shivam565's blog

By shivam565, history, 2 years ago, In English

How to find total number of subarrays with sum atmost k?

Constrains :
-1e4 <= a[i] <= 1e4
1 <= n <= 1e5

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2 years ago, # |
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We can use sliding window technique to solve the problem.
Here, i and j represent starting and ending points of the sliding window.
Initially i = j = 0.
Now, we will traverse the whole array and try to add elements.

  • If sum < k, j++. So, number of sub-arrays produced = j-i. Also add arr[j] to the sum.
  • If sum >= k, we will subtract arr[i] from sum so that again sum<k. So, i++.
CODE
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2 years ago, # |
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Convert the statement to it's equivalent in terms of prefix sums i.e $$$pre_r - pre_l <= k$$$.

Now iterating over $$$r$$$, we need to find number of $$$l$$$ such that $$$pre_l >= pre_r - k$$$, which can be computed using ordered set of all $$$pre_l$$$.

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    2 years ago, # ^ |
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    but in this case, I have to iterate on all the prefix values >= pre(r)-k. How you will handle this thing while iterating the array?

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      2 years ago, # ^ |
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      use pbds!

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      13 months ago, # ^ |
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      You can use pbds or alternatively, compress the values of the prefix sum and use a data structure like segment tree or fenwick tree to count the values.