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I cant get the logic for the question in the above link .

I have seen a few submissions but why is it that summation of the values of A = no of pairs of A and B satisfying the given relation??

Asked by: Proma_Roy on April 7, 2019, 1:04 p.m. Last updated on April 7, 2019, 1:04 p.m.

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1 Answer(s)


The condition required is a^2+b<=y.

where, a can be any positive integer(non-zero)

and b varies from 1-700 inclusive.

we will exploit the fact here that b is bounded and can vary a for a given value of b.

So a^2<=(y-b) or a<=sqrt(y-b)

maximum value of a satisfying the above relation will be the floor value of sqrt(y-b) and 

numbers 1,2,3,4------,floor_value(sqrt(y-b)) will satisfy the above relation for that value of b.

So we just add all values of floor_value(sqrt(y-b)) for each b from 1-700(inclusive).

Here is the code,

using namespace std;
int  main()
    long long t;
        long long y,count=0;//since y can vary till 10^10
        for(int b=1;b<=700;b++)
                if(y>b)//y should be greater than b else sqrt(y-b) will give wrong value
                long long int numbers_of_a=floor(sqrt((double)(y-b)));

Anupam_Singh last updated on April 7, 2019, 1:04 p.m. 0    Reply    Upvote   

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