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1. Mathematical Functions

Functions that return true or false (boolean values).

1.1 isPrime

boolean isPrime(int number) {
    // if number is evenly divided by any number less than number
    // (except 1) then it is prime
    // otherwise, not prime
    for (int i = 2; i < number; i++) {
        if ((number % i) == 0) {
            return false;
        }
    }
    return true;
    
}

void setup() {
    println("isPrime(100): " + isPrime(100));
    println("isPrime(101): " + isPrime(101));
    println("isPrime(107): " + isPrime(107));
}

Sketch #1:

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Sketch #1 state: Loading...

1.2 GCD

Greatest common divisor: the largest positive integer that divides all of the numbers without a remainder. For example, the GCD of 8 and 12 is 4.

Euclid's Algorithm (after https://en.wikipedia.org/wiki/Greatest_common_divisor):

1. Find the GCD of a and b
2. If a or b is zero, then return the other
3. if a > b, set a to a - b
4. if b > a, set b to b - a
5. go to step 2

Example:

1. Let a = 8, and b = 12
2. Neither is zero
3. a = 4 (12 - 8), b = 12
4. a = 4, b = 8 (12 - 4)
5. a = 4, b = 4 (8 - 4)
6. a = 0 (4 - 4), b = 4
6. return 4

int gcd(int a, int b) {
    if (a == 0)      // base case
        return b;
    else if (b == 0) // base case
      return a;
    else if (a > b)
      return gcd(a - b, b);
    else // 
      return gcd(a, b - a);
}

void setup() {
    println("gcd(8, 12): " + gcd(8, 12));
    println("gcd(3, 2): " + gcd(3, 2));
}

Sketch #4:

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Sketch #4 state: Loading...

1.3 isLeapyear

boolean isLeapyear(int year) {
    // if a year is evenly divided by 100
    // but it is not evenly divided by 400
    // it is a leapyear
    // else if a year is evenly divided by 4, it is a leap year
    // otherwise, not a leapyear
    return true;
}

void setup() {
    println("isLeapyear(2000): " + isLeapyear(2000) + " (should be true)");
    println("isLeapyear(1904): " + isLeapyear(1904) + " (should be true)");
    println("isLeapyear(1900): " + isLeapyear(1900) + " (should be false)");
    println("isLeapyear(1901): " + isLeapyear(1901) + " (should be false)");
}

Sketch #5:

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Sketch #5 state: Loading...