To solve this problem, we need to understand the pattern of the monkey's movement. The monkey moves up 'a' meters every odd second and down 'b' meters every even second. Here are the steps to solve this problem: 1. First, we need to determine how many complete cycles of "up and down" the monkey makes. A complete cycle is made in two seconds (one odd and one even). So, we divide 'n' by 2 using integer division to get the number of complete cycles. 2. Each complete cycle contributes a net movement of 'a - b' meters (up 'a' meters and down 'b' meters). So, we multiply the number of complete cycles by 'a - b' to get the total movement from the complete cycles. 3. If 'n' is

A monkey is climbing a tree. For the first second and all the consecutive odd seconds, the monkey goes up by a𝑎 meters and for every consecutive even second after the first, the monkey comes down by b𝑏 meters.Find the height the monkey reaches after n𝑛 seconds.InputThe first line has two integers a𝑎 and b𝑏 (0≤b≤a≤0≤𝑏≤𝑎≤ 104104)The second line has a single integer n𝑛 (00 ≤n≤≤𝑛≤ 105105)OutputPrint a single integer, the height reached by the monkey after n𝑛 secondsExampleinputCopy5 34outputCopy4NoteThe monkey moves 55 meters up in the 1st1𝑠𝑡 and 3rd3𝑟𝑑 second and 33 meters down in the 2nd2𝑛𝑑 and 4th4𝑡ℎ second, thus the monkey reaches 5+5−3−3=45+5−3−3=4 meters after 44 seconds.

Question

A monkey is climbing a tree. For the first second and all the consecutive odd seconds, the monkey goes up by a𝑎 meters and for every consecutive even second after the first, the monkey comes down by b𝑏 meters.Find the height the monkey reaches after n𝑛 seconds.InputThe first line has two integers a𝑎 and b𝑏 (0≤b≤a≤0≤𝑏≤𝑎≤ 104104)The second line has a single integer n𝑛 (00 ≤n≤≤𝑛≤ 105105)OutputPrint a single integer, the height reached by the monkey after n𝑛 secondsExampleinputCopy5 34outputCopy4NoteThe monkey moves 55 meters up in the 1st1𝑠𝑡 and 3rd3𝑟𝑑 second and 33 meters down in the 2nd2𝑛𝑑 and 4th4𝑡ℎ second, thus the monkey reaches 5+5−3−3=45+5−3−3=4 meters after 44 seconds.

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Solution 1

To solve this problem, we need to understand the pattern of the monkey's movement. The monkey moves up 'a' meters every odd second and down 'b' meters every even second.

Here are the steps to solve this problem:

First, we need to determine how many complete cycles of "up and down" the monkey makes. A complete cycle is made in two seconds (one odd and one even). So, we divide 'n' by 2 using integer division to get the number of complete cycles.
Each complete cycle contributes a net movement of 'a - b' meters (up 'a' meters and down 'b' meters). So, we multiply the number of complete cycles by 'a - b' to get the total movement from the complete cycles.
If 'n' is

This problem has been solved

Solution 2

To solve this problem, we need to understand the pattern of the monkey's movement. The monkey moves up 'a' meters every odd second and down 'b' meters every even second.

Here are the steps to solve this problem:

First, we need to determine how many complete cycles of "up and down" the monkey makes in 'n' seconds. Each cycle is 2 seconds long (1 second up and 1 second down). So, the number of complete cycles is n // 2.
Each complete cycle contributes (a - b) meters to the total height. So, the height after all complete cycles is (n // 2) * (a - b).
If 'n' is an odd number, there will be one extra second where the monkey moves up 'a' meters. So, if n % 2 is 1, we add 'a' to the total height.
The final height of the monkey is the sum of the height after all complete cycles and the possible extra 'a' meters if 'n' is odd.

Here is a Python code snippet that implements these steps:

a, b = map(int, input().split())
n = int(input())
height = (n // 2) * (a - b)
if n % 2:
    height += a
print(height)

This code first reads the values of 'a', 'b', and 'n'. It then calculates the height after all complete cycles and adds the extra 'a' meters if 'n' is odd. Finally, it prints the total height.

This problem has been solved

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