Do not understand why my loop doesnt go frther than 2 - c

I'm trying to write a program (c) that the input is integer between 2 to 20.
and the output will be all the irreducible fractions between 0 to 1, that their denominator<=(input number).
for example:
input num=7
the output will be:
For denominator 2
1/2
For denominator 3
1/3
2/3
For denominator 4
1/4
3/4
For denominator 5
1/5
2/5
3/5
4/5
For denominator 6
1/6
5/6
For denominator 7
1/7
2/7
3/7
4/7
5/7
6/7
my problem is that the the counter i of the first loop doesnt go farther than 2, and the printf line in the j loop doesn't happen
Cant's understant what im doing wrong.
Thanks for helping.
int main()
{
int num, i, k, j, a, b;
printf("Please enter natural denominator < 20\n");
scanf("%d", &num);
for (i = 2; i < num ; i++) { /* loop for denomiator */
printf("For denominator %d\n", i);
for (k = 1; k < i; k++) { /* loop for numerator */
for (j = k; j > 0; j--) {
a = k % j;
b = i % j;
if (a == 0 && b == 0) {
printf("%d/%d", k, i); /* this line doesn't print for any input */
}
}
}
}
return 0;
}

In addition to the problemyou are describing (for which starrify has given a solution) there is also a flaw in your logic.
Instead of skipping entries that can be simplified, you are printing them more than once.
The problem can be solved by modifying your innermost loop like this:
int canBeSimplified = 0;
for (j = k; j > 1; j--) {
a = k % j;
b = i % j;
if (a == 0 && b == 0) {
canBeSimlified = 1;
}
}
if (!canBeSimplified) {
printf("%d/%d\n", k, i);
}

I guess you shall have your standard library function prototypes introduced by including the header:
#include <stdio.h>
The problem, as I guess, is that you're using a 64-bit system (that's important since on such platforms sizeof(int)!=sizeof(void*)), and as you didn't include the prototypes for function scanf and printf, all its parameters (and also return values) are treated as of type int.
On my laptop with the header included there's no problem with your code. If you have any further problems or simply including the header doesn't solve your problem, please let me know, better with some method for me to reproduce your problem.
Also, I guess you may want to have a new line at your output by changing this line:
printf("%d/%d", k, i);
into this:
printf("%d/%d\n", k, i);

First - fix (i = 2; i < num ; i++) to (i = 2; i <= num ; i++), or your program won't process last number.
Second - "%d/%d\n" instead of "%d/%d" to write numbers on separate lines.
Third, I fixed previous two and now have:
Please enter natural denominator < 20
3
For denominator 2
1/2
For denominator 3
1/3
2/3
Press any key to continue...
And yes, if you had some changes in your code after it was built and tested, you have to build it again before running. Check that.

