I've been trying to solve the SPOJ problem of Prime number Generator Algorithm.
Here is the question
Peter wants to generate some prime numbers for his cryptosystem. Help
him! Your task is to generate all prime numbers between two given
numbers!
Input
The input begins with the number t of test cases in a single line
(t<=10). In each of the next t lines there are two numbers m and n (1
<= m <= n <= 1000000000, n-m<=100000) separated by a space.
Output
For every test case print all prime numbers p such that m <= p <= n,
one number per line, test cases separated by an empty line.
It is very easy, but the online judge is showing error, I didn't get what the problem meant by 'test cases' and why that 1000000 range is necessary to use.
Here is my code.
#include<stdio.h>
main()
{
int i, num1, num2, j;
int div = 0;
scanf("%d %d", &num1, &num2);
for(i=num1; i<=num2; i++)
{
for(j=1; j<=i; j++)
{
if(i%j == 0)
{
div++;
}
}
if(div == 2)
{
printf("%d\n", i);
}
div = 0;
}
return 0;
}
I can't comment on the alogirthm and whether the 100000 number range allows optimisations but the reason that your code is invalid is because it doesn't seem to be parsing the input properly. The input will be something like:
2
123123123 123173123
987654321 987653321
That is the first line will give the number of sets of input you will get with each line then being a set of inputs. Your program, at a glance, looks like it is just reading the first line looking for two numbers.
I assume the online judge is just looking for the correct output (and possibly reasonable running time?) so if you correct for the right input it should work no matter what inefficiencies are in your algorithm (as others have started commenting on).
The input begins with the number t of test cases in a single line (t<=10)
you haven't got test cases in your programm.
Its wrong
And sorry for my English
2 - //the number of test cases
1 10 - // numbers n,m
3 5 - // numbers
Your programm will work only in first line.
#include <stdio.h>
#include <math.h>
int main()
{
int test;
scanf("%d",&test);
while(test--)
{
unsigned int low,high,i=0,j=2,k,x=0,y=0,z;
unsigned long int a[200000],b[200000];
scanf("%d",&low);
scanf("%d",&high);
for(i=low;i<=high;i++)
a[x++]=i;
for(i=2;i<=32000;i++)
b[y++]=i;
i=0;
while(b[i]*b[i]<=high)
{
if(b[i]!=0)
{
k=i;
for(;k<y;k+=j)
{
if(k!=i)
{
b[k]=0;
}
}
}
i+=1;j+=1;
}
for(i=0;i<y;i++)
{
if(b[i]!=0 && (b[i]>=low && b[i]<=sqrt(high)))
printf("%d\n",b[i]);
}
int c=0;
for(i=0;i<y;i++)
{
if(b[i]!=0 && (b[i]>=1 && b[i]<=sqrt(high)))
b[c++]=b[i];
}
int m=a[0];
for(i=0;i<c;i++)
{
z=(m/b[i])*b[i];k=z-m;
if(k!=0)
k += b[i];
for(;k<x;)
{
if(a[k]!=0)
{
a[k]=0;
}
k+=b[i];
}
}
for(i=0;i<x;i++)
{
if(a[i]!=0 && (a[i]>=2 && a[i]<=(high)))
printf("%d\n",a[i]);
}
printf("\n");
}
return 0;
}
To find primes between m,n where 1 <= m <= n <= 1000000000, n-m<=100000, you need first to prepare the core primes from 2 to sqrt(1000000000) < 32000. Simple contiguous sieve of Eratosthenes is more than adequate for this. (Having sieved the core bool sieve[] array (a related C code is here), do make a separate array int core_primes[] containing the core primes, condensed from the sieve array, in an easy to use form, since you have more than one offset segment to sieve by them.)
Then, for each given separate segment, just sieve it using the prepared core primes. 100,000 is short enough, and without evens it's only 50,000 odds. You can use one pre-allocated array and adjust the addressing scheme for each new pair m,n. The i-th entry in the array will represent the number o + 2i where o is an odd start of a given segment.
See also:
Is a Recursive-Iterative Method Better than a Purely Iterative Method to find out if a number is prime?
