Maximum subarray sum2

#1

i cant understand why we written
currentsum = cumsum[j] - cumsum[i-1];
i am trying but not able to understand it

#2

Hello @Diwyanshu,

Cumulative Sum:
A cumulative sum is a sequence of partial sums of a given sequence.
Example:
A[]={1,2,3,-1,5,6} //Original array
Cum_Sum[]={0,1,3,6,5,10,16} //Cumulative Sum
//An extra element 0 is added as first element because Cum_Sum of index i depends upon Cum_Sum of index i-1.

Cum_Sum[i]=Cum_Sum[i-1]+A[i-1]
//Here we are storing the Cum_Sum for index i=0 of array A[] at i=1 of Cum_Sum[]
//i.e. cumulative sum for index i of A[] at i+1 of Cum_Sum[]

Start i from 1 to 6(n):
Cum_Sum[0]=0
Cum_Sum[1]=Cum_Sum[0]+A[0]=0+1=1
Cum_Sum[2]=Cum_Sum[1]+A[1]=1+2=3
…
…So on

What is the significance of the Cumulative Sum:
We can find the sum of all elements of a subset of an array.
How?
Sum of elements of subset starting from the index i to j
Subset_Sum=Cum_Sum[j+1]-Cum_sum[i]=10-1=9

Why not Subset_Sum = Cum_Sum[j] - Cum_Sum[i-1] ?
For i=0, i-1 will become -1 which is not a valid index.
To avoid this, I have added the first element of my Cum_Sum[] array as 0.

example:
Sum of elements of subset starting from the index i=1 to j=4
Subset_Sum=Cum_Sum[5]-Cum_sum[1]=10-1=9

You might find the formulas different from what they have taken in the video.
Don’t worry about that.
Just understand the concept that will help you to understand the difference.

Hope, this would help.
Give a like if you are satisfied.