常見Iterative式
- Factorial
- 最大公因數 GCD (Greatest Common Division)
- Fibonacci Number
- 1+2+3+…+n
- 1^2+2^2+3^2+…+n^2
- 1!+2!+3!+…+n!
- x^n
Iteration 疊代、跌代
定義：不斷利用目前求得的數值，再求得新數值，再用新數值繼續求得下一個新的值。
實作方式：使用迴圈(for、while、do-while)
| Development | Define | Goal |
|---|---|---|
| Incremental | staging and scheduling strategy | improve your process |
| Iterative | rework scheduling strategy | improve your product |
Iteration
1. Factorial
#include <stdio.h>
int main(void) {
int i;
int sum = 1, n;
for(i = 1; i <= n; i++){
sum *= i;
}
printf("%d", sum);
}
2. 最大公因數 GCD (Greatest Common Division)
#include <stdio.h>
int main(void) {
int k;
int a, b;
scanf("%d %d", &a, &b);
while(a % b != 0){
k = a % b;
a = b;
b = k;
}
printf("%d", b);
}
3. Fibonacci Number
#include <stdio.h>
int main(void) {
int i = 0, n;
int fib[n];
fib[0] = 0;
fib[1] = 1;
scanf("%d", &n);
for(i = 2; i <= n; i++){
fib[i] = fib[i -1] + fib[i - 2];
}
for(i = 2; i <= n; i++){
printf("%d\n", fib[i]);
}
}
4. 1+2+3+…+n
#include <stdio.h>
int main(void) {
int i, n;
int sum = 0;
scanf("%d", &n);
for(i = 1; i <= n; i++){
sum += i;
}
printf("%d", sum);
}
5. 1^2+2^2+3^2+…+n^2
#include <stdio.h>
int main(void)
{
int i, sum=0;
int n;
scanf("%d", &n);
if(n <= 0) return 0;
for(i = 0; i <= n; i++){
sum += i * i;
}
printf("%d", sum);
return 0;
}
6. 1!+2!+3!+…+n!
#include <stdio.h>
int main(void) {
int i = 0, n;
int sum = 1, total = 0;
scanf("%d", &n);
for(i = 1; i <= n; i++){
sum *= i;
total += sum;
}
printf("%d", total);
}
7. x^n
#include <stdio.h>
/* Iteration : x ^ n */
int main(void) {
int x;
int i; // counter
int n; // power
int sum = 1;
scanf("%d%d", &x, &n);
for(i = 1; i <= n; i++){
sum *= x;
}
printf("%d^%d is %d", x, n, sum);
return 0;
}