Using one-dimesional array in recursion - c++

Recently I've been working on partition problem. I've done a research and I found that it can be solved using an algorithm on wiki page. Here's the pseudo algorithm:
INPUT: A list of integers S
OUTPUT: True if S can be partitioned into two subsets that have equal sum
1 function find_partition( S ):
2 N ← sum(S)
3 P ← empty boolean table of size (\lfloor N/2 \rfloor + 1) by (n + 1)
4 initialize top row (P(0,x)) of P to True
5 initialize leftmost column (P(x, 0)) of P, except for P(0, 0) to False
6 for i from 1 to \lfloor N/2 \rfloor
7 for j from 1 to n
8 P(i, j) ← P(i, j-1) or P(i-S[j-1], j-1)
9 return P(\lfloor N/2 \rfloor , n)
Using recursion you can calculate if certain sum from integers in array can be reached, if it can be reached it returns true. I start with sumOfTheIntegers/2 and I go back to 0, until I find a solution. When I found the biggest possible sum of the integers that is lower or equal to the average I calculate the difference between the the 2 groups of integers with (average-lowestSumLowerorEqualtoAverage)*2.
But then I confront with problem how can I include one dimensional array in the recursion?
Here's the code, it should probably work, but I haven't tested it yet, because of the problem. So maybe the code contains small errors. But that's not the problem, I'll fix it later.
#include <iostream>
#include <cmath>
using namespace std;
bool matrix (int a, int b)
{
if(b == -1) return true;
else if (a == -1) return false;
else if(matrix(a-1, b) == true) return true;
else if(matrix(a-1,b-numbers[a-1]) == true) return true;
else return false;
}
int main()
{
int number, sum = 0;
cin >> number;
int numbers[number];
for(int i = 0; i<number; i++)
{
cin >> numbers[i];
sum += numbers[i];
}
double average = sum/2.0;
for(int i = floor(sum/2); i!= 0; i--)
{
if(matrix(number+1, i) == true)
{
cout << abs(average-i)*2;
break;
}
}
return 0;
}

The easiest (but certainly not the best) way is to introduce a global variable:
#include <vector>
std::vector<int> numbers;
/* ... */
int main(){
int number;
cin >> number;
numbers.resize(number);
/* ... */
}
Another possibility is to use an additional parameter:
bool matrix (int a, int b, const std::vector<int>& numbers)
{
if(b == -1) return true;
else if (a == -1) return false;
else if(matrix(a-1, b,numbers) == true) return true;
else if(matrix(a-1,b-numbers[a-1],numbers) == true) return true;
else return false;
}
Note that int numbers[number] is actually using a compiler-specific extension (VLA) and is not part of the C++ standard (see Does C++ support Variable Length Arrays? and Why aren't variable-length arrays part of the C++ standard?).

Pass it as an argument to the function
bool matrix (int a, int b, int num_arr[])
{
...
matrix(a-1,b,num_arr);
...
}

Related

How to print the b-th prime number coming after n?

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.

