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Binary Gap: Find longest sequence of zeros in binary representation of an integer.
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 representation 1000010001 and contains two binary gaps: one of length 4 and one of length 3. The number 20 has binary representation 10100 and contains one binary gap of length 1. The number 15 has binary representation 1111 and has no binary gaps.
Write a function:
class Solution { public int solution(int N); }that, given a positive integer N, returns the length of its longest binary gap. The function should return 0 if N doesn’t contain a binary gap.
For example, given N = 1041 the function should return 5, because N has binary representation 10000010001 and so its longest binary gap is of length 5.
- Assume that
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N is an integer within the range [1..2,147,483,647].
Complexity: expected worst-case time complexity is O(log(N)); expected worst-case space complexity is O(1).
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Odd Occurrences In Array: Find value that occurs in odd number of elements.
A non-empty zero-indexed 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:
A[0] = 9 A[1] = 3 A[2] = 9
A[3] = 3 A[4] = 9 A[5] = 7
A[6] = 9the elements at indexes 0 and 2 have value 9, the elements at indexes 1 and 3 have value 3, the elements at indexes 4 and 6 have value 9, the element at index 5 has value 7 and is unpaired. Write a function:
class Solution { public int solution(int[] A); }that, given an array A consisting of N integers fulfilling the above conditions, returns the value of the unpaired element.
For example, given array A such that:
A[0] = 9 A[1] = 3 A[2] = 9
A[3] = 3 A[4] = 9 A[5] = 7
A[6] = 9the function should return 7, as explained in the example above.
- Assume that
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N is an odd integer within the range [1..1,000,000]; each element of array A is an integer within the range [1..1,000,000,000]; all but one of the values in A occur an even number of times. Complexity:
expected worst-case time complexity is O(N); expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).
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Cyclic Rotation: Rotate an array to the right by a given number of steps. A zero-indexed 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 index and 6 is moved to the first place).
The goal is to rotate array A K times; that is, each element of A will be shifted to the right K times.
Write a function:
class Solution { public int[] solution(int[] A, int K); }that, given a zero-indexed array A consisting of N integers and an integer K, returns the array A rotated K times.
For example, given
A = [3, 8, 9, 7, 6]
K = 3the function should return [9, 7, 6, 3, 8]. Three rotations were made:
[3, 8, 9, 7, 6] -> [6, 3, 8, 9, 7]
[6, 3, 8, 9, 7] -> [7, 6, 3, 8, 9]
[7, 6, 3, 8, 9] -> [9, 7, 6, 3, 8]For another example, given
A = [0, 0, 0]
K = 1
the function should return [0, 0, 0]Given:
A = [1, 2, 3, 4]
K = 4
the function should return [1, 2, 3, 4]- Assume that
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N and K are integers within the range [0..100]; each element of array A is an integer within the range [−1,000..1,000]. In your solution, focus on correctness. The performance of your solution will not be the focus of the assessment.
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Frog Jump: Count minimal number of jumps from position X to Y. 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 target.
Write a function:
class Solution { public int solution(int X, int Y, int D); }that, given three integers X, Y and D, returns the minimal number of jumps from position X to a position equal to or greater than Y.
For example, given:
X = 10
Y = 85
D = 30the function should return 3, because the frog will be positioned as follows:
after the first jump, at position 10 + 30 = 40 after the second jump, at position 10 + 30 + 30 = 70 after the third jump, at position 10 + 30 + 30 + 30 = 100 Assume that::
X, Y and D are integers within the range [1..1,000,000,000]; X ≤ Y.
Complexity:
expected worst-case time complexity is O(1); expected worst-case space complexity is O(1).
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Perm Missing Element: Find the missing element in a given permutation. A zero-indexed 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:
class Solution { public int solution(int[] A); }that, given a zero-indexed array A, returns the value of the missing element.
For example, given array A such that:
A[0] = 2
A[1] = 3
A[2] = 1
A[3] = 5the function should return 4, as it is the missing element.
- Assume that
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N is an integer within the range [0..100,000]; the elements of A are all distinct; each element of array A is an integer within the range [1..(N + 1)]. Complexity:
expected worst-case time complexity is O(N); expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).
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Tape Equilibrium: Minimize the value |(A[0] + … + A[P-1]) - (A[P] + … + A[N-1])|.
A non-empty zero-indexed 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: A[0], A[1], …, A[P − 1] and A[P], A[P + 1], …, A[N − 1].
The difference between the two parts is the value of: |(A[0] + A[1] + … + A[P − 1]) − (A[P] + A[P + 1] + … + A[N − 1])|
In other words, it is the absolute difference between the sum of the first part and the sum of the second part.
For example, consider array A such that:
A[0] = 3
A[1] = 1
A[2] = 2
A[3] = 4
A[4] = 3We can split this tape in four places:
P = 1, difference = |3 − 10| = 7
P = 2, difference = |4 − 9| = 5
P = 3, difference = |6 − 7| = 1
P = 4, difference = |10 − 3| = 7Write a function:
class Solution { public int solution(int[] A); }that, given a non-empty zero-indexed array A of N integers, returns the minimal difference that can be achieved.
