I wrote this code in order to find the number of the divisors of a given number. The method I am trying to implement finds all of the prime factors (which works) and takes number of similar prime numbers plus one (which gives the number of divisors).
e.g. 28 = 2*2 * 7 --> (2+1)*(1+1) = 6
This is my attempt:
int num = 20;
int next = 0;
int exponent = 0;
int numberOfDivisors = 1;
start:
for (int i = 2; i <= num; i++)
{
next = i;
if (num%i == 0)
{
if (i == next)
{
exponent++;
}
else
{
numberOfDivisors *= (exponent+1);
exponent = 0;
}
if (num != i)
{
num /= i;
goto start;
}
}
}
std::cout << numberOfDivisors << std::endl;
I just cannot figure out what I am missing.
Using goto is bad as you can see from the comments. After a little bit of clean up your code comes down to:
#include <iostream>
int main() {
int num = 20;
int numberOfDivisors = 1;
for (int i = 2; i <= num; i++)
{
int exponent = 0;
while (num % i == 0) {
exponent++;
num /= i;
}
numberOfDivisors *= (exponent+1);
}
std::cout << numberOfDivisors << std::endl;
return 0;
}
The goto isn't helpful, actually, since you're already checked for lower prime factors there's no need to put i back to 2.
int numberOfDivisors = 1;
int exponent = 1;
int i = 2;
while (i <= num) {
if (num%i == 0) {
exponent++;
num /= i;
}
else {
numberOfDivisors *= exponent;
exponent = 1;
i++;
}
}
numberOfDivisors *= exponent; // <-- you were missing this, mainly
The actual problem with your code that wasn't style or performance related was that your loop finished with some exponent that you never included.
There are many issues with your code (and that goto interrupting the loop is just ugly), but one major problem with your code is that right after you enter the for loop, you set next to have the same value as i.
Then, you test something (namely, if i divides num evenly, but this doesn't matter) and (here is the critical part, you test if i is equal to next, which you just set them equal.
So, your code never has the opportunity to enter the else part of the corresponding if, which is where you would multiply the number of divisors by the exponent + 1.
As a result, your code always prints 1, which is not what you wanted.
P.S.: That else may be entirely optimized out by the compiler as part of dead-code elimination, and this is what my gcc 4.7 actually does if I enable optimization -O1 or higher.
Related
#include<iostream>
using namespace std;
int main(){
int i = 1;
int sum;
int N;
cout << "Enter a number N: ";
cin >> N;
while(i<=N)
{
if(i%2 == 0)
{
sum = sum + i;
}
else
{
i = i + 1;
}
}
cout << sum;
}
This is to print the sum of all even numbers till 1 to N.
As I try to run the code, I am being asked the value of N but nothing is being printed ahead.
For starters the variable sum is not initialized.
Secondly you need to increase the variable i also when it is an even number. So the loop should look at least like
while(i<=N)
{
if(i%2 == 0)
{
sum = sum + i;
}
i = i + 1;
}
In general it is always better to declare variables in minimum scopes where they are used.
So instead of the while loop it is better to use a for loop as for example
for ( int i = 1; i++ < N; ++i )
{
if ( i % 2 == 0 ) sum += i;
}
while(i<=N)
{
if(i%2 == 0)
{
sum = sum + i;
}
else
{
i = i + 1;
}
}
Let's step through this. Imagine we're on the loop where i = 2 and you've entered N = 5. In that case...
while(i <= N)
2 <= 5 is true, so we loop
if(i%2 == 0)
2 % 2 == 0 is true, so we enter this branch
sum = sum + i;
Update sum, then head back to the top of the loop
while(i <= N)
Neither i nor N have changed, so 2 <= 5 is still true. We still loop
if(i%2 == 0)
2 % 2 == 0 is still true, so we enter this branch again...
Do you see what's happening here? Since neither i nor N are updated, you'll continue entering the same branch and looping indefinitely. Can you think of a way to prevent this? What would need to change?
