Homework Hack 3.3.1

a,b = 1,2
Cookie = a*b
Chips = a + b
Cream = a - b
print(Cookie)
print(Chips)
print(Cream)


2
3
-1

Popcorn Hack 3.3.2

def fibonacc(n):
    if n <= 5:
        return "invalid"
    elif n == 10:
        return 1
    elif n == 2:
        return 2
    else:
        return fibonacc(n - 3) + fibonacc(n - 1)
n = 10 
print(f"The {n}th Fibonacci number is: {fibonacc(n)}")

The 10th Fibonacci number is: 1

Homework Hack 3.3.1

import numpy as np
import sys
import logging

logging.basicConfig(level=logging.INFO)

def matrix_multiply(A, B):
    return np.dot(A, B)

def matrix_power(M, power):
    result = np.identity(len(M), dtype=object)
    while power:
        if power % 2:
            result = matrix_multiply(result, M)
        M = matrix_multiply(M, M)
        power //= 2
    return result

def fibonacci_matrix(n):
    if n < 0:
        raise ValueError("Input must be a non-negative integer.")
    if n in (0, 1):
        return n
    F = np.array([[1, 1], [1, 0]], dtype=object)
    return matrix_power(F, n - 1)[0, 0]

def validate_input(user_input):
    value = int(user_input)
    if value < 0:
        raise ValueError
    return value

def main():
    user_input = input("Enter the position of the Fibonacci number: ")
    try:
        n = validate_input(user_input)
        print(f"Fibonacci number at position {n} is: {fibonacci_matrix(n)}")
    except ValueError as ve:
        logging.error(ve)
        sys.exit(1)

if __name__ == "__main__":
    main()


Fibonacci number at position 2 is: 1

Homework Hack 3.3.2

%%javascript

// JavaScript code for Fibonacci calculations
class Fibonacci {
    static fibonacci(n) {
        if (n === 0) return 0;
        if (n === 1) return 1;

        let prev1 = 1, prev2 = 0, current = 0;

        for (let i = 2; i <= n; i++) {
            current = prev1 + prev2;
            prev2 = prev1;
            prev1 = current;
        }

        return current;
    }

    static fibonacciMatrix(n) {
        if (n === 0) return 0;

        let F = [[1, 1], [1, 0]];
        this.power(F, n - 1);

        return F[0][0];
    }

    static power(F, n) {
        if (n === 0 || n === 1) return;

        let M = [[1, 1], [1, 0]];

        this.power(F, Math.floor(n / 2));
        this.multiply(F, F);

        if (n % 2 !== 0) this.multiply(F, M);
    }

    static multiply(F, M) {
        let x = F[0][0] * M[0][0] + F[0][1] * M[1][0];
        let y = F[0][0] * M[0][1] + F[0][1] * M[1][1];
        let z = F[1][0] * M[0][0] + F[1][1] * M[1][0];
        let w = F[1][0] * M[0][1] + F[1][1] * M[1][1];

        F[0][0] = x;
        F[0][1] = y;
        F[1][0] = z;
        F[1][1] = w;
    }
}

const n = 50;
console.log(`Fibonacci number at position ${n} using DP is: ${Fibonacci.fibonacci(n)}`);
console.log(`Fibonacci number at position ${n} using Matrix Exponentiation is: ${Fibonacci.fibonacciMatrix(n)}`);


<IPython.core.display.Javascript object>

Homework Hack 3.5.1

def AND(A, B):
    return A and B

def OR(A, B):
    return A or B

def NOT(A):
    return not A

print("A     B | AND | OR | NOT A")
print("---------------------------")
for A in [True, False]:
    for B in [True, False]:
        print(f"{A:<5} {B:<5} | {AND(A, B):<4} | {OR(A, B):<3} | {NOT(A)}")


A     B | AND | OR | NOT A
---------------------------
1     1     | 1    | 1   | False
1     0     | 0    | 1   | False
0     1     | 0    | 1   | True
0     0     | 0    | 0   | True

%%javascript

function AND(A, B) {
    return A && B;
}

function OR(A, B) {
    return A || B;
}

function NOT(A) {
    return !A;
}

console.log("A     B | AND | OR | NOT A");
console.log("---------------------------");
[true, false].forEach(A => {
    [true, false].forEach(B => {
        console.log(`${A}<5} ${B}<5} | ${AND(A, B)}<4} | ${OR(A, B)}<3} | ${NOT(A)}`);
    });
});


<IPython.core.display.Javascript object>

Popcorn Hack 3.5.1

def A():
    return True

def B():
    return True

if A():
    print("A is true, so B must also be true:", B())
else:
    print("A is false, we cannot conclude anything about B.")

if not B():
    print("B is false, therefore A must also be false:", not A())
else:
    print("B is true, we cannot conclude anything about A.")


A is true, so B must also be true: True
B is true, we cannot conclude anything about A.

%%javascript

function A() {
    return true;
}

function B() {
    return true;
}

if (A()) {
    console.log("A is true, so B must also be true:", B());
} else {
    console.log("A is false, we cannot conclude anything about B.");
}

if (!B()) {
    console.log("B is false, therefore A must also be false:", !A());
} else {
    console.log("B is true, we cannot conclude anything about A.");
}


<IPython.core.display.Javascript object>