How to find size of largest subset of a sub-sequence equal to a sum

I have this problem from hackerearth
Given an array of N integers, C cards and S sum. Each card can be used
either to increment or decrement an integer in the given array by 1.
Find if there is any subset (after/before using any no.of cards) with
sum S in the given array.
Input Format
First line of input contains an integer T which denotes the no. of
testcases. Each test case has 2 lines of input. First line of each
test case has three integers N(size of the array), S(subset sum) and
C(no. of cards). Second line of each test case has N integers of the
array(a1 to aN) seperated by a space.
Constraints
1<=T<=100 1<=N<=100 1<=S<=10000 0<=C<=100 1<=ai<=100
Output Format
Print TRUE if there exists a subset with given sum else print FALSE.
So this is basically a variation of the subset sum problem, but instead of finding out whether a given subset with a sum S exists, we need to find the largest subset from sequence index to N-1 that has a value of s and compare it's length with our C value to see if it is greater. If it is, then we have enough elements to modify the sum using our C cards, and then we print out our answer. Here is my code for that
#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;
int N, S, C;
int checkSum(int index, int s, vector<int>& a, vector< vector<int> >& dP) {
if (dP[index][s] != -1)
return dP[index][s];
int maxNums = 0; // size of maximum subset array
for (int i = index; i < N; i++) {
int newSum = s - a[i];
int l = 0;
if (newSum == 0) {
l = 1;
} if (newSum > 0) {
if (i < (N-1)) { // only if we can still fill up sum
l = checkSum(i + 1, newSum, a, dP);
if (l > 0) // if it is possible to create this sum
l++; // include l in it
} else {
// l stays at 0 for there is no subset that can create this sum
}
} else {
// there is no way to create this sum, including this number, so skip it;
if (i == (N-1))
break; // don't go to the next level
// and l stays at 0
}
if (l > maxNums) {
maxNums = l;
}
}
dP[index][s] = maxNums;
return maxNums;
}
int main() {
int t;
cin >> t;
while (t--) {
cin >> N >> S >> C;
vector<int> a(N);
for (int i = 0; i < N; i++)
cin >> a[i];
vector< vector<int> > dP(N, vector<int>(S + C + 2, -1));
bool possible = false;
for (int i = 0; i <= C; i++) {
int l = checkSum(0, S-i, a, dP);
int m = checkSum(0, S+i, a, dP);
if ( (l > 0 && l >= i) || (m > 0 && m >= i) ) {
cout << "TRUE" << endl;
possible = true;
break;
}
}
if (!possible)
cout << "FALSE" << endl;
}
return 0;
}
So basically, 0 means it's not possible to create a subset equal to s from elements index to N-1, and -1 means we haven't computed it yet. And any other value indicates the size of the largest subset that sums up to s. This code isn't passing all the test cases. What's wrong?
You miss an else in following line
} if (newSum > 0) {
This make your program has an unexpected early break before updating maxNums by l in some cases.
For example, N=1, S=5, C=0, a={5}
Potential logic problem
You have limited the no. of card to be used to not exceed the subset size while the question never state you cannot apply multiple cards to same integers.
I mean l >= i and m >= i in
if ( (l > 0 && l >= i) || (m > 0 && m >= i) ) {
Seems you have logic flaw.
You need to find the shortest subset (with sum in range S-C..S+C) and compare it's size with C. If subset is shorter, it is possible to make needed sum.