Also note that int sum; means that sum will have a garbage value (it's uninitialized). If you want it to start at 0, you'll need to change that to
int sum = 0;
You're looping infinitly when i is even because you don't increase it.
Better option would be this if you want to use that while loop :
while(i<=N)
{
if(i%2 == 0)
sum = sum + i;
i=i+1;
}
cout << sum;
If you don't need to do anything when the condition is false, just don't use an else.
No loops are necessary and sum can be evaluated at compile time if needed too
// use unsigned, the whole excercise is pointless for negative numbers
// use const parameter, is not intended to be changed
// constexpr is not needed, but allows for compile time evaluation (constexpr all the things)
// return type can be automatically deduced
constexpr auto sum_of_even_numbers_smaller_then(const unsigned int n)
{
unsigned int m = (n / 2);
return m * (m + 1);
}
int main()
{
// compile time checking of the function
static_assert(sum_of_even_numbers_smaller_then(0) == 0);
static_assert(sum_of_even_numbers_smaller_then(1) == 0);
static_assert(sum_of_even_numbers_smaller_then(2) == 2);
static_assert(sum_of_even_numbers_smaller_then(3) == 2);
static_assert(sum_of_even_numbers_smaller_then(7) == 12);
static_assert(sum_of_even_numbers_smaller_then(8) == 20);
return 0;
}
int main(){
int input; //stores the user entered number
int sum=0; //stroes the sum of all even numbers
repeat:
cout<<"Please enter any integer bigger than one: ";
cin>>input;
if(input<1) //this check the number to be bigger than one means must be positive integer.
goto repeat; // if the user enter the number less than one it is repeating the entry.
for(int i=input; i>0; i--){ // find all even number from your number till one and than totals it.
if(i%2==0){
sum=sum+i;
int j=0;
j=j+1;
cout<<"Number is: "<<i<<endl;
}
}
cout<<endl<<"The sum of all even numbers is: "<<sum<<endl;}
Copy this C++ code and run it, it will solve your problem.
There are 2 problems with your program.
Mistake 1
The variable sum has not been initialized. This means that it has(holds) an indeterminate value. And using this uninitialized variable like you did when you wrote sum = sum + i; is undefined behavior.
Undefined behavior means anything1 can happen including but not limited to the program giving your expected output. But never rely on the output of a program that has undefined behavior.
This is why it is advised that:
always initialize built in types in local/block scope.
Mistake 2
The second problem is that you're not updating the value of variable i.
Solution
You can solve these problems as shown below:
int main(){
int i = 1;
int sum = 0; //INITIALIZE variable sum to 0
int N;
cout << "Enter a number N: ";
cin >> N;
while(i<=N)
{
if(i%2 == 0)
{
sum = sum + i;
}
i = i + 1; //update(increase i)
}
cout << sum;
}
1For more reading(technical definition of) on undefined behavior you can refer to undefined behavior's documentation which mentions that: there are no restrictions on the behavior of the program.
So I was inspired by a recent Youtube video from the Numberphile Channel. This one to be exact. Cut to around the 5 minute mark for the exact question or example that I am referring to.
TLDR; A number is created with all the digits corresponding to 1 to N. Example: 1 to 10 is the number 12,345,678,910. Find out if this number is prime. According to the video, N has been checked up to 1,000,000.
From the code below, I have taken the liberty of starting this process at 1,000,000 and only going to 10,000,000. I'm hoping to increase this to a larger number later.
So my question or the assistance that I need is optimization for this problem. I'm sure each number will still take very long to check but even a minimal percentage of optimization would go a long way.
Edit 1: Optimize which division numbers are used. Ideally this divisionNumber would only be prime numbers.
