 # Lifeguard Problem - CodeVita

https://codeofgeeks.com/lifeguard-probe/

I have given my best and I think this problem really requires some advanced concept.

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I think a ternary search for the answer would be okay here, as the time function will be kinda unimodal having only one minima.

Can anyone throw a light on it? I am very curious to know how to solve it.

If you look below, the code in python is already given, but I am not sure how this works. Can anyone explain?

``````    import math
x1 = int(input())
y1 = int(input())
x2 = int(input())
y2 = int(input())
f = float(input())
if y1+y2 == 0:
a = x1*f
a = int(a)
print("{0 : .6f}".format(a))``````

This can be solved using calculus as below:

• step1: consider any point P1(x,0) on the beach-sea interface
• step2: calculate the time taken from source to point P(x,0) = T1(function of x)
• step3: calculate the time take from P(x,0) to destination = T2(function of x)
• step4: let Y = T1 + T2 (now Y becomes a function of x)
• step5: now u just need to minimize Y for which differentiate it w.r.t x(i.e. find d(Y)/dx)
• step6: solve for d(Y)/dx = 0 (at this step the value “V” will cancel out so do not worry about
that).
• step7: after step 6 u will get a value of x(may be more than one) then u need to varify whether
this value of x corresponds to minimum or maximum(i.e. u need to find second order
derivative of Y w.r.t x).

I hope this helps u ,all the steps are pretty standard(12th class syllabus).
happy learning!..

sea interface

But to solve that, we must know how to find the roots of f(x)=0, where degree is 4.

Anyone, please suggest how to move further.

X_solution=[(-y_l)*( (x_l-x_w) / (y_l-y_w) )]+x_l
Apply this solution,it will definitely work

this is from codeofgeeks right? it is totally incorrect…

Even I am unable to understand the logic. but in my opinion It has been uploaded by some user not the site

doesn’t seem so…i tried ur logic…still getting a wa

Yes, I realised its incorrect. So how to solve this problem?

Ternary search bro i said it earlier… you will find it a bit similar to

The only problem here in this codevita problem is that they are asking an accuracy upto 6 digits after decimal… its troublesome to keep that level of precision using square root function.

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