Problem A non-empty array A consisting of N integers is given. A triplet (X, Y, Z), such that 0 ≤ X < Y < Z < N, is called a double slice. The sum of double slice (X, Y, Z) is the total of AX + 1 + AX + 2 + … + AY − 1 + AY + 1 + AY + 2 + … + AZ − 1. For example, array A such that: contains the…
Problem A non-empty array A consisting of N integers is given. The leader of this array is the value that occurs in more than half of the elements of A. An equi leader is an index S such that 0 ≤ S < N − 1 and two sequences A0, A1, …, AS and AS + 1, AS + 2, …, AN − 1 have leaders of the same value…
Problem An array A consisting of N integers is given. The dominator of array A is the value that occurs in more than half of the elements of A. For example, consider array A such that The dominator of A is 3 because it occurs in 5 out of 8 elements of A (namely in those with indices 0, 2, 4, 6 and…
Problem You are going to build a stone wall. The wall should be straight and N meters long, and its thickness should be constant; however, it should have different heights in different places. The height of the wall is specified by an array H of N positive integers. HI is the height of the wall from…
Problem A string S consisting of N characters is called properly nested if: S is empty; S has the form “(U)” where U is a properly nested string; S has the form “VW” where V and W are properly nested strings. For example, string ”(()(())())” is properly nested but string ”())” isn’t. Write a…
Problem You are given two non-empty arrays A and B consisting of N integers. Arrays A and B represent N voracious fish in a river, ordered downstream along the flow of the river. The fish are numbered from 0 to N − 1. If P and Q are two fish and P < Q, then fish P is initially upstream of fish Q…
Problem 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…
Problem An array A consisting of N integers is given. A triplet (P, Q, R) is triangular if 0 ≤ P < Q < R < N and: For example, consider array A such that: Triplet (0, 2, 4) is triangular. Write a function: that, given an array A consisting of N integers, returns 1 if there exists a triangular…
Problem We draw N discs on a plane. The discs are numbered from 0 to N − 1. An array A of N non-negative integers, specifying the radiuses of the discs, is given. The J-th disc is drawn with its center at (J, 0) and radius AJ. We say that the J-th disc and K-th disc intersect if J ≠ K and the J-th…
Problem A non-empty array A consisting of N integers is given. The product of triplet (P, Q, R) equates to AP _ AQ _ AR (0 ≤ P < Q < R < N). For example, array A such that: 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,…
Problem Write a function 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: the function should return 3, because there are 3 distinct values appearing in array A, namely 1, 2 and…
Problem A non-empty array A consisting of N integers is given. The consecutive elements of array A represent consecutive cars on a road. Array A contains only 0s and/or 1s: 0 represents a car traveling east, 1 represents a car traveling west. The goal is to count passing cars. We say that a pair of…
Problem A non-empty array A consisting of N integers is given. A pair of integers (P, Q), such that 0 ≤ P < Q < N, is called a slice of array A (notice that the slice contains at least two elements). The average of a slice (P, Q) is the sum of AP + AP + 1 + … + AQ divided by the length of the slice…
Problem A DNA sequence can be represented as a string consisting of the letters A, C, G and T, which correspond to the types of successive nucleotides in the sequence. Each nucleotide has an impact factor, which is an integer. Nucleotides of types A, C, G and T have impact factors of 1, 2, 3 and…
Problem Write a function: that, given three integers A, B and K, returns the number of integers within the range A..B that are divisible by K, i.e.: { i : A ≤ i ≤ B, i mod K = 0 } For example, for A = 6, B = 11 and K = 2, your function should return 3, because there are three numbers divisible by…
Problem A non-empty array A consisting of N integers is given. Array A represents numbers on a tape. Any integer P, such that 0 < P < N, splits this tape into two non-empty parts: The difference between the two parts is the value of: In other words, it is the absolute difference between the sum of…
Problem An array A consisting of N different integers is given. The array contains integers in the range 1..(N + 1), which means that exactly one element is missing. Your goal is to find that missing element. Write a function: that, given an array A, returns the value of the missing element. For…
Problem A non-empty array A consisting of N integers is given. A permutation is a sequence containing each element from 1 to N once, and only once. For example, array A such that: is a permutation, but array A such that: is not a permutation, because value 2 is missing. The goal is to check whether…
Problem An array A consisting of N integers is given. Rotation of the array means that each element is shifted right by one index, and the last element of the array is moved to the first place. For example, the rotation of array A = 3, 8, 9, 7, 6 is 6, 3, 8, 9, 7 (elements are shifted right by one…
Problem This is a demo task. Write a function: that, given an array A of N integers, returns the smallest positive integer (greater than 0) that does not occur in A. For example, given A = 1, 3, 6, 4, 1, 2, the function should return 5. Given A = 1, 2, 3, the function should return 4. Given A = −…
Problem You are given N counters, initially set to 0, and you have two possible operations on them: increase(X) − counter X is increased by 1, max counter − all counters are set to the maximum value of any counter. A non-empty array A of M integers is given. This array represents consecutive…
Problem A small frog wants to get to the other side of a river. The frog is initially located on one bank of the river (position 0) and wants to get to the opposite bank (position X+1). Leaves fall from a tree onto the surface of the river. You are given an array A consisting of N integers…
Problem A small frog wants to get to the other side of the road. The frog is currently located at position X and wants to get to a position greater than or equal to Y. The small frog always jumps a fixed distance, D. Count the minimal number of jumps that the small frog must perform to reach its…
Problem function solution(A); that, given an array A of N integers, returns the smallest positive integer (greater than 0) that does not occur in A. For example, given A = 1, 3, 6, 4, 1, 2, the function should return 5. Given A = 1, 2, 3, the function should return 4. Given A = −1, −3, the function…
Problem A non-empty array A consisting of N integers is given. The array contains an odd number of elements, and each element of the array can be paired with another element that has the same value, except for one element that is left unpaired. For example, in array A such that: the elements at…
Problem A binary gap within a positive integer N is any maximal sequence of consecutive zeros that is surrounded by ones at both ends in the binary representation of N. For example, number 9 has binary representation 1001 and contains a binary gap of length 2. The number 529 has binary…