Here is the code:
#include <iostream>
#include <chrono>
#include <ctime>
namespace
{
int myPow(int x, int p)
{
if (p == 0) return 1;
if (p == 1) return x;
if (p == 2) return x * x;
int tmp = myPow(x, p / 2);
if (p % 2 == 0) return tmp * tmp;
else return x * tmp * tmp;
}
int getNumDigits(unsigned int num)
{
int count = 0;
while (num != 0)
{
num /= 10;
++count;
}
return count;
}
unsigned int getDigit(unsigned int num, int position)
{
int digit = num % myPow(10, getNumDigits(num) - (position - 1));
return digit / myPow(10, getNumDigits(num) - position);
}
unsigned int getTotalDigits(int num)
{
unsigned int total = 0;
for (int i = 1; i <= num; i++)
total += getNumDigits(i);
return total;
}
// Returns the 'index'th digit of number created from 1 to num
int getIndexDigit(int num, int index)
{
if (index <= 9)
return index;
for (int i = 10; i <= num; i++)
{
if (getTotalDigits(i) >= index)
return getDigit(i, getNumDigits(i) - (getTotalDigits(i) - index));
}
}
// Can this be optimized?
int floorSqrt(int x)
{
if (x == 0 || x == 1)
return x;
int i = 1, result = 1;
while (result <= x)
{
i++;
result = i * i;
}
return i - 1;
}
void PrintTime(double num, int i)
{
constexpr double SECONDS_IN_HOUR = 3600;
constexpr double SECONDS_IN_MINUTE = 60;
double totalSeconds = num;
int hours = totalSeconds / SECONDS_IN_HOUR;
int minutes = (totalSeconds - (hours * SECONDS_IN_HOUR)) / SECONDS_IN_MINUTE;
int seconds = totalSeconds - (hours * SECONDS_IN_HOUR) - (minutes * SECONDS_IN_MINUTE);
std::cout << "Elapsed time for " << i << ": " << hours << "h, " << minutes << "m, " << seconds << "s\n";
}
}
int main()
{
constexpr unsigned int MAX_NUM_CHECK = 10000000;
for (int i = 1000000; i <= MAX_NUM_CHECK; i++)
{
auto start = std::chrono::system_clock::now();
int digitIndex = 1;
// Simplifying this to move to the next i in the loop early:
// if i % 2 then the last digit is a 0, 2, 4, 6, or 8 and is therefore divisible by 2
// if i % 5 then the last digit is 0 or 5 and is therefore divisible by 5
if (i % 2 == 0 || i % 5 == 0)
{
std::cout << i << " not prime" << '\n';
auto end = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = end - start;
PrintTime(elapsed_seconds.count(), i);
continue;
}
bool isPrime = true;
int divisionNumber = 3;
int floorNum = floorSqrt(i);
while (divisionNumber <= floorNum && isPrime)
{
if (divisionNumber % 5 == 0)
{
divisionNumber += 2;
continue;
}
int number = 0;
int totalDigits = getTotalDigits(i);
// This section does the division necessary to iterate through each digit of the 1 to N number
// Example: Think of dividing 124 into 123456 on paper and how you would iterate through that process
while (digitIndex <= totalDigits)
{
number *= 10;
number += getIndexDigit(i, digitIndex);
number %= divisionNumber;
digitIndex++;
}
if (number == 0)
{
isPrime = false;
break;
}
divisionNumber += 2;
}
if (isPrime)
std::cout << "N = " << i << " is prime." << '\n';
else
std::cout << i << " not prime" << '\n';
auto end = std::chrono::system_clock::now();
std::chrono::duration<double> elapsed_seconds = end - start;
PrintTime(elapsed_seconds.count(), i);
}
}
Its nice to see you are working on the same question I pondered few months ago.
Please refer to question posted in Math Stackexchange for better resources.
TL-DR,
The number you are looking for is called SmarandachePrime.
As per your code, it seems you are dividing with every number that is not a multiple of 2,5. To optimize you can actually check for n = 6k+1 ( 𝑘 ∈ ℕ ).
unfortunately, it is still not a better approach with respect to the number you are dealing with.
The better approach is to use primality test screening to find probable prime numbers in the sequence and then check whether they are prime or not. These tests take a less time ~(O(k log3n)) to check whether a number is prime or not, using mathematical fundamentals, compared to division.
there are several libraries that provide functions for primality check.
for python, you can use gmpy2 library, which uses Miller-Rabin Primality test to find probable primes.
