Finding a substring, with some additional conditions

Question

I\'m given a string which looks like this:

1011010100

And my task is to find the length of a substring which number of nulls is always <= nu

Answer 1

Here goes my algorithm:

Start from right side:

 1. if you find 0 increment the value of count
 2. if you find 1 decrement the count

Store these values in an array i.e. v[]. e.g.

a[] = {1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1}

v[] = {0, 1, 0,-1, 0, 1, 0, 1, 2, 1, 2, 1, 0, -1}

Now the problem reduces to find indexes from V i.e. i, j such that v[i] < v[j] and i.

proof:

if you see here i=0 and j=11 is the possible answer and values are v[i]=0, v[j]=1. This means that till j we have one 0 extra in the string and as the v[i]=0 that means from i to j window size the extra 0 is cancelled by putting extra 1. Hence the answer.

Hope it helps. please let me know if you have doubt. Thanks.