Find n primes after a given prime number, without using any function that checks for primality
offset sieve of Eratoshenes
A word about terminology: this is not a "segmented sieve". That refers to the sieving of successive segments, one after another, updating the core primes list as we go. Here the top limit is known in advance and its square root is very small.
The same core primes are used to sieve each separate offset segment, so this may be better described as an "offset" sieve of Eratosthenes. For each segment being sieved, only the core primes not greater than its top limit's square root need be used of course; but the core primes are not updated while each such offset segment is sieved (updating the core primes is the signature feature of the "segmented" sieve).
For such small numbers you can simply search for all primes between 1 and 1000000000.
Take 62.5 mByte of RAM to create a binary array (one bit for each odd number, because we already know that no even number (except of 2) is a prime).
Set all bits to 0 to indicate that they are primes, than use a Sieve of Eratosthenes to set bits to 1 of all number that are not primes.
Do the sieve once, store the resulting list of numbers.
int num;
bool singleArray[100000];
static unsigned long allArray[1000000];
unsigned long nums[10][2];
unsigned long s;
long n1, n2;
int count = 0;
long intermediate;
scanf("%d", &num);
for(int i = 0; i < num; ++i)
{
scanf("%lu", &n1);
scanf("%lu", &n2);
nums[i][0] = n1;
nums[i][1] = n2;
}
for(int i = 0; i < 100000; ++i)
{
singleArray[i] = true;
}
for(int i = 0; i < num; ++i)
{
s = sqrt(nums[i][1]);
for(unsigned long k = 2; k <= s; ++k)
{
for (unsigned long j = nums[i][0]; j <= nums[i][1]; ++j)
{
intermediate = j - nums[i][0];
if(!singleArray[intermediate])
{
continue;
}
if((j % k == 0 && k != j) || (j == 1))
{
singleArray[intermediate] = false;
}
}
}
for(unsigned long m = nums[i][0]; m <= nums[i][1]; ++m)
{
intermediate = m - nums[i][0];
if(singleArray[intermediate])
{
allArray[count++] = m;
}
}
for(int p = 0; p < (nums[i][1] - nums[i][0]); ++p)
{
singleArray[p] = true;
}
}
for(int n = 0; n < count; ++n)
{
printf("%lu\n", allArray[n]);
}
}
Your upper bound is 10^9. The Sieve of Eratosthenes is O(N loglogN) which is too much for that bound.
Here are a few ideas:
Faster primality tests
The problem with a naive solution where you loop over the range [i, j] and check whether each number is prime is that it takes O(sqrt(N)) to test whether a number is prime which is too much if you deal with several cases.
However, you could try a smarter primality testing algorithm. Miller-Rabin is polynomial in the number of bits of N, and for N <= 10^9, you only need to check a = 2, 7 and 61.
Note that I haven't actually tried this, so I can't guarantee it would work.
Segmented sieve
As #KaustavRay mentioned, you could use a segmented sieve. The underlying idea is that if a number N is composite, then it has a prime divisor that is at most sqrt(N).
We use the Sieve of Eratosthenes algorithm to find the prime numbers below 32,000 (roughly sqrt(10^9)), and then for each number in the range [i, j] check whether there is any prime below 32,000 that divides it.
By the prime number theorem about one in log(N) numbers are prime which is small enough to squeeze in the time limit.
#include <iostream>
using namespace std;
int main() {
// your code here
unsigned long int m,n,i,j;int N;
cin>>N;
for(;N>0;N--)
{
cin>>m>>n;
if(m<3)
switch (n)
{
case 1: cout<<endl;continue;
case 2: cout<<2<<endl;
continue;
default:cout<<2<<endl;m=3;
}
if(m%2==0) m++;
for(i=m;i<=n;i+=2)
{
for(j=3;j<=i/j;j+=2)
if(i%j==0)
{j=0;break;}
if(j)
cout<<i<<endl;
}
cout<<endl;
}return 0;}
Related
I have to print numbers between two limits n and m, t times.
I created t variable, and two pointers n, m that points to reserved blocks of memory for t integer values.
I use pointers instead of array to do faster operations.
Outer for loop iterates for every test cases and increasing m and n pointers.
Inner for loop prints primes from m[i] to n[i].