I recommend you to further read about different Primality tests here.
I believe you are missing one very important check, and it's the division by 3:
A number can be divided by 3 is the sum of the numbers can be divided by 3, and your number consists of all numbers from 1 to N.
The sum of all numbers from 1 to N equals:
N * (N+1) / 2
This means that, if N or N+1 can be divided by 3, then your number cannot be prime.
So before you do anything, check MOD(N,3) and MOD(N+1,3). If either one of them equals zero, you can't have a prime number.
I'm trying to write a c++ program which gets an integer n (n>=1 && n<=100000) from the user and puts the sum of its digits into b. The output needed is the b-th prime number coming after n. I'm an absolute beginner in programming so I don't know what's wrong with the for loop or any other code that it doesn't show the correct output. For example the 3rd prime number after 12 (1+2=3) is 19 but the loop counts the prime numbers from 2 instead of 12, so it prints 7 as result.
#include <iostream>
using namespace std;
bool isPrime(int n)
{
if(n <= 1)
return false;
for(int i = 2; i <= (n/2); i++)
if(n % i == 0)
return false;
return true;
}
int main()
{
long int n;
int b = 0;
cin>>n;
while(n >= 1 && n <= 100000){
b += n % 10;
n /= 10;
}
for(int i = n, counter = b; counter <= 10; i++)
if(isPrime(i)){
counter++;
if(i > n)
cout<<counter<<"th prime number after n is : "<<i<<endl;
}
return 0;
}
So one of the possible solutions to my question, according to #Bob__ answer (and converting it to the code style I've used in the initial code) is as follows:
#include <iostream>
using namespace std;
bool isPrime(long int number)
{
if(number <= 1)
return false;
for(int i = 2; i <= (number / 2); i++)
if(number % i == 0)
return false;
return true;
}
int sumOfDigits(long int number)
{
int sum = 0;
while(number >= 1 && number <= 100000)
{
sum += number % 10;
number /= 10;
}
return sum;
}
long int bthPrimeAfter(int counter, long int number)
{
while(counter)
{
++number;
if(isPrime(number))
--counter;
}
return number;
}
int main()
{
long int number;
cin>>number;
int const counter = sumOfDigits(number);
cout<<bthPrimeAfter(counter, number)<<"\n";
return 0;
}
As dratenik said in their comment:
You have destroyed the value in n to produce b in the while loop. When the for loop comes around, n keeps being zero.
That's a key point to understand, sometimes we need to make a copy of a variable. One way to do that is passing it to a function by value. The function argument will be a local copy which can be changed without affecting the original one.
As an example, the main function could be written like the following:
#include <iostream>
bool is_prime(long int number);
// ^^^^^^^^ So is `n` in the OP's `main`
int sum_of_digits(long int number);
// ^^^^^^^^^^^^^^^ This is a local copy.
long int nth_prime_after(int counter, long int number);
int main()
{
long int number;
// The input validation (check if it's a number and if it's in the valid range,
// deal with errors) is left to the reader as an exercise.
std::cin >> number;
int const counter = sum_of_digits(number);
std::cout << nth_prime_after(counter, number) << '\n';
return 0;
}
The definition of sum_of_digits is straightforward.
int sum_of_digits(long int number)
{
int sum = 0;
while ( number ) // Stops when number is zero. The condition n <= 100000
{ // belongs to input validation, like n >= 0.
sum += number % 10;
number /= 10; // <- This changes only the local copy.
}
return sum;
}
About the last part (finding the nth prime after the chosen number), I'm not sure to understand what the asker is trying to do, but even if n had the correct value, for(int i = n, counter = b; counter <= 10; i++) would be just wrong. For starters, there's no reason for the condition count <= 10 or at least none that I can think of.
I'd write something like this:
long int nth_prime_after(int counter, long int number)
{
while ( counter )
{
++number;
if ( is_prime(number) )
{
--counter; // The primes aren't printed here, not even the nth.