For example, given:
A[0] = 3
A[1] = 1
A[2] = 2
A[3] = 4
A[4] = 3the function should return 1, as explained above.
- Assume that
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N is an integer within the range [2..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); expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
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Permutation Check: Check whether array A is a permutation.
A non-empty zero-indexed 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:
A[0] = 4
A[1] = 1
A[2] = 3
A[3] = 2is a permutation, but array A such that:
A[0] = 4
A[1] = 1
A[2] = 3is not a permutation, because value 2 is missing.
The goal is to check whether array A is a permutation.
Write a function:
class Solution { public int solution(int[] A); }that, given a zero-indexed array A, returns 1 if array A is a permutation and 0 if it is not.
For example, given array A such that:
A[0] = 4
A[1] = 1
A[2] = 3
A[3] = 2the function should return 1.
Given array A such that:
A[0] = 4
A[1] = 1
A[2] = 3the function should return 0.
- Assume that
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N is an integer within the range [1..100,000]; each element of array A is an integer within the range [1..1,000,000,000]. Complexity:
expected worst-case time complexity is O(N); expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).
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Distinct: Compute number of distinct values in an array.
Write a function
class Solution { public int solution(int[] A); }that, given a zero-indexed array A consisting of N integers, returns the number of distinct values in array A.
- Assume that
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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]. 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] = 1the function should return 3, because there are 3 distinct values appearing in array A, namely 1, 2 and 3.
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).
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Triangle: Determine whether a triangle can be built from a given set of edges.
A zero-indexed 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] = 20Triplet (0, 2, 4) is triangular.
Write a function:
class Solution { public int solution(int[] A); }that, given a zero-indexed 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] = 20the function should return 1, as explained above. Given array A such that:
A[0] = 10 A[1] = 50 A[2] = 5
A[3] = 1the function should return 0.
- Assume that
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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]. 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).
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MaxProductOfThree: Maximize A[P] * A[Q] * A[R] for any triplet (P, Q, R).
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] = 6contains 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 = 60Your goal is to find the maximal product of any triplet.
Write a function:
class Solution { public int solution(int[] 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] = 6the function should return 60, as the product of triplet (2, 4, 5) is maximal.
- Assume that
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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).
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Number Of Disc Intersections: Compute the number of intersections in a sequence of discs.
We draw N discs on a plane. The discs are numbered from 0 to N − 1. A zero-indexed 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 A[J].
We say that the J-th disc and K-th disc intersect if J ≠ K and the J-th and K-th discs have at least one common point (assuming that the discs contain their borders).
The figure below shows discs drawn for N = 6 and A as follows:
A[0] = 1
A[1] = 5
A[2] = 2
A[3] = 1
A[4] = 4
A[5] = 0There are eleven (unordered) pairs of discs that intersect, namely:
discs 1 and 4 intersect, and both intersect with all the other discs; disc 2 also intersects with discs 0 and 3. Write a function:
class Solution { public int solution(int[] A); }that, given an array A describing N discs as explained above, returns the number of (unordered) pairs of intersecting discs. The function should return −1 if the number of intersecting pairs exceeds 10,000,000.
Given array A shown above, the function should return 11, as explained above.
- Assume that
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N is an integer within the range [0..100,000]; each element of array A is an integer within the range [0..2,147,483,647]. 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).
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Brackets: Determine whether a given string of parentheses (multiple types) is properly nested.
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:
class Solution { public int solution(String 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
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N is an integer within the range [0..200,000]; string S consists only of the following characters: "(", "{", "[", "]", "}" and/or ")".
- Complexity
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expected worst-case time complexity is O(N); expected worst-case space complexity is O(N) (not counting the storage required for input arguments).
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Nesting: Determine whether a given string of parentheses (single type) is properly nested.
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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 function:
class Solution { public int solution(String S); }that, given a string S consisting of N characters, returns 1 if string 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
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N is an integer within the range [0..1,000,000]; string S consists only of the characters "(" and/or ")".
- Complexity
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expected worst-case time complexity is O(N); expected worst-case space complexity is O(1) (not counting the storage required for input arguments).
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StoneWall: Cover "Manhattan skyline" using the minimum number of rectangles.
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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. H[I] is the height of the wall from I to I+1 meters to the right of its left end. In particular, H[0] is the height of the wall’s left end and H[N−1] is the height of the wall’s right end.
The wall should be built of cuboid stone blocks (that is, all sides of such blocks are rectangular). Your task is to compute the minimum number of blocks needed to build the wall.
Write a function:
class Solution { public int solution(int[] H); }that, given an array H of N positive integers specifying the height of the wall, returns the minimum number of blocks needed to build it.
For example, given array H containing N = 9 integers:
H[0] = 8 H[1] = 8 H[2] = 5
H[3] = 7 H[4] = 9 H[5] = 8
H[6] = 7 H[7] = 4 H[8] = 8the function should return 7. The figure shows one possible arrangement of seven blocks.
- Assume that
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N is an integer within the range [1..100,000]; each element of array H is an integer within the range [1..1,000,000,000].
- Complexity
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expected worst-case time complexity is O(N); expected worst-case space complexity is O(N), beyond input storage (not counting the storage required for input arguments).