Related

Prime Number between given interval

Given below is the code for finding prime numbers between the interval entered by the user.
#include <stdio.h>
int main() {
int n1, n2, i, flag;
scanf("%d%d", &n1, &n2);
for (i = n1; i <= n2; i++) {
flag = prime(i);
if (flag == 1)
printf("\n%d", i);
}
return 0;
}
int prime(int n) {
int j, flag = 1;
for (j = 2; j <= n / 2; j++) {
if (n % j == 0) {
flag = 0;
break;
}
}
return flag;
}
Can anyone explain me how this code deals with odd number, which are not prime (for ex: 15, 21, 25, etc)
int prime(int n) {
int j, flag = 1;
for (j = 2; j <= n / 2; j++) {
if (n % j == 0) {
flag = 0;
break;
}
}
return flag;
}
See in this prime function, when we observe the iteration of for loop if value of n is 15 then it will look like this:
for (j = 2; j <= 15 / 2; j++)
I agree this is true. Because 2<7.
Since the condition is true we will enter inside the for loop:
if(n%j==0){
flag=0;
break;
}
Now, since n=15 and j=2, value of n%j=1, which is obviously not equals to 0; so if loop will not be executed and the prime function will return flag =1; and the main function will print 15 as a prime.
But, after Executing the program the code is showing the correct results: it's not showing 15 as a prime.
So can anyone please help me understand the logic behind this code? (Actually I want to understand how this code is eliminating non-prime odd numbers.)
You checked the execution for j==2, but since there is a for loop for(j=2;j<=n/2;j++). The code will run from j=2 to j=n/2. So, if you consider all the iterations, you will realize that the function is working fine.
The first if statement is false, so for j==2, the program won't go inside the if statement.
The loop will iterate for the next value of j, which is 3. Since 15%3 == 0, the program will execute the statements within the if statement and return that 15 is not a prime number.
for(j=2;j<=n/2;j++){
if(n%j==0){
flag=0;
break;
}
}
In the case of n=15, the loop starts at i=2, the test i<=n/2 is true because 2<=7, then 15%2 is 1, hence the loop proceeds and i is incremented to 3, the loop test is true again because 3<=7 but 15%3 is 0 so flag is set to 0 and returned.
Note these remarks:
the code does not have a recursive function. You merely call a function prime() to check each number in the interval for primality.
prime() should be defined or at least declared before the main() function that calls it.
you can test the return value of prime(i) directly. No need for a flag variable.
for prime numbers, the loop will iterate way too far: you can change the test to j <= n / j to stop at the square root of n.
you can return directly from the loop body.
you should output the newline after the number.
Here is a modified version:
#include <stdio.h>
int isprime(int n) {
int j;
for (j = 2; j <= n / j; j++) {
if (n % j == 0)
return 0;
}
return 1;
}
int main() {
int n1, n2, i;
if (scanf("%d%d", &n1, &n2) != 2)
return 1;
for (i = n1; i <= n2; i++) {
if (isprime(i))
printf("%d\n", i);
}
return 0;
}
Can anyone explain me how this code deals with odd number, which are not prime (for ex: 15, 21, 25, etc)
int prime(int n) {
int j, flag = 1;
for (j = 2; j <= n / 2; j++) {
if (n % j == 0) {
flag = 0;
break;
}
}
return flag;
}
Well this function doesn't need to handle specially nonprime numbers, based on the fact that if we can divide the number n by something (be prime or not), the number will be compose. What it does it to get out of the loop (with flag changed into 0) as soon as it finds a number j that divides n.
There's an extra optimization, that can save you a lot of time, that consists on calculating numbers until the integer rounded down square root of n as, if you can divide the number by a number that is greater than the square root, for sure there will be a number that is less than the square root that also divides n (the result of dividing the original number by the first will give you a number that is lower than the square root) so you only need to go up until the square root. While calculating the square root can be tedious (there's a library function, but let's go on), it is only done once, so it is a good point to use it. Also, you can initialy try dividing the number by two, and then skip all the even numbers, by adding 2 to j, instead of incrementing.
#include <math.h>
/* ... */
int prime(unsigned n) {
/* check for special cases */
if (n >= 1 && n <= 3) return TRUE; /* all these numbers are prime */
if (n % 2 == 0) return FALSE; /* all these numbers are not */
/* calculate (only once) the rounded down integer square root */
int j, square_root = isqrt(n); /* see below */
for (j = 3; j <= square_root; j += 2) { /* go two by two */
if (n % j == 0)
return FALSE;
}
/* if we reach here, all tests failed, so the number must be prime */
return TRUE;
}
While there's a sqrt() function in <math.h>, I recommend you to write an integer version of the square root routine (you can devise it easily) so you don't need to calculate it in full precision (just to integer precision).
/* the idea of this algorithm is that we have two numbers between 1 and n,
* the greater being the arithmetic mean between the previous two, while
* the lower is the result of dividing the original n by the arithmetic mean.
* it is sure than if we select the arithmetic mean, the number will be
* between the previous ones, and if I divide n by a number that is lower,
* the quotient will be higher than the original number. By the way, the
* arithmetic mean is always bigger than the square root, so the quotient
* will be smaller. At each step, both numbers are closer to each other, and
* so, the smaller is closer to the result of dividing n by itself (and this
* is the square root!)
*/
unsigned isqrt(unsigned n)
{
unsigned geom = 1, arith = n;
while (geom < arith) {
arith = (geom + arith) / 2;
geom = n / arith;
}
/* return the smaller of the two */
return arith;
}
so, your program would be:
#include <stdio.h>
#define FALSE (0)
#define TRUE (!FALSE)
unsigned isqrt(unsigned n)
{
unsigned geom = 1, arith = n;
while (geom < arith) {
arith = (geom + arith) / 2;
geom = n / arith;
}
return arith;
}
int prime(unsigned n) {
/* check for special cases */
if (n >= 1 && n <= 3) return TRUE;
if (n % 2 == 0) return FALSE;
/* calculate (only once) the rounded down integer square root */
int j, square_root = isqrt(n);
for (j = 3; j <= square_root; j += 2) {
if (n % j == 0) {
return FALSE;
}
}
return TRUE;
}
int main() {
unsigned n1, n2, i;
scanf("%u%u", &n1, &n2);
for (i = n1; i <= n2; i++) {
if (prime(i))
printf("%u\n", i);
}
return 0;
}
If you try your version against this one, with values like 2000000000 and 2000000100 you will see how this is saving a lot of calculations (indeed, for the cases below, the case of considering only the odd numbers when going throug the loop will take out of it half the numbers ---this is 1000000000 tests---, but the square root will reduce the number of tests to its square root ---only around 40000 tests--- for each number!!!).
$ primes
2000000000 2000000100
2000000011
2000000033
2000000063
2000000087
2000000089
2000000099
$ _
Your version takes (on my system) this execution time:
$ echo 2000000000 2000100000 | time primes0 >/dev/null
3.09user 0.00system 0:03.09elapsed 99%CPU (0avgtext+0avgdata 1468maxresident)k
0inputs+0outputs (0major+69minor)pagefaults 0swaps
$ _
while the version proposed takes:
$ echo 2000000000 2000100000 | time primes >/dev/null
0.78user 0.00system 0:00.78elapsed 99%CPU (0avgtext+0avgdata 1572maxresident)k
0inputs+0outputs (0major+72minor)pagefaults 0swaps
$ _

