All Tracks Math Problem

Palindromic Sum
Tag(s):

FFT, Math, Medium-Hard

Problem
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Given an array $$A$$ of length $$N$$, find the number of non empty sub-arrays such that sum of all the elements in the sub-array is a palindrome. In other words, you have to find number of pairs $$(i,\;j)$$ such that $$\sum_{x=i}^j A_x$$ is a palindrome where $$(1 \le i \le j \le N)$$.

Input Format:
First line contains an integer, $$N$$ $$(1 \le N \le 5 * 10^5)$$. Second line contains $$N$$ space separated integers, $$A_i$$ $$(1 \le A_i \le 2 * 10^6)$$, elements of the array $$A$$. The sum of all the elements in the array is in the range $$[1, 2 * 10^6]$$.

Output Format:
Print an integer, number of non empty sub-arrays such that sum of all the elements in the sub-array is a palindrome.

SAMPLE INPUT
4
10 1 12 3

SAMPLE OUTPUT
3
Explanation

The 3 sub-arrays are $$(10,\;1)$$, $$(1)$$ and $$(3)$$.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

HackerEarth Collegiate Cup - Mirror Round

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