Code
#include <stdio.h>
#include <stdlib.h>
int is_prime(int);
int main(void) {
int t;
int *n = malloc(sizeof(int) * t);
int *m = malloc(sizeof(int) * t);
scanf("%d", &t);
for (int i = 0; i < t; i++, m++, n++) {
scanf("%d %d", &m[i], &n[i]);
for (int j = m[i]; j <= n[i]; j++) {
if (is_prime(j)) {
printf("%d\n", j);
}
}
if (i < t - 1) printf("\n");
}
return 0;
}
int is_prime(int num)
{
if (num <= 1) return 0;
if (num % 2 == 0 && num > 2) return 0;
for(int i = 3; i < num / 2; i+= 2){
if (num % i == 0)
return 0;
}
return 1;
}
Problem: http://www.spoj.com/problems/PRIME1/
Code is correctly compiling on http://ideone.com but I'm giving "time limit exceeded" error when I'm trying submit this code on SPOJ. How can I reduce execution time of this prime number generator?
As #Carcigenicate suggests, you're exceeding the time limit because your prime generator is too slow; and it's too slow since you're using an inefficient algorithm.
Indeed, you should not simply test each consecutive number for primality (which, by the way, you're also doing ineffectively), but rather rule out multiple values at once using known primes (and perhaps additional primes which you compute). For example, you don't need to check multiples of 5 and 10 (other than the actual value 5) for primality, since you know that 5 divides them. So just "mark" the multiples of various primes as irrelevant.
... and of course, that's just for getting you started, there are all sort of tricks you could use for optimization - algorithmic and implementation-related.
I know that you are looking for algorithm improvements, but the following technical optimizations might help:
If you are using Visual Studio, you can use alloca instead of malloc, so that n and m go in the stack instead of the heap.
You can also try to rewrite your algorithm using arrays instead of pointers to put n and m in the stack.
If you want to keep using pointers, use the __restrict keyword after the asterisks, which alerts the compiler that you don't make references of the two pointers.
You can even do it without using pointers or arrays
#include <stdio.h>
#include<math.h>
int is_prime(long n){
if (n == 1 || n % 2 == 0)
return 0;
if (n == 2)
return 1;
for (long i = 3; i <= sqrt(n); i += 2) {
if(n % i == 0)
return 0;
}
return 1;
}
int main() {
int t;
scanf("%d",&t);
while(t--) {
long n, m;
scanf("%ld %ld",&n,&m);
for (long i = n; i <= m; i++) {
if (is_prime(i) == 1)
printf("%ld\n",i);
}
}
return 0;
}
There are several ways to improve the primality check for an integer n. Here are a few that you might find useful.
Reduce the number of checks: A well known theorem is giving the fact that if you want to look for factors of n, let say n = a * b, then you can look for a divisor between 1 and sqrt(n). (Proof is quite easy, the main argument being that we have three cases, either a = b = sqrt(n), or we have a < sqrt(n) < b or b < sqrt(n) < a. And, whatever case we fall in, there will be a factor of n between 1 and sqrt(n)).
Use a Sieve of Eratosthenes: This way allows to discard unnecessary candidates which are previously disqualified (see Sieve of Eratosthenes (Wikipedia))
Use probabilistic algorithms: The most efficient way to check for primality nowadays is to use a probabilistic test. It is a bit more complex to implements but it is way more efficient. You can find a few of these techniques here (Wikipedia).
I am trying to generate a list of all the prime numbers for the first 1000 numbers.
I am not sure where I am going wrong in my code. From what I can tell, my nested for loop is not reading dividing/reading the array correctly and then assigning that array the proper value. How can I fix it?
The program currently only generates all the odd numbers.
int main() {
int x = 1;
int arr[500];
int i, j, k;
int counter;
int primearray[500];
for (j = 0; j <= 500; j++) {
x += 2;
arr[j] = x;
for (k = 1; k <= 15; k++) {
counter = x % k;
if (counter == 0) {
primearray[j] = x;
} else {
break;
}
}
for (i = 0; i < 500; i++) {
printf("%d ", primearray[i]);
}
}
Please invest time in learning how to indent your code. Choose a style that suits you and use it consistently: this will make your programs easier to read, and in turn easier to understand.