Improving optimization of nested loop

I'm making a simple program to calculate the number of pairs in an array that are divisible by 3 array length and values are user determined.
Now my code is perfectly fine. However, I just want to check if there is a faster way to calculate it which results in less compiling time?
As the length of the array is 10^4 or less compiler takes less than 100ms. However, as it gets more to 10^5 it spikes up to 1000ms so why is this? and how to improve speed?
#include <iostream>
using namespace std;
int main()
{
int N, i, b;
b = 0;
cin >> N;
unsigned int j = 0;
std::vector<unsigned int> a(N);
for (j = 0; j < N; j++) {
cin >> a[j];
if (j == 0) {
}
else {
for (i = j - 1; i >= 0; i = i - 1) {
if ((a[j] + a[i]) % 3 == 0) {
b++;
}
}
}
}
cout << b;
return 0;
}
Your algorithm has O(N^2) complexity. There is a faster way.
(a[i] + a[j]) % 3 == ((a[i] % 3) + (a[j] % 3)) % 3
Thus, you need not know the exact numbers, you need to know their remainders of division by three only. Zero remainder of the sum can be received with two numbers with zero remainders (0 + 0) and with two numbers with remainders 1 and 2 (1 + 2).
The result will be equal to r[1]*r[2] + r[0]*(r[0]-1)/2 where r[i] is the quantity of numbers with remainder equal to i.
int r[3] = {};
for (int i : a) {
r[i % 3]++;
}
std::cout << r[1]*r[2] + (r[0]*(r[0]-1)) / 2;
The complexity of this algorithm is O(N).
I've encountered this problem before, and while I don't find my particular solution, you could improve running times by hashing.
The code would look something like this:
// A C++ program to check if arr[0..n-1] can be divided
// in pairs such that every pair is divisible by k.
#include <bits/stdc++.h>
using namespace std;
// Returns true if arr[0..n-1] can be divided into pairs
// with sum divisible by k.
bool canPairs(int arr[], int n, int k)
{
// An odd length array cannot be divided into pairs
if (n & 1)
return false;
// Create a frequency array to count occurrences
// of all remainders when divided by k.
map<int, int> freq;
// Count occurrences of all remainders
for (int i = 0; i < n; i++)
freq[arr[i] % k]++;
// Traverse input array and use freq[] to decide
// if given array can be divided in pairs
for (int i = 0; i < n; i++)
{
// Remainder of current element
int rem = arr[i] % k;
// If remainder with current element divides
// k into two halves.
if (2*rem == k)
{
// Then there must be even occurrences of
// such remainder
if (freq[rem] % 2 != 0)
return false;
}
// If remainder is 0, then there must be two
// elements with 0 remainder
else if (rem == 0)
{
if (freq[rem] & 1)
return false;
}
// Else number of occurrences of remainder
// must be equal to number of occurrences of
// k - remainder
else if (freq[rem] != freq[k - rem])
return false;
}
return true;
}
/* Driver program to test above function */
int main()
{
int arr[] = {92, 75, 65, 48, 45, 35};
int k = 10;
int n = sizeof(arr)/sizeof(arr[0]);
canPairs(arr, n, k)? cout << "True": cout << "False";
return 0;
}
That works for a k (in your case 3)
But then again, this is not my code, but the code you can find in the following link. with a proper explanation. I didn't just paste the link since it's bad practice I think.

using vector as function output

I'm trying to write a code shows all the numbers with the following characteristics:
the number itself is a prime number.
for each digit removed from the right the remaining number should still be a prime number.
Considering the number 293 for example: 293 itself is a prime number if we delete the digit on the right we have 29 which is still a prime number, and if we delete the right digit again we have 2 which is still prime.
I'm trying to write a code that gets the integer n<=8 from the user and shows all the n-digit numbers that have the characteristics stated above. My algorithm is to write a recursive function (show) that returns the vector v.
If n=1 then it just shows the numbers 2-3-5-7... if n!=1 it should call show(n-1) and multiply all the generated numbers by 10 and add them up with odd numbers... then it should check if the new number is prime. If so it should be added to the vector.
My problem is the code only works for n=1. Here is my code:
#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>
#include <iterator>
using namespace std;
bool isPrime(int a)
{
int i, p = 0;
if (a == 1)
return false;
else
{
for (i = a - 1; i > sqrt(a); i--)
if (a % i == 0)
p++;
if (p != 0)
return false;
else
return true;
}
}
vector<int> show(int n)
{
vector<int> v;
int i, j;
if (n == 1)
{
v.push_back(2);
v.push_back(3);
v.push_back(5);
v.push_back(7);
}
else
{
show(n - 1);
if (n != 1)
for (i = 0; i < v.size(); i++)
{
for (j = 1; j <= 9; j += 2)
if (isPrime((v.at(i) * 10) + j))
v.at(i) = (v.at(i) * 10) + j;
}
}
return v;
}
int main()
{
int n, s = 0, i;
cin >> n;
show(n);
for (i = 0; i < show(n).size(); i++)
cout << show(n).at(i) << endl;
system("pause");
return 0;
}
In addition to comments on question, take a look at the show(n - 1) line. Shouldn't you be saving the return value: v = show(n - 1)?
Also, it will be better to pass the vector as a reference, in this way you avoid the copy of vector's content (in your case it doesn't have much impact since vector will not grow too much, but imagine using large values for n).