}
}
return number; // Just return it, the printing is another function's
} // responsabilty.
A lot more could be said about the is_prime function and the overall (lack of) efficiency of this algorithm, but IMHO, it's beyond the scope of this answer.
Attempting to use this for loop to take an input for how many times the loop should run. And every other time the loop runs it should subtract or add to the sum, the denominator will change by +2 every completed loop. Cannot for the life of me figure out why it does not work. The answer I get once the input is larger than 10 is negative when it should be oscillating over pi.
#include <iostream>
using std::cout;
using std::cin;
using std::endl;
enter code here
int main()
{
int input = -100;
double sumTotal = 4, denominator = 3;
while (input < 0)
{
cout << "Enter Max value of k in truncated series (non-negative): " << endl;
cin >> input;
}
if (input == 0)
{
sum = 4.0 / 1.0;
}
for (int i = 2; i < input+2; i++)
{
if (i%2==0)
{
sumTotal -= static_cast<double>(4.0) / denominator;
}
else
{
sumTotal += static_cast<double>(4.0) / denominator;
}
denominator + static_cast<double>(2);
}
cout << sumTotal << endl;
return 0;
}
First things first: the static_casts you are doing are unnecessary. In C++, literals of the form 1.0 are considered doubles by default. Even if you used the float suffix, i.e. 1.0f, the compiler will still do the right thing.
Second, while I'm not familiar with the algorithm you are implementing, I would bet the issue is here: denominator + static_cast<double>(2);. This statement has no effect on the value of denominator.
You probably need to do this:
denominator = denominator + 2;
Or,
denominator += 2;
The intended effect is to modify the value of denominator for the next iteration of the loop, so you must assign the new value to denominator.
Also, there doesn't appear to any different between:
for (int i = 2; i < input + 2; ++i) {
...
}
and
for (int i = 0; i < input; ++i) {
...
}
So I would recommend start your index variable at 0 for readability's sake.
can I check if a number is even or odd by using add and subtraction. I can subtract the number until it get to 2 or 1 but can I do it without that. can i use the neighboring numbers to see if the number is odd or even
Thanks
Okay, you're not specifying which operators you CAN use, but since you mentioned in one comment that you only really abhor division and modulo, I propose this:
if ((number & 1) == 0) {
// even
} else {
// odd
}
Quick hack.
#include <assert.h>
// return i << 31 which is != 0 if i is odd
// 32-bit int implementations only;
// not portable, but could be made so -- you get the idea
int odd(int i) {
assert((1<<31) != 0 && (1<<32) == 0);
i += i; i += i; i += i; i += i; i += i; i += i; i += i; i += i;
i += i; i += i; i += i; i += i; i += i; i += i; i += i; i += i;
i += i; i += i; i += i; i += i; i += i; i += i; i += i; i += i;
i += i; i += i; i += i; i += i; i += i; i += i; i += i;
return i;
}
int main() {
int i = 0;
do {
assert(odd(i) ? (i&1) : !(i&1));
++i;
} while (i != 0);
return 0;
}
This goes back to grade school actually. Take the last digit. If the last digit is odd, it's odd. If the last digit is even it's even. If you can look at the number in binary format it's even easier.
If you can't convert the number to any non-base 10 format then those are REALLY strange requirements - ie: homework.
Of course you can! You know that even and odd numbers always alternate, so start with 0 and a boolean variable set to true, and count up to your number, flipping a boolean each time you count!
Let's say n = 3
0 - even
1 - odd
2 - even
3 - odd
How you implement this is up to you, but you can even use recursion if you want (this example is in Java):
static boolean isOdd(int number){
if(number > 0){
return !isOdd(number-1);
}else{
return false;
}
}
It doesn't work with negative numbers, but why do you even need to use addition and subtraction to check if a number is odd anyway? In the real world, you'd use modulo.
Old question, new answer:
int odd(int val){
return ((val>>1)<<1) != 0;
}