Perfect Subarray
InterviewMemory limit1024 MB
Count the contiguous non-empty subarrays whose total sum is a perfect square, with array values between -100 and 100.
- Level
Medium6 of 10
- Topics
- Prefix sum, Hash map, Math, Implementation
- Solved
- No attempts yet
Problem
Cristobal has an array of N (possibly negative) integers. The i-th integer in his array is Ai. A contiguous non-empty subarray of Cristobal's array is perfect if its total sum is a perfect square. A perfect square is a number that is the product of a non-negative integer with itself. For example, the first five perfect squares are 0, 1, 4, 9 and 16.
How many subarrays are perfect? Two subarrays are different if they start or end at different indices in the array, even if the subarrays contain the same values in the same order.
Input
The first line of the input gives the number of test cases, T. T test cases follow. The first line of each test case contains the integer N. The second line contains N integers describing Cristobal's array. The i-th integer is Ai.
Output
For each test case, output one line containing Case #x: y, where x is the test case number (starting from 1) and y is the number of perfect subarrays.
Limits
- 1 ≤ T ≤ 100.
- -100 ≤ Ai ≤ 100, for all i.
Hint
In sample case #1, there is one perfect subarray: [2 2] whose sum is 22.
In sample case #2, there are three perfect subarrays:
[9], whose total sum is 32.[1], whose total sum is 12.[30 30 9 1 30], whose total sum is 102.
In sample case #3, there are nine perfect subarrays:
[4], whose total sum is 22.[4 0], whose total sum is 22.[4 0 0], whose total sum is 22.[0], whose total sum is 02.[0 0], whose total sum is 02.[0 0 16], whose total sum is 42.[0], whose total sum is 02.[0 16], whose total sum is 42.[16], whose total sum is 42.
Note: We do not recommend using interpreted/slower languages for the test set 2 of this problem.