Determining if a number is prime

I have perused a lot of code on this topic, but most of them produce the numbers that are prime all the way up to the input number. However, I need code which only checks whether the given input number is prime.
Here is what I was able to write, but it does not work:
void primenumber(int number)
{
if(number%2!=0)
cout<<"Number is prime:"<<endl;
else
cout<<"number is NOt prime"<<endl;
}
I would appreciate if someone could give me advice on how to make this work properly.
Update
I modified it to check on all the numbers in a for loop.
void primenumber(int number)
{
for(int i=1; i<number; i++)
{
if(number%i!=0)
cout<<"Number is prime:"<<endl;
else
cout<<"number is NOt prime"<<endl;
}
}
bool isPrime(int number){
if(number < 2) return false;
if(number == 2) return true;
if(number % 2 == 0) return false;
for(int i=3; (i*i)<=number; i+=2){
if(number % i == 0 ) return false;
}
return true;
}
My own IsPrime() function, written and based on the deterministic variant of the famous Rabin-Miller algorithm, combined with optimized step brute forcing, giving you one of the fastest prime testing functions out there.
__int64 power(int a, int n, int mod)
{
__int64 power=a,result=1;
while(n)
{
if(n&1)
result=(result*power)%mod;
power=(power*power)%mod;
n>>=1;
}
return result;
}
bool witness(int a, int n)
{
int t,u,i;
__int64 prev,curr;
u=n/2;
t=1;
while(!(u&1))
{
u/=2;
++t;
}
prev=power(a,u,n);
for(i=1;i<=t;++i)
{
curr=(prev*prev)%n;
if((curr==1)&&(prev!=1)&&(prev!=n-1))
return true;
prev=curr;
}
if(curr!=1)
return true;
return false;
}
inline bool IsPrime( int number )
{
if ( ( (!(number & 1)) && number != 2 ) || (number < 2) || (number % 3 == 0 && number != 3) )
return (false);
if(number<1373653)
{
for( int k = 1; 36*k*k-12*k < number;++k)
if ( (number % (6*k+1) == 0) || (number % (6*k-1) == 0) )
return (false);
return true;
}
if(number < 9080191)
{
if(witness(31,number)) return false;
if(witness(73,number)) return false;
return true;
}
if(witness(2,number)) return false;
if(witness(7,number)) return false;
if(witness(61,number)) return false;
return true;
/*WARNING: Algorithm deterministic only for numbers < 4,759,123,141 (unsigned int's max is 4294967296)
if n < 1,373,653, it is enough to test a = 2 and 3.
if n < 9,080,191, it is enough to test a = 31 and 73.
if n < 4,759,123,141, it is enough to test a = 2, 7, and 61.
if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11.
if n < 3,474,749,660,383, it is enough to test a = 2, 3, 5, 7, 11, and 13.
if n < 341,550,071,728,321, it is enough to test a = 2, 3, 5, 7, 11, 13, and 17.*/
}
To use, copy and paste the code into the top of your program. Call it, and it returns a BOOL value, either true or false.
if(IsPrime(number))
{
cout << "It's prime";
}
else
{
cout<<"It's composite";
}
If you get a problem compiling with "__int64", replace that with "long". It compiles fine under VS2008 and VS2010.
How it works:
There are three parts to the function. Part checks to see if it is one of the rare exceptions (negative numbers, 1), and intercepts the running of the program.
Part two starts if the number is smaller than 1373653, which is the theoretically number where the Rabin Miller algorithm will beat my optimized brute force function. Then comes two levels of Rabin Miller, designed to minimize the number of witnesses needed. As most numbers that you'll be testing are under 4 billion, the probabilistic Rabin-Miller algorithm can be made deterministic by checking witnesses 2, 7, and 61. If you need to go over the 4 billion cap, you will need a large number library, and apply a modulus or bit shift modification to the power() function.
If you insist on a brute force method, here is just my optimized brute force IsPrime() function:
inline bool IsPrime( int number )
{
if ( ( (!(number & 1)) && number != 2 ) || (number < 2) || (number % 3 == 0 && number != 3) )
return (false);
for( int k = 1; 36*k*k-12*k < number;++k)
if ( (number % (6*k+1) == 0) || (number % (6*k-1) == 0) )
