BITMASK3 - Editorial

editorial
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1

Problem Link:

Practice
Contest

Difficulty:

Easy-Medium

Prerequisites:

Binary Search

Problem:

Find the maximum number x for which the sum of x natural numbers don’t exceeds the litres of water available.

Explanation:

Given that the first bucket has a capacity of 1 litre, second bucket has capacity of 2 litres and so on.
So we just need the maximum number x so that 1+2+3+....+x <=n, where n is the litres of the water available. Thus, problem is a searching problem, we are just searching for the required x.

First approach is we can use linear search to find the value of x but it will exceed the time limit. So, we have to think of a more efficient searching approach.

Next approach is to use the binary search as it is very efficient and very well within the time limit of the problem.

Solution:

Author’s solution can be found here.

2

Why can’t we just use the formula for Sum of first n natural numbers? (n*(n+1))/2 = N

This was mine, I don’t know why I was getting TLE.

I mean, I’m okay with getting a wrong answer (I just re-read the question and saw the line, “The bucket will be considered filled if it has atleast 1 litre in it.”) But why am I getting a TLE? Is the sqrt() function that heavy/slow?

3

import math
for t in range(input()):
s=int(raw_input())
a=1
b=1
c=-2s
d=b**2-4ac
if d>0:
x1=-b+math.sqrt(d)
x1=x1/2a
print int(math.ceil(x1))

4

It is because the problem is not that easy. The time limit of the problem is very less. So you can’t use the linear approach. The problem was designed that way.

5

I based my solution on this editorial but I got a WA response.
Can someone point out the mistake in my code.

And I am trying to understand the approach used in the following solutions…
singh_8 and sayan009 but cant get it…

6

@goof_expert

Hi.
See in line 22, you should be checking for <=N (you did <N instead).

  • in line 22’s “if” satisfies, i.e mid * (mid-1) / 2 <= N, then the result var should be set to mid-1 (you did mid instead).

Hope it helps.

7

I used the formula for sum of first n natural numbers and got a WA,
but a simple linear approach for summing up the first n natural numbers gave AC, instead of TLE.

8

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9

You can use the formula (n*(n+1))/2=N and convert them into a quadratic equation to solve the problem. You can check my solution for this problem link text
Here i use sheree dharacharya formula to find the solution. And it accepted in one go.

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