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.
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:
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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.
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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.
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If 'n' is
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:
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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.
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Each complete cycle contributes (a - b) meters to the total height. So, the height after all complete cycles is (n // 2) * (a - b).
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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.
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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.
Similar Questions
Sam and David are trying out a new wall at the rock-climbing gym. Sam starts up the wall first. After he is 5 feet in the air, David starts climbing up the wall next to Sam. They climb at the same speed up the wall. Let d be David's height up the wall, in feet, and let s be Sam's height up the wall, in feet.The equation s=d+5 represents this situation. Graph the equation.1234567891012345678910dsDavid's height, in feetSam's height, in feetSubmit
A. Only Plusestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputKmes has written three integers a𝑎, b𝑏 and c𝑐 in order to remember that he has to give Noobish_Monk a×b×c𝑎×𝑏×𝑐 bananas.Noobish_Monk has found these integers and decided to do the following at most 55 times:pick one of these integers;increase it by 11.For example, if a=2𝑎=2, b=3𝑏=3 and c=4𝑐=4, then one can increase a𝑎 three times by one and increase b𝑏 two times. After that a=5𝑎=5, b=5𝑏=5, c=4𝑐=4. Then the total number of bananas will be 5×5×4=1005×5×4=100.What is the maximum value of a×b×c𝑎×𝑏×𝑐 Noobish_Monk can achieve with these operations?InputEach test contains multiple test cases. The first line of input contains a single integer t𝑡 (1≤t≤10001≤𝑡≤1000) — the number of test cases. The description of the test cases follows.The first and only line of each test case contains three integers a𝑎, b𝑏 and c𝑐 (1≤a,b,c≤101≤𝑎,𝑏,𝑐≤10) — Kmes's integers.OutputFor each test case, output a single integer — the maximum amount of bananas Noobish_Monk can get.ExampleinputCopy22 3 410 1 10outputCopy100600
ProblemSuppose Jeremiah is a diver for his summer swim team. The function h(x)=−4.9x2+8x+5ℎ(𝑥)=−4.9𝑥2+8𝑥+5 represents Jeremiah's height (hℎ) in meters above the water x𝑥 seconds after he leaves the diving board.What is the initial height of the diving board?At what time did Jeremiah reach his maximum height?What was Jeremiah’s maximum height?Sketch a graph of the function. (You can use your calculator for this or create a table of values.) SolutionThe initial height of the diving board is when the time is zero.h(0)=−4.9x2+8x+5ℎ(0)=−4.9𝑥2+8𝑥+5h(0)=−4.9(0)2+8(0)+5ℎ(0)=−4.9(0)2+8(0)+5h(0)=0+0+5ℎ(0)=0+0+5h(0)=5ℎ(0)=5The initial height of the diving board is 55 m.The time at which Jeremiah reaches his maximum height is the x𝑥-coordinate of the vertex.x=−b2a𝑥=−𝑏2𝑎x=𝑥=2(2( ))x=−8−9.8𝑥=−8−9.8x=0.82𝑥=0.82 secIt took Jeremiah seconds to reach his maximum height.The maximum height was reached Jeremiah at seconds. The maximum height is the y𝑦-coordinate of the vertex.h(t)=−4.9x2+8x+5ℎ(𝑡)=−4.9𝑥2+8𝑥+5h(0.82)=−4.9(0.82)2+8(0.82)+5ℎ(0.82)=−4.9(0.82)2+8(0.82)+5h(0.82)=−3.29+6.56+5ℎ(0.82)=−3.29+6.56+5h(0.82)=8.27ℎ(0.82)=8.27 mThe maximum height reached by Jeremiah was m.CheckQuestion 8
ProblemEarlier, you were told about a toy rocket fired into the air from the top of a barn. Its height (hℎ) above the ground in yards after x𝑥 seconds is given by the function:h(x)=−5x2+10x+20ℎ(𝑥)=−5𝑥2+10𝑥+20What was the maximum height of the rocket? SolutionThe maximum height was reached by the rocket at one second as you found in part b from the previous example. It takes second to reach the maximum height. We will substitute that value in for x𝑥 in our function and simplify.The maximum height reached by the rocket was yards. What is the time it takes for the rocket to hit the ground? (Use a graph or any other method to solve.)It takes approximately seconds for the rocket to hit the ground. (Round to the nearest tenth.)CheckQuestion 9
Emily bicycles her way to school everyday. If the equation 𝑑(𝑡)=2.5𝑡 represents the distance in meters in t seconds, then how far is she from her home after 150 seconds?
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