As I'm writing this, your posted code doesn't even compile because a closing curly brace } is missing: such editing mistakes are made possible by misleading indentation. Also note that in a properly written C program you must remember to #include any standard headers that are used:
#include <stdio.h> // for `printf()`
Rather than try to fix your algorithm, which at first glance doesn't make any sense to me anyway, I will try to help you restructure your program.
Keep main() simple
Given that the goal of your program is checking which of the first 1000 natural numbers are prime, the main() function should do no more than loop through those numbers and print the ones which are prime, like this:
for (int n=0; n < 1000; ++n)
if (is_prime(n))
printf("%d\n", n);
Putting them in an array instead of printing is equally easy:
int prime_array[500]; // array of primes
int k=0; // current index in array of primes
for (int n=0; n < 1000; ++n)
if (is_prime(n))
prime_array[k++] = n;
Break up the program in several functions
In accordance to the previous idea, write short and simple functions that do one thing, and do it well. In your case, you should write the is_prime() function to determine if a number is prime or not. You can start from here:
///
/// #brief Checks if a number is prime.
/// #param [in] n Number to be checked
/// #returns Whether `n` is prime or not.
/// #retval 1 If `n` is prime.
/// #retval 0 If `n` is not prime.
///
int is_prime(int n)
{
// TODO: add code here
}
Decide how to check for primality
There is a Primality test article on Wikipedia that you should read.
First, you must correctly handle these special cases:
0 is not prime
1 is not prime
2 is prime
// TODO: also check 1 and 2 in a similar fashion
if (n == 0)
return 0;
After this is done, you can use a naive and inefficient algorithm that checks the other numbers:
// try divisors from 2 to n-1
for (int d=2; d < n; ++d)
if (n % d == 0) // if the division was even,
return 0; // the number is not prime
return 1; // if we get here, the number is prime
If you want to use a faster (but more complicated) algorithm for checking primes, look back at the Wikipedia article linked above. Notice how you'd only have to change the code inside is_prime() and the rest of the program would work the same, unchanged.
As I understood from your code, arr is an array of possible candidates and primearray is an array of approved ones. No every candidate will be approved one so you need different variables for indexing them.
The second issue is the algorithm for approving candidates. From this part of your code (I changed some indents)
for (k = 1; k <= 15; k++) {
counter = x%k;
if (counter == 0) {
primearray[j] = x;
} else {
break;
}
follows that you approve a candidate if it is divisible by all integers from 1 to 15 - I am sorry but prime numbers have not this property.
I think you could refer to this code which will generate all prime numbers up to the number that you specify. I think this will be more optimised.
void main()
{
int n, i, j, temp=0;
printf("Enter a number \n");
scanf("%d", &n);
printf(" Prime numbers -\n");
for(i=2; i<n+1; i++)
{
temp = 0;
for(j=2; j<i; j++)
{
if(i%j == 0)
{
temp = 1;
break;
}
}
if(temp == 0)
{
printf("%d \n", i);
}
}
getch();
}
Is there any simple way to make this small program faster? I've made it for an assignment, and it's correct but too slow. The aim of the program is to print the nth pair of primes where the difference between the two is two, given n.
#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
bool isPrime(int number) {
for (int i = 3; i <= number/2; i += 2) {
if (!(number%i)) {
return 0;
}
}
return 1;
}
int findNumber(int n) {
int prevPrime, currentNumber = 3;
for (int i = 0; i < n; i++) {
do {
prevPrime = currentNumber;
do {
currentNumber+=2;
} while (!isPrime(currentNumber));
} while (!(currentNumber - 2 == prevPrime));
}
return currentNumber;
}
int main(int argc, char *argv[]) {
int numberin, numberout;
scanf ("%d", &numberin);
numberout = findNumber(numberin);
printf("%d %d\n", numberout - 2, numberout);
return 0;
}
I considered using some kind of array or list that would contain all primes found up until the current number and divide each number by this list instead of all numbers, but we haven't really covered these different data structures yet so I feel I should be able to solve this problem without. I'm just starting with C, but I have some experience in Python and Java.
