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MINEAT - Editorial

2
2

PROBLEM LINK:

Div1, Div2
Practice

Author: Praveen Dhinwa
Tester: Triveni Mahatha
Editorialist: Adarsh Kumar

DIFFICULTY:

Easy-Medium

PREREQUISITES:

Binary search

PROBLEM:

You are given an array $A$ of $N$ integers. You need to find the smallest $K$ that satisfies this inequality; $\sum \limits_{i=1}^N \left \lceil \frac{A[i]}{K} \right \rceil \le H$, where $\left \lceil \right \rceil$ indicates the ceil function.

EXPLANATION:

According to the problem statement, Chef will need $\left \lceil \frac{A[i]}{K} \right \rceil$ hours to finish the $i^{th}$ pile. Hence, we need to find the smallest $K$ that satisfies this inequality; $\sum \limits_{i=1}^N \left \lceil \frac{A[i]}{K} \right \rceil \le H$.

subtask #1

Iterate over values of $K$ from $1$ to $MAX$ and break whenever you find the solution. Time complexity for the same will be $O(N.MAX)$, where $MAX$ is maximum element that can be present in the array.

subtask #2

For this subtask we need something better than brute-force. Hence, we will try to make some-observations first. Lets name the left side of our function as cost function. Observe that, our cost function is inversely proportional to $K$. Our cost function will decrease while $K$ increases. At some point it will become smaller than $H$. We need to find this point. Observe that, this problem has reduced to standard formulation of binary search problem. We just need to binary search on values of $K$ now and change the limits of $K$ according to the difference between our cost function and $H$. For more implementation details, you can have a look at attached solutions.

Time Complexity:

$O(N.log(MAX))$

AUTHOR'S AND TESTER'S SOLUTIONS

Setter's solution
Tester's solution

This question is marked "community wiki".

asked 10 Mar, 07:31

adkroxx's gravatar image

7★adkroxx
306719
accept rate: 7%

edited 13 Mar, 15:05

admin's gravatar image

0★admin ♦♦
19.5k348496535


why can't I see the solution?? the links don't work

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answered 12 Mar, 17:26

imsandy26's gravatar image

2★imsandy26
1
accept rate: 0%

unable to see the solutions , bucket policy needs to be updated .

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answered 12 Mar, 21:47

acodebreaker2's gravatar image

1★acodebreaker2
1.2k11
accept rate: 19%

I have a doubt. For the following test case:

5 7 9 3 8 10 5

The answer should be 6. So taking k=6, the above inequality will be calculated as following:

9/6 + 3/6 + 8/6 + 10/6 + 5/6 (Ceil of all the terms are added) 2 + 1 + 2 + 2 + 1 =8

Hour available is 7, so am I doing something. If there's any problem in logic, please point out the correct solution to above test case and logic.

Thanks

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answered 12 Mar, 23:53

philomath_mht's gravatar image

2★philomath_mht
1
accept rate: 0%

@philomath_mht the ans. will be 8 as you can only divide maximum (7-5)=2 bunch of bananas and the minimum required bananas that should be eaten is 8. 9/8 + 3/8 + 8/8 + 10/8 + 5/8 = 2 + 1 + 1 + 2 + 1 = 7

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answered 13 Mar, 02:06

mittal_ash7's gravatar image

2★mittal_ash7
01
accept rate: 0%

edited 13 Mar, 02:12

Simple binary search : Link to solution https://www.codechef.com/viewsolution/17582805

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answered 13 Mar, 03:23

beginner_1111's gravatar image

4★beginner_1111
1979
accept rate: 15%

can anyone tell me what is the mistake?
https://www.codechef.com/viewsolution/17824477

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answered 13 Mar, 20:22

dharmick's gravatar image

3★dharmick
1
accept rate: 0%

Change int to long long && float to double. Here's your modified solution :

https://www.codechef.com/viewsolution/17827412

@dharmick

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answered 14 Mar, 03:13

i_love_nidhi_j's gravatar image

1★i_love_nidhi_j
11
accept rate: 0%

edited 14 Mar, 03:15

! Should have tried this. Was just too lazy to do it :p

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answered 14 Mar, 09:08

harendrasingh's gravatar image

3★harendrasingh
382
accept rate: 7%

Please tell what's wrong with my solution here

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answered 15 Mar, 16:57

surajumang08's gravatar image

3★surajumang08
5
accept rate: 0%

you can look at my code. its almost similar to your code(99%same) link -https://www.codechef.com/viewsolution/17841451 Do upvote if you find useful.

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answered 15 Mar, 18:00

ankush23's gravatar image

3★ankush23
314
accept rate: 0%

edited 15 Mar, 18:00

https://www.codechef.com/viewsolution/17841507

Can someone tell me what's wrong with this???

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answered 15 Mar, 18:43

rak_9792's gravatar image

2★rak_9792
112
accept rate: 0%

https://www.codechef.com/viewsolution/17889934

can someone tell me what's wrong with this??

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answered 18 Mar, 21:02

rohitp12's gravatar image

1★rohitp12
2
accept rate: 0%

Can someone tell me what is the mistake in my code: https://www.codechef.com/viewsolution/17768075

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answered 28 Mar, 22:10

vaibhavsarda's gravatar image

4★vaibhavsarda
1
accept rate: 0%

link

answered 21 Apr, 18:12

purendra_'s gravatar image

1★purendra_
1
accept rate: 0%

I was getting a PA with my solution and just after I changed ** ans += std::ceil((float)a[i]/k); to ans += (a[i] + hr - 1)/hr ; **

it go AC...will someone please explain how the latter is different then the first one?

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answered 01 Aug, 01:26

thesmartguy's gravatar image

3★thesmartguy
22
accept rate: 0%

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question asked: 10 Mar, 07:31

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last updated: 01 Aug, 01:26