Given n , k , find the number of pairs (i,j) such that 0<=i<j<=n and k divides (j-i) Testcases up to 1e5 , (k<=n) up to 1e9 Sample:- input (5,2) , output 6
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Given n , k , find the number of pairs (i,j) such that 0<=i<j<=n and k divides (j-i) Testcases up to 1e5 , (k<=n) up to 1e9 Sample:- input (5,2) , output 6
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Auto comment: topic has been updated by TheSleepyDevil (previous revision, new revision, compare).
i had an idea where the answer is just summation ((n)/k) + ((n-1)/k) + ... till n is k-1 , but idk if that's true or not , or how to calculate it fast
Let j-i=q*k
j-i=x
x=k,2*k,3*k....,(n/k)*k
Let n/k=t (integer division)
n>=j>=x
Number of solutions is n-k+1+(n-2*k+1)+(n-3*k+1)...(n-t+1)=n*t+t-k*t*(t+1)/2
can u explain a bit more ?
UPD: nvm , got it , thanks <3
j-i is multiple of k
All multiples of k<=n are k,2*k,3*k,,,t*k
Let x=q*k
j-i=x
As i>=0 Hence j>=x
also j<=n
Number of such j is n-x+1
x ranges from k,2*k,...t*k