To find pairs of primes which differ by 2, you only need to find one prime and then add 2 and test if it is also prime.
if (isPrime(x) && isPrime(x+2)) { /* found pair */ }
To find primes the best algorithm is the Sieve of Eratosthenes. You need to build a lookup table up to (N) where N is the maximum number that you can get. You can use the Sieve to get in O(1) if a number is prime. While building the Sieve you can build a list of sorted primes.
If your N is big you can also profit from the fact that a number P is prime iif it doesn't have any prime factors <= SQRT(P) (because if it has a factor > SQRT(N) then it should also have one < SQRT(N)). You can build a Sieve of Eratosthenes with size SQRT(N) to get a list of primes and then test if any of those prime divides P. If none divides P, P is prime.
With this approach you can test numbers up to 1 billion or so relatively fast and with little memory.
Here is an improvement to speed up the loop in isPrime:
bool isPrime(int number) {
for (int i = 3; i * i <= number; i += 2) { // Changed the loop condition
if (!(number%i)) {
return 0;
}
}
return 1;
}
You are calling isPrime more often than necessary. You wrote
currentNummber = 3;
/* ... */
do {
currentNumber+=2;
} while (!isPrime(currentNumber));
...which means that isPrime is called for every odd number. However, when you identified that e.g. 5 is prime, you can already tell that 10, 15, 20 etc. are not going to be prime, so you don't need to test them.
This approach of 'crossing-out' multiples of primes is done when using a sieve filter, see e.g. Sieve of Eratosthenes algorithm in C for an implementation of a sieve filter for primes in C.
Avoid testing ever 3rd candidate
Pairs of primes a, a+2 may only be found a = 6*n + 5. (except pair 3,5).
Why?
a + 0 = 6*n + 5 Maybe a prime
a + 2 = 6*n + 7 Maybe a prime
a + 4 = 6*n + 9 Not a prime when more than 3 as 6*n + 9 is a multiple of 3
So rather than test ever other integer with + 2, test with
a = 5;
loop {
if (isPrime(a) && isPrime(a+2)) PairCount++;
a += 6;
}
Improve loop exit test
Many processors/compilers, when calculating the remainder, will also have available, for nearly "free" CPU time cost, the quotient. YMMV. Use the quotient rather than i <= number/2 or i*i <= number to limit the test loop.
Use of sqrt() has a number of problems: range of double vs. int, exactness, conversion to/from integer. Recommend avoid sqrt() for this task.
Use unsigned for additional range.
bool isPrime(unsigned x) {
// With OP's selective use, the following line is not needed.
// Yet needed for a general purpose `isPrime()`
if (x%2 == 0) return x == 2;
if (x <= 3) return x == 3;
unsigned p = 1;
unsigned quotient, remainder;
do {
p += 2;
remainder = x%p;
if (remainder == 0) return false;
quotient = x/p; // quotient for "free"
} while (p < quotient); // Low cost compare
return true;
}
Well, there are lots of such questions available in SO as well as other forums. However, none of these helped.
I wrote a program in "C" to find number of primes within a range. The range i in long int. I am using Sieve of Eratosthenes" algorithm. I am using an array of long ints to store all the numbers from 1 till the limit. I could not think of a better approach to achieve without using an array. The code works fine, till 10000000. But after that, it runs out of memory and exits. Below is my code.
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
typedef unsigned long uint_32;
int main() {
uint_32 i, N, *list, cross=0, j=4, k, primes_cnt = 0;
clock_t start, end;
double exec_time;
system("cls");
printf("Enter N\n");
scanf("%lu", &N);
list = (uint_32 *) malloc( (N+1) * sizeof(uint_32));
start = clock();
for(i=0; i<=N+1; i++) {
list[i] = i;
}
for(i=0; cross<=N/2; i++) {
if(i == 0)
cross = 2;
else if(i == 1)
cross = 3;
else {
for(j=cross+1; j<=N; j++) {
if(list[j] != 0){
cross = list[j];
break;
}
}
}
for(k=cross*2; k<=N; k+=cross) {
if(k <= N)
list[k] = 0;
}
}
for(i=2; i<=N; i++) {
if(list[i] == 0)
continue;
else
primes_cnt++;
}
printf("%lu", primes_cnt);
end = clock();
exec_time = (double) (end-start);
printf("\n%f", exec_time);
return 0;
}
I am stuck and can't think of a better way to achieve this. Any help will be hugely appreciated. Thanks.
