All Tracks Algorithms Sorting Problem

Sum of Digits
Tag(s):

Ad-Hoc, Easy, approved

Problem
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You are given an array of N distinct numbers. Now, we call the Digit Value of a number to be the sum of its digits..

Now, a subset is a set of not-necessarily-contiguous array elements. We call the value of a set to be the the maximum over the Digit Value of all elements it contains.

Now, you need to find the summation of the values of all \(2^{N}-1\) non-empty subsets of this array. As the answer can be rather large, print it Modulo \( 10^9+7 \). Can you do it ?

Input Format :

The first line contains a single integer N. The next line contains N space separated integers, where the \(i^{th}\) integer denotes \(A[i]\).

Output Format :

Print the summation of the value of each non-empty subset of the given array Modulo \(10^9+7\).

Constraints :

\( 1 \le N \le 10^{5} \)

\( 0 \le A[i] \le 10^{18} \)

SAMPLE INPUT
3
10 20 30
SAMPLE OUTPUT
17
Explanation

The subsets of this array and their values are :

  1. (10) : 1

  2. (20) : 2

  3. (30) : 3

  4. (10,20) : 2

  5. (10, 30) : 3

  6. (20,30) : 3

  7. (10,20,30 ) : 3

Thus, the final answer is \( (1+2+3+2+3+3+3 ) \) = \(17\)

Time Limit: 1.0 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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Accolite

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Accolite Java Developer Hiring Challenge

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