the largest palindrome made from the product of two 3-digit numbers. using c .whats wrong in my code?

Program not working, not giving output, I don't know what to do, where the problem is.
I'm trying to find out the largest palindrome made from the product of two 3-digit numbers.
#include <stdio.h>
main() {
int i, k, j, x;
long int a[1000000], palindrome[1000000], great, sum = 0;
// for multiples of two 3 digit numbers
for (k = 0, i = 100; i < 1000; i++) {
for (j = 100; j < 1000; j++) {
a[k] = i * j; // multiples output
k++;
}
}
for (i = 0, x = 0; i < 1000000; i++) {
// for reverse considered as sum
for (; a[i] != 0;) {
sum = sum * 10 + a[i] % 10;
}
// for numbers which are palindromes
if (sum == a[i]) {
palindrome[x] = a[i];
x++;
break;
}
}
// comparison of palindrome number for which one is greatest
great = palindrome[0];
for (k = 0; k < 1000000; k++) {
if (great < palindrome[k]) {
great = palindrome[k];
}
}
printf("\ngreatest palindrome of 3 digit multiple is : ", great);
}
What do you mean with "not working"?
There are two things, from my point of view:
1) long int a[1000000], palindrome[1000000]
Depending on you compile configuration you could have problems compiling your code.
Probably the array is too big to fit in your program's stack address space.
In C or C++ local objects are usually allocated on the stack. Don't allocate it local on stack, use some other place instead. This can be achieved by either making the object global or allocating it on the global heap.
#include <stdio.h>
long int a[1000000], palindrome[1000000], great, sum = 0;
main() {
int i, k, j, x;
2) printf("\ngreatest palindrome of 3 digit multiple is : ", great);
I will change it by :
printf("\ngreatest palindrome of 3 digit multiple is %li: ", great);
Regards.
Compiling and running your code on an on-line compiler I got this:
prog.c:3:1: warning: type specifier missing, defaults to 'int' [-Wimplicit-int]
main() {
^
prog.c:34:61: warning: data argument not used by format string [-Wformat-extra-args]
printf("\ngreatest palindrome of 3 digit multiple is : ", great);
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ^
2 warnings generated.
Killed
Both the warnings should be taken into account, but I'd like to point out the last line. The program was taking too much time to run, so the process was killed.
It's a strong suggestion to change the algorithm, or at least to fix the part that checks if a number is a palindrome:
for (; a[i] != 0;) { // <-- If a[i] is not 0, this will never end
sum = sum * 10 + a[i] % 10;
}
I'd use a function like this one
bool is_palindrome(long x)
{
long rev = 0;
for (long i = x; i; i /= 10)
{
rev *= 10;
rev += i % 10;
}
return x == rev;
}
Also, we don't need any array, we could just calculate all the possible products between two 3-digits number using two nested for loops and check if those are palindromes.
Starting from the highest numbers, we can store the product, but only if it's a palindrome and is bigger than any previously one found, and stop the iteration of the inner loop as soon as the candidate become less then the stored maximum. This would save us a lot of iterations.
Implementing this algorithm, I found out a maximum value of 906609.

