Why we are setting freq[0]=1;

#1

i don’t understand this in the code.

Divisilble subarray using pigeonhole principle
#2

@premang
it is done to handle all subarray starting from index 0.

for example
consider mod cumulative sum is
1 2 3 0 4 5 6 6.

here if u see 0 is there that means from index 0 ,to index 3 sum is divisible by n.
now if we initialise freq[0]=1 then freq[0] total count will be 2.
and using formula 2*(2-1)/2 = 1 we get 1 which is correct.
but if we dont initialise freq[0] with 1 then freq[0] total count will be 1.
and using formual 1*(1-1)/2 =0 we get 0. which is wrong .

#3

i dont understand anything.
to be specific
mod cumulative sum,
1 2 3 0 4 5 6 6.
if we dont get sum%n ZERO then why we are storing freq[0]=1. That is totally wrong.

#4

see if we dont get any sum%n zero inside our array then freq[0] contribution in our answer will 0.
because freq[0] * ( freq[0]-1 ) / 2 => 1 * (1-1) / 2 => 0.

clearly it will not affect our answer.

but if there exist some sum%n zero then freq[0]=1 initialisation plays an important role.
please watch this -> https://www.youtube.com/watch?v=p5Cm_r4T1Rw
and dry run the code on some testcase.

#5

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