Edit:
My aim is to generate and print all prime numbers below the range. As printing consumed a lot of time, I thought of getting the first step right.
There are other algorithm that does not require you to generate prime number up to N to count number of prime below N. The easiest algorithm to implement is Legendre Prime Counting. The algorithm requires you to generate only sqrt(N) prime to determine the number of prime below N.
The idea behind the algorithm is that
pi(n) = phi(n, sqrt(n)) + pi(sqrt(n)) - 1
where
pi(n) = number of prime below N
phi(n, m) = number of number below N that is not divisible by any prime below m.
That's mean phi(n, sqrt(n)) = number of prime between sqrt(n) to n. For how to calculate the phi, you can go to the following link (Feasible implementation of a Prime Counting Function)
The reason why it is more efficient is because it is easiest to compute phi(n, m) than to compute pi(n). Let say that I want to compute phi(100, 3) means that how many number below or equal to 100 that does not divisible by 2 and 3. You can do as following. phi(100, 3) = 100 - 100/2 - 100/3 + 100/6.
Your code uses about 32 times as much memory as it needs. Note that since you initialized list[i] = i the assignment cross = list[j] can be replaced with cross = j, making it possible to replace list with a bit vector.
However, this is not enough to bring the range to 264, because your implementation would require 261 bytes (2 exbibytes) of memory, so you need to optimize some more.
The next thing to notice is that you do not need to go up to N/2 when "crossing" the numbers: √N is sufficient (you should be able to prove this by thinking about the result of dividing a composite number by its divisors above √N). This brings memory requirements within your reach, because your "crossing" primes would fit in about 4 GB of memory.
Once you have an array of crossing primes, you can build a partial sieve for any range without keeping in memory all ranges that precede it. This is called the Segmented sieve. You can find details on it, along with a simple implementation, on the page of primesieve generator. Another advantage of this approach is that you can parallelize it, bringing the time down even further.
You can tweak the algorithm a bit to calculate the prime numbers in chunks.
Load a part of the array (as much as fits the memory), and in addition hold a list of all known prime numbers.
Whenever you load a chunk, first go through the already known prime numbers, and similar to the regular sieve, set all non primes as such.
Then, go over the array again, mark whatever you can, and add to the list the new prime numbers found.
When done, you'll have a list containing all your prime numbers.
I could see that the approach you are using is the basic implementation of Eratosthenes, that first stick out all the 2's multiple and then 3's multiple and so on.
But I have a better solution to the question. Actually, there is question on spoj PRINT. Please go through it and do check the constraints it follows. Below is my code snippet for this problem:
#include<stdio.h>
#include<math.h>
#include<cstdlib>
int num[46500] = {0},prime[5000],prime_index = -1;
int main() {
/* First, calculate the prime up-to the sqrt(N) (preferably greater than, but near to
sqrt(N) */
prime[++prime_index] = 2; int i,j,k;
for(i=3; i<216; i += 2) {
if(num[i] == 0) {
prime[++prime_index] = i;
for(j = i*i, k = 2*i; j<=46500; j += k) {
num[j] = 1;
}
}
}
for(; i<=46500; i+= 2) {
if(num[i] == 0) {
prime[++prime_index] = i;
}
}
int t; // Stands for number of test cases
scanf("%i",&t);
while(t--) {
bool arr[1000005] = {0}; int m,n,j,k;
scanf("%i%i",&m,&n);
if(m == 1)
m++;
if(m == 2 && m <= n) {
printf("2\n");
}
int sqt = sqrt(n) + 1;
for(i=0; i<=prime_index; i++) {
if(prime[i] > sqt) {
sqt = i;
break;
}
}
for(; m<=n && m <= prime[prime_index]; m++) {
if(m&1 && num[m] == 0) {
printf("%i\n",m);
}
}
if(m%2 == 0) {
m++;
}
for(i=1; i<=sqt; i++) {
j = (m%prime[i]) ? (m + prime[i] - m%prime[i]) : (m);
for(k=j; k<=n; k += prime[i]) {
arr[k-m] = 1;
}
}
for(i=0; i<=n-m; i += 2) {
if(!arr[i]) {
printf("%i\n",m+i);
}
}
printf("\n");
}
return 0;
}
I hope you got the point:
And, as you mentioned that your program is working fine up-to 10^7 but above it fails, it must be because you must be running out of the memory.