Why does this prime number algorithm work?

#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
int main() {
int anz;
scanf("%d", &anz);
time_t start = time(0);
int *primZ = malloc(anz * sizeof(int));
primZ[0] = 2;
int Num = 0;
for (int i = 1, num = 3; i < anz; num += 2) {
for (int j = 1; j < i; j++) {
if (num % primZ[j] == 0) {
num += 2;
j = 0;
}
//this part
if (primZ[j] > i / 2)
break;
}
primZ[i] = num;
i++;
printf("%d ,",num);
}
time_t delta = time(0) - start;
printf("%d", delta);
getchar();
getchar();
return 0;
}
The code works perfectly fine, the question is why. The part if(primZ[j] > i/2) makes the program 2 - 3 times faster. It was actually meant to be if(primZ[j] > num/3) which makes perfect sense because num can only be an odd number. But it is the number of found prime numbers. It makes no sense to me. Please explain.
You check if the prime is composite by checking if it divisible by already found prime numbers. But in doing so you only have to check up to and including the square root of the number because any number larger than that that divides the number will leave a smaller number than the square root of the number.
For example 33 is composite, but you only have to check numbers up to 5 to realize that, you don't need to check it being divisible by 11 because it leaves 3 (33/11=3) which we already checked.
This means that you could improve your algorithm by
for (int j = 1; j < i; j++) {
if( primZ[j]*primZ[j] > num )
break;
if (num % primZ[j] == 0) {
num += 2;
j = 0;
}
}
The reason you can get away with comparing with cutting of at i/2 is due to the distribution of the prime numbers. The prime counting function is approximately i = num/log(num) and then you get that i/2 > sqrt(num).
The reason is that the actual bound is much tighter than num/3 - you could use:
if (primZ[j] > sqrt(num))
The reason for that being that if a prime higher than the square root of num divides num, there must also be a lower prime that does (since the result of such a division must be lower than the square root).
This means that as long as i/2 is higher than sqrt(num), the code will work. What happens is that the number of primes lower than a number grows faster than the square root of that number, meaning that (completely accidentally) i/2 is a safe bound to use.
You can check out how your i value behaves here - they call it pi(x), the number of primes less than x.
It makes sense, since if n has two factors one of them is surely less than or equal to n/2, sense the program found no factors of i in primZ that are less than or equal to i/2 it means there's no factors of i -except 1 of course-.
Sense primZ is sorted in ascending order and j only increases, when primeZ[j] > i/2 it indicates that there's no factors of i in primZ that are less than i/2.
P.S.The point of starting the search is stated in the first part of the for statement num=3 , and the recurring statement num += 2 ensures you only test odd numbers

How to use exponents using a for loop

I am working on a functions HW for my programming class and Im trying to write a function that will allow me to do exponent math (in a simple form). (Oh and I can't use the actual exponent function, I have to write my own function using for loops, if statements or other things like that.)
EX: user enters base and then enters the power to raise it by. So the user enters:
5
3
it should be 5 to the 3rd power, so it should output 125 (5x5x5). However my for loop is not working properly. How should I structure my for loop to properly handle exponent math?
code:
int main(){
int base, pow;
scanf("%d", &base);
scanf("%d", &pow);
int i;
for (i=0; i<=pow; i++) {
i *= base;
printf("%d\n", i);
}
printf("%d", i);
Well you're using the same variable for the loop and the result. You don't want to do that.
int j = 1;
for(i = 0; i < pow; i++)
{
j*= base;
}
Is what you want. You're also off by one on the loop count. With i <= pow you have
i=0, j * 5 = 5, i=1
i=1, j * 5 = 25,i=2
i=2, j * 5 = 125,i=3. This is where you want to stop but 3 <= 3 so it goes again.
i=3, j *5 = 625,i=4. 4 is not <= 3 so it will then stop here.
The loop is obviously wrong:
for (i=0; i<=pow; i++) {
i *= base;
printf("%d\n", i);
}
You are multiplying the loop counter by base for some reason, which will not yield any good.
The right one would be:
int result = 1;
for (i=0; i < pow; i++) {
result *= base;
}
You want an accumulator that starts at 1 and is multiplied by the base each time. This accumulator should also not be i (since this will change at each step of the for loop).
Try
int base, pow;
scanf("%d", &base);
scanf("%d", &pow);
int i, accumulator;
accumulator = 1
for (i=0; i<pow; i++) {
accumulator *= base;
printf("%d\n", accumulator);
}
printf("%d", accumulator);

