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BITMASK3 - Editorial

Problem Link:

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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.

asked 11 May, 08:24

hsagarthegr8's gravatar image

2★hsagarthegr8
161
accept rate: 0%

edited 29 May, 14:15

admin's gravatar image

0★admin ♦♦
17.1k347485513


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?

link

answered 11 May, 11:27

arvindpunk's gravatar image

3★arvindpunk
311
accept rate: 0%

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.

(12 May, 14:35) hsagarthegr82★

import math for t in range(input()): s=int(raw_input()) a=1 b=1 c=-2s d=b2-4ac if d>0: x1=-b+math.sqrt(d) x1=x1/2a print int(math.ceil(x1))

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answered 11 May, 15:40

srvshrm's gravatar image

2★srvshrm
1
accept rate: 0%

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...

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answered 20 May, 09:15

goof_expert's gravatar image

3★goof_expert
312
accept rate: 0%

@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.

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answered 29 May, 01:34

sandeepg97's gravatar image

5★sandeepg97
1011
accept rate: 0%

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question asked: 11 May, 08:24

question was seen: 591 times

last updated: 29 May, 14:15