return (false);
return true;
}
}
How this brute force piece works:
All prime numbers (except 2 and 3) can be expressed in the form 6k+1 or 6k-1, where k is a positive whole number. This code uses this fact, and tests all numbers in the form of 6k+1 or 6k-1 less than the square root of the number in question. This piece is integrated into my larger IsPrime() function (the function shown first).
If you need to find all the prime numbers below a number, find all the prime numbers below 1000, look into the Sieve of Eratosthenes. Another favorite of mine.
As an additional note, I would love to see anyone implement the Eliptical Curve Method algorithm, been wanting to see that implemented in C++ for a while now, I lost my implementation of it. Theoretically, it's even faster than the deterministic Rabin Miller algorithm I implemented, although I'm not sure if that's true for numbers under 4 billion.
You need to do some more checking. Right now, you are only checking if the number is divisible by 2. Do the same for 2, 3, 4, 5, 6, ... up to number. Hint: use a loop.
After you resolve this, try looking for optimizations.
Hint: You only have to check all numbers up to the square root of the number
I would guess taking sqrt and running foreach frpm 2 to sqrt+1 if(input% number!=0) return false;
once you reach sqrt+1 you can be sure its prime.
C++
bool isPrime(int number){
if (number != 2){
if (number < 2 || number % 2 == 0) {
return false;
}
for(int i=3; (i*i)<=number; i+=2){
if(number % i == 0 ){
return false;
}
}
}
return true;
}
Javascript
function isPrime(number)
{
if (number !== 2) {
if (number < 2 || number % 2 === 0) {
return false;
}
for (var i=3; (i*i)<=number; i+=2)
{
if (number % 2 === 0){
return false;
}
}
}
return true;
}
Python
def isPrime(number):
if (number != 2):
if (number < 2 or number % 2 == 0):
return False
i = 3
while (i*i) <= number:
if(number % i == 0 ):
return False;
i += 2
return True;
If you know the range of the inputs (which you do since your function takes an int), you can precompute a table of primes less than or equal to the square root of the max input (2^31-1 in this case), and then test for divisibility by each prime in the table less than or equal to the square root of the number given.
This code only checks if the number is divisible by two. For a number to be prime, it must not be evenly divisible by all integers less than itself. This can be naively implemented by checking if it is divisible by all integers less than floor(sqrt(n)) in a loop. If you are interested, there are a number of much faster algorithms in existence.
If you are lazy, and have a lot of RAM, create a sieve of Eratosthenes which is practically a giant array from which you kicked all numbers that are not prime.
From then on every prime "probability" test will be super quick.
The upper limit for this solution for fast results is the amount of you RAM. The upper limit for this solution for superslow results is your hard disk's capacity.
I follow same algorithm but different implementation that loop to sqrt(n) with step 2 only odd numbers because I check that if it is divisible by 2 or 2*k it is false. Here is my code
public class PrimeTest {
public static boolean isPrime(int i) {
if (i < 2) {
return false;
} else if (i % 2 == 0 && i != 2) {
return false;
} else {
for (int j = 3; j <= Math.sqrt(i); j = j + 2) {
if (i % j == 0) {
return false;
}
}
return true;
}
}
/**
* #param args
*/
public static void main(String[] args) {
for (int i = 1; i < 100; i++) {
if (isPrime(i)) {
System.out.println(i);
}
}
}
}
Use mathematics first find square root of number then start loop till the number ends which you get after square rooting.
check for each value whether the given number is divisible by the iterating value .if any value divides the given number then it is not a prime number otherwise prime.
Here is the code
bool is_Prime(int n)
{
int square_root = sqrt(n); // use math.h
int toggle = 1;
for(int i = 2; i <= square_root; i++)
