1. Fibonacci Numbers in a Given Range

This task requires implementing a function to compute Fibonacci numbers and another to count how many Fibonacci numbers lie between two given positive integers m and n (0 < m < n ≤ 100000).

The Fibonacci sequence is defined as: fib(0) = fib(1) = 1, and for any k > 1, fib(k) = fib(k-1) + fib(k-2).

Function Signature:

• fib(n) — returns the n-th Fibonacci number.
• PrintFN(m, n) — returns a list of all Fibonacci numbers in the range [m, n].

Sample Test Program:

# 请在这里填写答案

m, n, i = input().split()
n = int(n)
m = int(m)
i = int(i)
b = fib(i)
print("fib({0}) = {1}".format(i, b))
fiblist = PrintFN(m, n)
print(len(fiblist))

Sample Input:

20 100 6

Sample Output:

fib(6) = 13
4

Implementation:

def fib(n):
    """Return the n-th Fibonacci number (with fib(0)=fib(1)=1)."""
    if n == 0 or n == 1:
        return 1
    return fib(n-1) + fib(n-2)

def PrintFN(m, n):
    """Return a list of Fibonacci numbers in the range [m, n]."""
    result = []
    k = 0
    while fib(k) <= n:
        if fib(k) >= m:
            result.append(fib(k))
        k += 1
    return result

Note: The recursive fib function is simple but inefficient for large n. An iterative version would be better for production code.

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2. Sum of Primes in a Given Range

This task requires implementing a function to check weather a number is prime, and another function to compute the sum of all prime numbers between two given positive integers x and y (x ≤ y).

Function Siganture:

• isPrime(n) — returns True if n is prime, False otherwise.
• primeSum(x, y) — returns the sum of all primes in the range [x, y].

Sample Test Program:

# 请在这里填写答案

x, y = map(int, input().split())
print(primeSum(x, y))

Sample Input:

2 8

Sample Output:

17

Implementation:

def isPrime(n):
    """Return True if n is a prime number, otherwise False."""
    if n <= 1:
        return False
    for i in range(2, int(n**0.5) + 1):
        if n % i == 0:
            return False
    return True

def primeSum(x, y):
    """Return the sum of all prime numbers in the inclusive range [x, y]."""
    total = 0
    for num in range(x, y + 1):
        if isPrime(num):
            total += num
    return total

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These examples demonstrate fundamental programming patterns: recursive/iterative number generation and primality testing with range summation.