C+= (Codeforces 1368A)
Tags: Greedy, brute force

Leo has developed a new programming language C+=. In C+=, integer variables can only be changed with a "+=" operation that adds the right-hand side value to the left-hand side variable. For example, performing "a += b" when a = $$$2$$$, b = $$$3$$$ changes the value of a to $$$5$$$ (the value of b does not change).In a prototype program Leo has two integer variables a and b, initialized with some positive values. He can perform any number of operations "a += b" or "b += a". Leo wants to test handling large integers, so he wants to make the value of either a or b strictly greater than a given value $$$n$$$. What is the smallest number of operations he has to perform?

Input: The first line contains a single integer $$$T$$$ ($$$1 \leq T \leq 100$$$) — the number of test cases.Each of the following $$$T$$$ lines describes a single test case, and contains three integers $$$a, b, n$$$ ($$$1 \leq a, b \leq n \leq 10^9$$$) — initial values of a and b, and the value one of the variables has to exceed, respectively.

Output: For each test case print a single integer — the smallest number of operations needed. Separate answers with line breaks.

Note: In the first case we cannot make a variable exceed $$$3$$$ in one operation. One way of achieving this in two operations is to perform "b += a" twice.

Sample Inputs:
2
1 2 3
5 4 100

Sample Outputs:
2
7

Solution (Python):
t = int(input())
for _ in range(t):
    (a, b, n) = map(int, input().split())
    cnt = 0
    while a <= n or b <= n:
        if a >= b:
            b += a
            cnt += 1
        else:
            a += b
            cnt += 1
    print(cnt - 1)

Solution (Python):
t = int(input())
for i in range(t):
    (a, b, n) = map(int, input().split())
    count = 0
    summ = 0
    while summ <= n:
        if a > b:
            b += a
            summ = b
            count += 1
        else:
            a += b
            summ = a
            count += 1
    print(count)

Solution (Python):
number = int(input())
for i in range(number):
    counter = 0
    (a, b, t) = map(int, input().split())
    while a <= t and b <= t:
        if a < b:
            a += b
        else:
            b += a
        counter += 1
    print(counter)