Determine Prime Numbers using SINGLE do-while Loop

I wrote this program per my professor's instruction. Turns out he wanted us to use a SINGLE do-while loop. While I did technically do that... this won't fly. I can't figure out how to do it without using a for-loop or at least another loop of some other type. He said it could use continue or break statements--but that it might not be necessary.
I would appreciate not just re-writing my code--while this is handy, I don't learn from it well.
I appreciate any and all help.
int main() {
int max, x, n = 2; //init variables
//start n at 2 because 1 isn't prime ever
//asks user for max value
printf("Enter max number: ");
scanf("%i", &max);
/*prints prime numbers while the max value
is greater than the number being checked*/
do {
x = 0; //using x as a flag
for (int i = 2; i <= (n / 2); i++) {
if ((n % i) == 0) {
x = 1;
break;
}
}
if (x == 0) //if n is prime, print it!
printf("%i\n", n);
n++; //increase number to check for prime-ness
} while (n < max);
return 0;
}
This is definitely doable. The trick is to have a test variable, and each iteration through your while loop, check the test variable against your current number. Always start the test variable at 2 (every natural number > 0 is divisible by 1)
Cases to consider:
Our current number is divisible by the test variable -- number is NOT prime, increase the current number and reset the test variable.
Our test variable is greater than the square root of the current number. By definition, it CANNOT divide the current number, so the current number has to be prime (we have tried all numbers lower than the square root of the current number and none of them divide it). Increase the current number and reset the test variable.
Lastly, if either above case isn't true, we have to try the next number higher. Increment the test variable.
I have not provided the code as you asked to not have it re-written, but can provide if you would like.
EDIT
#include <stdio.h>
#include <math.h>
int main(void)
{
int max = 20;
int current = 4;
int checker = 2;
do{
if(checker > sqrt((double)current))
{
checker = 2;
printf("%d is prime\n",current);
current++;
}
else if(current % checker == 0)
{
checker = 2;
printf("%d is NOT prime\n",current);
current++;
}
else
checker++;
}while(current < max);
}
Output:
4 is NOT prime
5 is prime
6 is NOT prime
7 is prime
8 is NOT prime
9 is NOT prime
10 is NOT prime
11 is prime
12 is NOT prime
13 is prime
14 is NOT prime
15 is NOT prime
16 is NOT prime
17 is prime
18 is NOT prime
19 is prime
I won't give you the exact code, but two pointers that should help you:
First, a for loop can be written as a while loop (and, vice versa)
for (int i=0; i< 100; ++i)
...
would become:
int i=0;
while (i < 100)
{
...
++i;
}
Second, two nested loops can become a single one, in any number of ways:
for (int i=0; i< 100; ++i)
for (int j=0; j< 100; ++j)
...
Becomes
for (int z=0; z< 100*100; ++z)
{
i = z / 100;
j = z % 100;
}
The above shows two for loops, but you can perform similar transforms on other loops.
Think Eratosthenes sieve. In this method we strike composite numbers out of a table, so that in the end only primes remain. For simplicity, the table contains only odd numbers. You start pointing at 3, which is a prime. Strike out 3*3, 3*5... Finish your run over the table (it's finite), point at 5. It's not striked out, thus a prime. Strike out 15, 25... check 7, prime, strike 21, 35... check 9, already striked out, move on to 11...
Questions:
You have just checked a number, what is the next number to check?
How do you know you've ran out of numbers to check?
Write down answers to these questions, and you have a one-loop prime-finding algorithm.

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