NOTE: I'm sharing my code only for knowledge purpose. Please, don't copy and paste it, until you get the point.
The assignment is :
Write a program that calculates the sum of the divisors of a number from input.
A number is considered perfect if the sum of it's divisiors equal the number (ex: 6 = 1+2+3 ;28 = 1 + 2 + 4 + 7 +14).
Another definition:
a perfect number is a number that is half the sum of all of its positive divisors (including itself)
Generate the first k perfect numbers (k<150).
The main problem with this is that it's confusing the two asking points don't really relate.
In this program i calculated the sum of divisors of an entered number, but i don't know how to relate it with the second point (Generate the first k perfect numbers (k<150)).
#include <stdio.h>
#include <stdlib.h>
main()
{
int x,i,y,div,suma,k;
printf("Introduceti numarul\n"); \\enter the number
scanf("%d",&x);
suma=0; \\sum is 0
for(i=1;i<=x;i++)
{
if(x%i==0)
suma=suma+i; \\sum=sum+i;
}
printf("Suma divizorilor naturali este: %d\n",suma); \\the sum of the divisors is
for(k=1;k<150;k++) \\ bad part
{
if (x==suma)
printf("%d",k);
}
}
Suppose you have a function which can tell whether a given integer is perfect or not:
int isPerfect(int);
(function body not shown)
Now your main program will look like:
int candidate;
int perfectNumbers;
for(candidate = 1, perfectNumbers = 0; perfectNumbers < 150; candidate++) {
if (isPerfect(candidate)) {
printf("Number %d is perfect\n", candidate);
perfectNumbers++;
}
}
EDIT
For the same program without functions:
int candidate;
int perfectNumbers;
for(candidate = 1, perfectNumbers = 0; perfectNumbers < 150; candidate++) {
[... here your algorithm to compute the sum of the divisors of "candidate" ...]
if (candidate*2 == sum_of_divisors) {
printf("Number %d is perfect\n", candidate);
perfectNumbers++;
}
}
EDIT2: Just a note on perfect numbers
As noted in the comments section below, perfect numbers are very rare, only 48th of them are known as of 2014. The sequence (A000396) also grows very fast: using 64-bit integers you'll be able to compute up to the 8th perfect number (which happen to be 2,305,843,008,139,952,128). In this case the variable candidate will wrap around and start "finding" "new" perfect numbers from the beginning (until 150 of them are found: actually 19 repetitions of the only 8 findable in 64-bit integers). Note though that your algorithm must not choke on a candidate equals to 0 or to negative numbers (only to 0 if you declare candidate as unsigned int).
I am interpreting the question to mean generate all numbers under 150 that could are perfect numbers.
Therefore, if your program works for calculating perfect numbers, you keep calculating them until the starting number is >= 150.
Hope that makes sense.
Well, here's my solution ..
First, you have to make a reliable way of getting divisors.Here's a function I made for that:
size_t
getdivisors(num, divisors)
long long num;
long long *divisors;
{
size_t divs = 0;
for(long long i = num; i > 0; --i)
if (num%i == 0)
divisors[divs++] = i;
return divs;
}
Second, you need to check if the number's divisors match the perfect number's divisors properties (the sum of them is half the number).
Here's a second function for that:
bool
isperfect(num)
long long num;
{
long long divisors[num/2+1];
size_t divs = getdivisors(num, divisors);
if (divs == 0)
return false;
long long n = 0;
for(int i = 1; i < divs; ++i)
n += divisors[i];
return (n == num);
}
Now, from your question, I think you need to print all perfect numbers less than 150, right ?
See this:
int
main(argc, argv)
int argc;
char ** argv;
{
for(int i = 1; i < 150; ++i)
if (isperfect(i))
printf("%d is perfect.\n", i);
return 0;
}
I hope that answers your question ..