Test results - Codility

Tasks Details

easy

1. CountTriangles

Count the number of triangles that can be built from a given set of edges.

100%

An array A consisting of N integers is given. A triplet (P, Q, R) is triangular if it is possible to build a triangle with sides of lengths A[P], A[Q] and A[R]. In other words, 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] = 12

There are four triangular triplets that can be constructed from elements of this array, namely (0, 2, 4), (0, 2, 5), (0, 4, 5), and (2, 4, 5).

Write a function:

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

that, given an array A consisting of N integers, returns the number of triangular triplets in this array.

For example, given array A such that:

A[0] = 10 A[1] = 2 A[2] = 5 A[3] = 1 A[4] = 8 A[5] = 12

the function should return 4, as explained above.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [0..1,000];

each element of array A is an integer within the range [1..1,000,000,000].

Solution

Programming language used Java 8

Time spent on task 1 minutes

Notes

not defined yet

Task timeline

Code: 01:52:16 UTC, java, verify, result: Passed

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import java.util.Arrays;

class Solution {
    
    // Encapsulation
    private int count = 0;
    private int[] A;

    public int solution(int[] A) {
        this.A = A;
        Arrays.sort(this.A);

        for (int p = 0; p < A.length - 2; p++) {

            int q = p + 1;
            int r = q + 1;

            while (q < A.length - 1) {
                if (r < A.length && isTriangular(p, q, r)) {
                    r++;
                } else {
                    count += (r - q - 1); // point
                    q++;
                }
            }
        }

        return count;
    }

    // abstraction
    private boolean isTriangular(int p, int q, int r) {
        return A[p] + A[q] > A[r] && A[q] + A[r] > A[p] && A[r] + A[p] > A[q];
    }
}

Analysis

▶

example
example, positive answer, length=6

✔

Code: 01:52:23 UTC, java, verify, result: Passed

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import java.util.Arrays;

class Solution {
    
    // Encapsulation
    private int count = 0;
    private int[] A;

    public int solution(int[] A) {
        this.A = A;
        Arrays.sort(this.A);

        for (int p = 0; p < A.length - 2; p++) {

            int q = p + 1;
            int r = q + 1;

            while (q < A.length - 1) {
                if (r < A.length && isTriangular(p, q, r)) {
                    r++;
                } else {
                    count += (r - q - 1); // point
                    q++;
                }
            }
        }

        return count;
    }

    // abstraction
    private boolean isTriangular(int p, int q, int r) {
        return A[p] + A[q] > A[r] && A[q] + A[r] > A[p] && A[r] + A[p] > A[q];
    }
}

Analysis

▶

example
example, positive answer, length=6

✔

Code: 01:52:28 UTC, java, final, score: 100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

import java.util.Arrays;

class Solution {
    
    // Encapsulation
    private int count = 0;
    private int[] A;

    public int solution(int[] A) {
        this.A = A;
        Arrays.sort(this.A);

        for (int p = 0; p < A.length - 2; p++) {

            int q = p + 1;
            int r = q + 1;

            while (q < A.length - 1) {
                if (r < A.length && isTriangular(p, q, r)) {
                    r++;
                } else {
                    count += (r - q - 1); // point
                    q++;
                }
            }
        }

        return count;
    }

    // abstraction
    private boolean isTriangular(int p, int q, int r) {
        return A[p] + A[q] > A[r] && A[q] + A[r] > A[p] && A[r] + A[p] > A[q];
    }
}

Analysis summary

The solution obtained perfect score.

Analysis

Detected time complexity:

O(N**2)

▶

example
example, positive answer, length=6

✔

▶

extreme_empty
empty sequence + [5,3,3]

✔

▶

extreme_single
1-element sequence + [5,3,3]

✔

▶

extreme_two_elems
2-element sequence + [5,3,3]

✔

▶

extreme_arith_overflow
overflow test, 3 MAXINTs + [5,3,3]

✔

▶

simple

✔

▶

medium1
chaotic sequence of values from [1..100K], length=30

✔

▶

medium2
chaotic sequence of values from [1..1K], length=50

✔

▶

large
chaotic sequence with values from [1..10], length=200

✔

▶

large2
1 followed by an ascending sequence of ~1K elements from [1..2K]

✔

▶

large_random
chaotic sequence of values from [1..1M], length=1K

✔

▶

large_the_same
sequence of the same value value

✔