Game With Array
Codeforces Round #643 (div. 2)
So, first of All, let's go through the thought process of the Solution
Consider n = 5 and sum = 5
1
1
1
1
1
The sum goes from 1 to 5
So, first of All, let's go through the thought process of the Solution
Consider n = 5 and sum = 5
1
1
1
1
1
The sum goes from 1 to 5
No possible Solution!!
So, first of All, let's go through the thought process of the Solution
Consider n = 5 and sum = 6
1
1
1
1
The sum goes from 1 to 6
still No possible Solution!!
1
1
1
1
2
So, first of All, let's go through the thought process of the Solution
Consider n = 5 and sum = 7
1
1
1
Both the cases The sum goes from 1 to 7
still No possible Solution!!
1
1
1
2
2
1
1
1
1
3
OR
So, first of All, let's take one more
Consider n = 5 and sum = 8
1
1
For all arrangements, The sum goes from 1 to 8
still No possible Solution!!
1
1
2
2
2
1
1
1
1
4
OR
There can be more arrangements too but they will all result in same sum
So, Question Arises Till what sum we will keep getting all sums
Consider n = 5 and sum = 10
2
For arrangement 1, The sum goes from 2 to 10
1
1
2
2
2
1
1
1
1
6
OR
2
For arrangement 2, The sum goes from 1 to 4 and from 6 to 10
So, Question Arises Till what sum we will keep getting all sums
Consider n = 5 and sum = 10
2
For arrangement 1, The sum goes from 2 to 10
And sum 1 is missing so it is the answer
1
1
2
2
2
1
1
1
1
6
OR
2
For arrangement 2, The sum goes from 1 to 4 and from 6 to 10
And sum 5 is missing so it is the answer
Conclusion
1
Observe sum >= 2n there is an answer
otherwise, there are no answers
Finding the answer
we have already talked about two of the arrangments you can take any arrangments of your choice
2
2
2
2
2
For this arrangement answer will always be 1
1
1
1
1
1
1
6
For this arrangement in which n-1 elements will have 1 and nth array index will contain sum - (n-1)
The Answer Will be number of ones + 1
Copy of Codeforces div 2(643) problem D
By Chirayu Jain
