Hello guys, i have a question like this. Given an array has length n, n <= 10^7, a[i] <= 10^9. Number K <= 10^9. How i can count number of subarray has average sum equal to K. Thanks for your time.
→ Pay attention
→ Streams
→ Top rated
| # | User | Rating |
|---|---|---|
| 1 | ecnerwala | 3649 |
| 2 | Benq | 3581 |
| 3 | orzdevinwang | 3570 |
| 4 | Geothermal | 3569 |
| 4 | cnnfls_csy | 3569 |
| 6 | tourist | 3565 |
| 7 | maroonrk | 3531 |
| 8 | Radewoosh | 3521 |
| 9 | Um_nik | 3482 |
| 10 | jiangly | 3468 |
→ Top contributors
| # | User | Contrib. |
|---|---|---|
| 1 | maomao90 | 174 |
| 2 | awoo | 164 |
| 3 | adamant | 162 |
| 4 | TheScrasse | 159 |
| 5 | nor | 158 |
| 6 | maroonrk | 156 |
| 7 | -is-this-fft- | 151 |
| 8 | SecondThread | 147 |
| 9 | orz | 146 |
| 10 | pajenegod | 145 |
→ Find user
→ Recent actions
Codeforces (c) Copyright 2010-2024 Mike Mirzayanov
The only programming contests Web 2.0 platform
Server time: Apr/25/2024 16:52:35 (k2).
Desktop version, switch to mobile version.
Supported by
Observe that decreasing every element $$$k$$$ will also decrease the average by $$$k$$$. Thus, if every element in the array is decreased by $$$k$$$, then the answer is equal to the number of subarrays with an average (or equivalently sum) of $$$0$$$.
Consider the prefix sum array $$$p$$$ generated by this new array. It is clear that the subarray $$$[l, r]$$$ has a sum of $$$0$$$ iff $$$p[l-1] = p[r]$$$.
The problem is now reduced to: given an array, count the number of equal pairs. This can be trivially solved by iterating through the array using an unordered_map, and can be solved in $$$O(n)$$$ time.