Codility. Train. Brackets ★

A string S consisting of N characters is considered to be properly nested if any of the following conditions is true:

• S is empty;
• S has the form "(U)" or "[U]" or "{U}" where U is a properly nested string;
• S has the form "VW" where V and W are properly nested strings.

For example, the string "{[()()]}" is properly nested but "([)()]" is not.

Write a function:

int solution(char *S);

that, given a string S consisting of N characters, returns 1 if S is properly nested and 0 otherwise.

For example, given S = "{[()()]}", the function should return 1 and given S = "([)()]", the function should return 0, as explained above.

Assume that:

• N is an integer within the range [0..200,000];
• string S consists only of the following characters: "(", "{", "[", "]", "}" and/or ")".

Complexity:

• expected worst-case time complexity is O(N);
• expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Codility. Train. Number-of-disc-intersections ★★★

Given an array A of N integers, we draw N discs in a 2D plane such that the I-th disc is centered on (0,I) and has a radius of A[I]. We say that the J-th disc and K-th disc intersect if J ≠ K and J-th and K-th discs have at least one common point.

Write a function:

def solution(A)

that, given an array A describing N discs as explained above, returns the number of pairs of intersecting discs. For example, given N=6 and:

A[0] = 1  A[1] = 5  A[2] = 2 
A[3] = 1  A[4] = 4  A[5] = 0  

intersecting discs appear in eleven pairs of elements:

• 0 and 1,
• 0 and 2,
• 0 and 4,
• 1 and 2,
• 1 and 3,
• 1 and 4,
• 1 and 5,
• 2 and 3,
• 2 and 4,
• 3 and 4,
• 4 and 5.

so the function should return 11.

The function should return −1 if the number of intersecting pairs exceeds 10,000,000.

Assume that:

• N is an integer within the range [0..100,000];
• each element of array A is an integer within the range [0..2147483647].

Complexity:

• expected worst-case time complexity is O(N*log(N));
• expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.

Codility. Train. Max-product-of-three ★★

A non-empty zero-indexed 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 zero-indexed 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.

Assume that:

• 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].

Complexity:

• expected worst-case time complexity is O(N*log(N));
• expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.