{
if(n%i==0)
{
toggle = 0;
break;
}
}
if(toggle)
return true;
else
return false;
}
bool check_prime(int num) {
for (int i = num - 1; i > 1; i--) {
if ((num % i) == 0)
return false;
}
return true;
}
checks for any number if its a prime number
Someone had the following.
bool check_prime(int num) {
for (int i = num - 1; i > 1; i--) {
if ((num % i) == 0)
return false;
}
return true;
}
This mostly worked. I just tested it in Visual Studio 2017. It would say that anything less than 2 was also prime (so 1, 0, -1, etc.)
Here is a slight modification to correct this.
bool check_prime(int number)
{
if (number > 1)
{
for (int i = number - 1; i > 1; i--)
{
if ((number % i) == 0)
return false;
}
return true;
}
return false;
}
Count by 6 for better speed:
bool isPrime(int n)
{
if(n==1) return false;
if(n==2 || n==3) return true;
if(n%2==0 || n%3==0) return false;
for(int i=5; i*i<=n; i=i+6)
if(n%i==0 || n%(i+2)==0)
return false;
return true;
}
There are several different approches to this problem.
The "Naive" Method: Try all (odd) numbers up to (the root of) the number.
Improved "Naive" Method: Only try every 6n ± 1.
Probabilistic tests: Miller-Rabin, Solovay-Strasse, etc.
Which approach suits you depends and what you are doing with the prime.
You should atleast read up on Primality Testing.
If n is 2, it's prime.
If n is 1, it's not prime.
If n is even, it's not prime.
If n is odd, bigger than 2, we must check all odd numbers 3..sqrt(n)+1, if any of this numbers can divide n, n is not prime, else, n is prime.
For better performance i recommend sieve of eratosthenes.
Here is the code sample:
bool is_prime(int n)
{
if (n == 2) return true;
if (n == 1 || n % 2 == 0) return false;
for (int i = 3; i*i < n+1; i += 2) {
if (n % i == 0) return false;
}
return true;
}
I came up with this:
int counter = 0;
bool checkPrime(int x) {
for (int y = x; y > 0; y--){
if (x%y == 0) {
counter++;
}
}
if (counter == 2) {
counter = 0; //resets counter for next input
return true; //if its only divisible by two numbers (itself and one) its a prime
}
else counter = 0;
return false;
}
This is a quick efficient one:
bool isPrimeNumber(int n) {
int divider = 2;
while (n % divider != 0) {
divider++;
}
if (n == divider) {
return true;
}
else {
return false;
}
}
It will start finding a divisible number of n, starting by 2. As soon as it finds one, if that number is equal to n then it's prime, otherwise it's not.
//simple function to determine if a number is a prime number
//to state if it is a prime number
#include <iostream>
using namespace std;
int isPrime(int x); //functioned defined after int main()
int main() {
int y;
cout << "enter value" << endl;
cin >> y;
isPrime(y);
return 0;
} //end of main function
//-------------function
int isPrime(int x) {
int counter = 0;
cout << "factors of " << x << " are " << "\n\n"; //print factors of the number
for (int i = 0; i <= x; i++)
{
for (int j = 0; j <= x; j++)
{
if (i * j == x) //check if the number has multiples;
{
cout << i << " , "; //output provided for the reader to see the
// muliples
++counter; //counts the number of factors
}
}
}
cout << "\n\n";
if (counter > 2) {
cout << "value is not a prime number" << "\n\n";
}
if (counter <= 2) {
cout << "value is a prime number" << endl;
}
}
Here is a simple program to check whether a number is prime or not:
#include <iostream>
using namespace std;
int main()
{
int n, i, m=0, flag=0;
cout << "Enter the Number to check Prime: ";
cin >> n;
m=n/2;
for(i = 2; i <= m; i++)
{
if(n % i == 0)
{
cout<<"Number is not Prime."<<endl;
flag=1;
break;
}
}
if (flag==0)
cout << "Number is Prime."<<endl;
return 0;
}
Here is a C++ code to determine that a given number is prime:
bool isPrime(int num)
{
if(num < 2) return false;
for(int i = 2; i <= sqrt(num); i++)
if(num % i == 0) return false;
return true;
}
PS Don't forget to include math.h library to use sqrt function
well crafted, share it with you:
bool isPrime(int num) {
if (num == 2) return true;
if (num < 2) return false;
