int j = 0;
while (j < 3) {
System.out.println("This may not be printed if the condition is false initially");
j++;
}
```
Excercise
---
ZeroJudge:
1. [因數分解](https://zerojudge.tw/ShowProblem?problemid=a010)
3. [數字翻轉](https://zerojudge.tw/ShowProblem?problemid=a038)
4. [阿姆斯壯數](https://zerojudge.tw/ShowProblem?problemid=a040)
5. [迴文](https://zerojudge.tw/ShowProblem?problemid=a022) // 需要Array
Multi-Level Loop
---
We can do something advanced bu using **multi-level loop**.
### 1. Multiplication Table:
Generate a multiplication table using nested loops. Allow the user to input the number up to which they want the table.
Example:
```
Enter the number for the multiplication table: 5
1 2 3 4 5
2 4 6 8 10
3 6 9 12 15
4 8 12 16 20
5 10 15 20 25
```
### 2. Print a Triangle Pattern:
Write a program to print a triangle pattern using nested loops.
Example:
```
Enter the height of the triangle: 5
*
**
***
****
*****
```
### 3. Matrix Transposition:
Write a program to transpose a given matrix. The user inputs the number of rows and columns, and then the matrix elements.
Example:
```
Enter the number of rows: 3
Enter the number of columns: 2
Enter matrix elements:
1 2
3 4
5 6
Transposed Matrix:
1 2 3
4 5 6
```
Ans
---
```c=
//因數分解
#include<stdio.h>
#include<stdbool.h>
int main(){
int n, remaining;
bool first;
scanf("%d", &n);
first = true;
remaining = n;
for(int i=2;i<=n;i++){
int count = 0;
while(remaining % i == 0){
remaining /= i;
count++;
}
if(count){
if(first){
first = false;
}else{
printf(" * ");
}
printf("%d", i);
if(count >= 2)
printf("^%d", count);
}
}
printf("\n");
return 0;
}
```
```c=
// Multiplication Table
#include<stdio.h>
int main(){
int n;
scanf("%d", &n);
int maxN = n*n;
int digits = 0;
int tempN = maxN;
while(tempN / 10 != 0){
tempN /= 10;
digits++;
}
int space = digits + 1;
for(int i=0;i<n;i++){
int start = i+1;
for(int j = 0;j<n;j++){
int num = start*(j+1);
int digits = 0;
int tempN = num;
while(tempN / 10 != 0){
tempN /= 10;
digits++;
}
printf("%d", num);
for(int k = 0;k<space-digits;k+=1){
printf(" ");
}
}
printf("\n");
}
return 0;
}
// at most t digits
// t + 1 space for 1 number
```
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