elementary
1. SqlSum
Calculate sum of elements.
100%
Correctness
100%
Performance
Not assessed

Given a table elements with the following structure:

create table elements ( v integer not null )

write an SQL query that returns the sum of the numbers in column v.

For example, given:

v --- 2 10 20 10

Solution
Programming language used SQL (PostgreSQL)
Total time used 4 minutes
Effective time used 3 minutes
easy
Find and correct bugs in a function that finds a value that occurs in more than half of the elements of an array.
100%
Correctness
100%
Performance
Not assessed

A non-empty array A consisting of N integers and sorted in a non-decreasing order (i.e. A[0] ≤ A[1] ≤ ... ≤ A[N−1]) is given. The leader of this array is the value that occurs in more than half of the elements of A.

You are given an implementation of a function:

class Solution { public int solution(int[] A); }

that, given a non-empty array A consisting of N integers, sorted in a non-decreasing order, returns the leader of array A. The function should return −1 if array A does not contain a leader.

For example, given array A consisting of ten elements such that:

A[0] = 2 A[1] = 2 A[2] = 2 A[3] = 2 A[4] = 2 A[5] = 3 A[6] = 4 A[7] = 4 A[8] = 4 A[9] = 6

the function should return −1, because the value that occurs most frequently in the array, 2, occurs five times, and 5 is not more than half of 10.

Given array A consisting of five elements such that:

A[0] = 1 A[1] = 1 A[2] = 1 A[3] = 1 A[4] = 50

the function should return 1.

The attached code is still incorrect for some inputs. Despite the error(s), the code may produce a correct answer for the example test cases. The goal of the exercise is to find and fix the bug(s) in the implementation. You can modify at most three lines.

Assume that:

• N is an integer within the range [1..100,000];
• each element of array A is an integer within the range [0..2,147,483,647];
• array A is sorted in non-decreasing order.

In your solution, focus on correctness. The performance of your solution will not be the focus of the assessment.

Solution
Programming language used Java 8
Total time used 10 minutes
Effective time used 3 minutes
medium
3. Equi
Find an index in an array such that its prefix sum equals its suffix sum.
70%
Correctness
95%
Performance
18%

An array A consisting of N integers is given. An equilibrium index of this array is any integer P such that 0 ≤ P < N and the sum of elements of lower indices is equal to the sum of elements of higher indices, i.e.

A[0] + A[1] + ... + A[P−1] = A[P+1] + ... + A[N−2] + A[N−1].

Sum of zero elements is assumed to be equal to 0. This can happen if P = 0 or if P = N−1.

For example, consider the following array A consisting of N = 8 elements:

A[0] = -1 A[1] = 3 A[2] = -4 A[3] = 5 A[4] = 1 A[5] = -6 A[6] = 2 A[7] = 1

P = 1 is an equilibrium index of this array, because:

• A[0] = −1 = A[2] + A[3] + A[4] + A[5] + A[6] + A[7]

P = 3 is an equilibrium index of this array, because:

• A[0] + A[1] + A[2] = −2 = A[4] + A[5] + A[6] + A[7]

P = 7 is also an equilibrium index, because:

• A[0] + A[1] + A[2] + A[3] + A[4] + A[5] + A[6] = 0

and there are no elements with indices greater than 7.

P = 8 is not an equilibrium index, because it does not fulfill the condition 0 ≤ P < N.

Write a function:

def solution(A)

that, given an array A consisting of N integers, returns any of its equilibrium indices. The function should return −1 if no equilibrium index exists.

For example, given array A shown above, the function may return 1, 3 or 7, as explained above.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [0..100,000];
• each element of array A is an integer within the range [−2,147,483,648..2,147,483,647].