Lesson 6: Sorting

1. Distinct

Instructions

Write a function

def solution(A)

that, given an array A consisting of N integers, returns the number of distinct values in array A.

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

 A[0] = 2    A[1] = 1    A[2] = 1
 A[3] = 2    A[4] = 3    A[5] = 1
the function should return 3, because there are 3 distinct values appearing in array A, namely 1, 2 and 3.

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 [−1,000,000..1,000,000].

My Answer

def solution(A):
    return len(set(A))

Score

• Time Complexity: O(N*log(N)) or O(N)
• Total Score: 100

2. MaxProductOfThree

Instructions

A non-empty array A consisting of N integers is given. The product of triplet (P, Q, R) equates to A[P] * A[Q] * A[R] (0 ≤ P < Q < R < N).

For example, array A such that:

  A[0] = -3
  A[1] = 1
  A[2] = 2
  A[3] = -2
  A[4] = 5
  A[5] = 6
contains the following example triplets:

(0, 1, 2), product is −3 * 1 * 2 = −6
(1, 2, 4), product is 1 * 2 * 5 = 10
(2, 4, 5), product is 2 * 5 * 6 = 60
Your goal is to find the maximal product of any triplet.

Write a function:

def solution(A)

that, given a non-empty array A, returns the value of the maximal product of any triplet.

For example, given array A such that:

  A[0] = -3
  A[1] = 1
  A[2] = 2
  A[3] = -2
  A[4] = 5
  A[5] = 6
the function should return 60, as the product of triplet (2, 4, 5) is maximal.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [3..100,000];
each element of array A is an integer within the range [−1,000..1,000].

My Answer

from heapq import nsmallest, nlargest

def solution(A):
    a, b = nsmallest(2, A)
    z, y, x = nlargest(3, A)
    return max(a*b*z, x*y*z)

Score

• Time Complexity: O(N*log(N)) or O(N)
• Total Score: 100
• Note: I definitely cheated on this one. I had absolutely no idea you could import basic libraries on Codility so my time complexity was very high using loops.

2. Triangle

Instructions

An array A consisting of N integers is given. A triplet (P, Q, R) is triangular if 0 ≤ P < Q < R < N and:

A[P] + A[Q] > A[R],
A[Q] + A[R] > A[P],
A[R] + A[P] > A[Q].
For example, consider array A such that:

  A[0] = 10    A[1] = 2    A[2] = 5
  A[3] = 1     A[4] = 8    A[5] = 20
Triplet (0, 2, 4) is triangular.

Write a function:

def solution(A)

that, given an array A consisting of N integers, returns 1 if there exists a triangular triplet for this array and returns 0 otherwise.

For example, given array A such that:

  A[0] = 10    A[1] = 2    A[2] = 5
  A[3] = 1     A[4] = 8    A[5] = 20
the function should return 1, as explained above. Given array A such that:

  A[0] = 10    A[1] = 50    A[2] = 5
  A[3] = 1
the function should return 0.

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].

My Answer

def solution(A):
    A.sort()

    for n in range(len(A)-2):
        if A[n] + A[n+1] > A[n+2]:
            return 1
    
    return 0

Score

• Time Complexity: O(N*log(N))
• Total Score: 100

4. NumberOfDiscIntersections

Wow I do not understand the task at all? Come back later?