if (num % 2 == 0) return false;
for (int i = num - 1; i > 1; i--) {
if (num % i == 0) return false;
}
return true;
}
There are many potential optimization in prime number testing.
Yet many answers here, not only are worse the O(sqrt(n)), they suffer from undefined behavior (UB) and incorrect functionality.
A simple prime test:
// Return true when number is a prime.
bool is_prime(int number) {
// Take care of even values, it is only a bit test.
if (number % 2 == 0) {
return number == 2;
}
// Loop from 3 to square root (n)
for (int test_factor = 3; test_factor <= number / test_factor; test_factor +=
2) {
if (number % test_factor == 0) {
return false;
}
}
return n > 1;
}
Do not use test_factor * test_factor <= number. It risks signed integer overflow (UB) for large primes.
Good compilers see nearby number/test_factor and number % test_factor and emit code that computes both for the about the time cost of one. If still concerned, consider div().
Avoid sqrt(n). Weak floating point libraries do not perform this as exactly as we need for this integer problem, possible returning a value just ever so less than an expected whole number. If still interested in a sqrt(), use lround(sqrt(n)) once before the loop.
Avoid sqrt(n) with wide integer types of n. Conversion of n to a double may lose precision. long double may fair no better.
Test to insure the prime test code does not behave poorly or incorrectly with 1, 0 or any negative value.
Consider bool is_prime(unsigned number) or bool is_prime(uintmax_t number) for extended range.
Avoid testing with candidate factors above the square root n and less than n. Such test factors are never factors of n. Not adhering to this makes for slow code.
A factor is more likely a small value that an large one. Testing small values first is generally far more efficient for non-primes.
Pedantic: Avoid if (number & 1 == 0) {. It is an incorrect test when number < 0 and encoded with rare ones' complement. Use if (number % 2 == 0) { and trust your compiler to emit good code.
More advanced techniques use a list of known/discovered primes and the Sieve of Eratosthenes.
#define TRUE 1
#define FALSE -1
int main()
{
/* Local variables declaration */
int num = 0;
int result = 0;
/* Getting number from user for which max prime quadruplet value is
to be found */
printf("\nEnter the number :");
scanf("%d", &num);
result = Is_Prime( num );
/* Printing the result to standard output */
if (TRUE == result)
printf("\n%d is a prime number\n", num);
else
printf("\n%d is not a prime number\n", num);
return 0;
}
int Is_Prime( int num )
{
int i = 0;
/* Checking whether number is negative. If num is negative, making
it positive */
if( 0 > num )
num = -num;
/* Checking whether number is less than 2 */
if( 2 > num )
return FALSE;
/* Checking if number is 2 */
if( 2 == num )
return TRUE;
/* Checking whether number is even. Even numbers
are not prime numbers */
if( 0 == ( num % 2 ))
return FALSE;
/* Checking whether the number is divisible by a smaller number
1 += 2, is done to skip checking divisibility by even numbers.
Iteration reduced to half */
for( i = 3; i < num; i += 2 )
if( 0 == ( num % i ))
/* Number is divisible by some smaller number,
hence not a prime number */
return FALSE;
return TRUE;
}
I Have Use This Idea For Finding If The No. Is Prime or Not:
#include <conio.h>
#include <iostream>
using namespace std;
int main() {
int x, a;
cout << "Enter The No. :";
cin >> x;
int prime(unsigned int);
a = prime(x);
if (a == 1)
cout << "It Is A Prime No." << endl;
else
if (a == 0)
cout << "It Is Composite No." << endl;
getch();
}
int prime(unsigned int x) {
if (x == 1) {
cout << "It Is Neither Prime Nor Composite";
return 2;
}
if (x == 2 || x == 3 || x == 5 || x == 7)
return 1;
if (x % 2 != 0 && x % 3 != 0 && x % 5 != 0 && x % 7 != 0)
return 1;
else
return 0;
}
if(number%2!=0)
cout<<"Number is prime:"<<endl;
The code is incredibly false. 33 divided by 2 is 16 with reminder of 1 but it's not a prime number...