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Create a function that takes in a positive integer up to 10^9 and returns its prime factorization as a list of tuples, where each tuple consists of a prime number and its corresponding exponent. The prime factorization should be sorted in ascending order based on the prime numbers. Additionally, the function should opt...
codefeedback
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Write a Python program to find the group of three numbers in a list that has the greatest product. The list will contain both positive and negative integers, and may also contain zeroes. You may assume that the list will always have at least three elements. #Example: Input: [2, 3, -2, -3, 4, -5] Output: The group of t...
codefeedback
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I have this problem : Minimum Falling Path Sum II with Constraints Description are as below: Given a square grid of integers `arr`, a falling path with non-zero shifts is a choice of exactly one element from each row of `arr`, such that no two elements chosen in adjacent rows are in the same column. Additionally, the c...
codefeedback
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Write a recursive script to iterate over all elements in a list, and sum up all integers greater than 100. The script should also exclude any duplicates from the sum and only consider integers that are divisible by 7. Additionally, you should implement the script using tail recursion and ensure that it has a time compl...
codefeedback
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Find the maximum product of three numbers in an array, where at least one of the numbers must be negative. Return 0 if no such triplet exists. [1, -5, -6, 10, 20, 15]
codefeedback
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Devise a function that takes a mixed alphanumeric sequence as an input parameter and yields the aggregate of all the distinct numerical digits encompassed within the string. string = "a1b2c3d4e5"
codefeedback
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Create a Python Search Algorithm to search for a given number in a given sorted array. The algorithm should return the index of the first occurrence of the number if it exists in the array, or -1 if it does not. The algorithm should have a time complexity of O(log n), where n is the length of the array. The original a...
codefeedback
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Given a list of numbers, find and print the difference between the largest and smallest prime numbers in the list. Additionally, the program should sort the list in descending order before finding the difference. list_of_numbers = [10, 7, 5, 12, 4]
codefeedback
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Complete the given code: /* Given two vectors "operator", and "operand". The "operator" vector has advanced mathematical operations, and the "operand" vector contains floating point numbers. Construct a mathematical expression using the two vectors and return its result. The advanced mathematical operations include:...
codefeedback
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You are given a 2D matrix representing a grid of cells. Each cell in the grid contains a non-negative integer value. Your task is to write a function to find the maximum sum of a path from the top-left cell to the bottom-right cell, moving only right or down at each step. The value of each cell represents the score gai...
codefeedback
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Write a Python function to check if a number is perfect or not. A number is said to be a perfect number if the sum of its proper divisors is equal to itself. Proper divisors of a number are all the divisors excluding the number itself. Your function should take in a positive integer as input and return a boolean valu...
codefeedback
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You are given a list of integers. Your task is to write a Python function that takes this list as input and returns two separate lists: one containing all the even numbers that are divisible by 2, and the other containing all the odd numbers that are divisible by 3. The function signature is: ```python def find_divisi...
codefeedback
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Given a binary tree, write a function that finds the deepest node in the tree. The tree is represented by a root node, which contains a value and references to its left and right child nodes. The function should return the value of the deepest node. To solve this problem, you can use a depth-first search (DFS) algorit...
codefeedback
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In a game called The Race, two participants utilize an unbiased coin and alternate turns. During Player 1's turn, a single coin toss occurs. A Heads outcome awards Player 1 a point, while a Tails outcome yields no points. Player 2's turn involves selecting a positive integer, $T$, and tossing the coin $T$ times. If all...
codefeedback
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You are given an array A of integers. Your task is to find the sum of bitwise XOR operations between all pairs of distinct elements in A, multiplied by the frequency of each element in the array. Write a function `xor_sum_with_frequency(A)` that takes in an array of integers A and returns the sum as described above. ...
codefeedback
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Sort the given array of numbers from least to greatest. The sorted array should also have the even numbers before the odd numbers. Additionally, you are not allowed to use any built-in sorting functions or libraries. [11, 5, 9, 3, 6]
codefeedback
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I am faced with this challenge: Minimizing the Quantity of Squares to Tile a Rectangle. The problem is defined as follows: Given a rectangular area with dimensions `n` x `m`, determine the least number of squares with integer sides required to completely tile the given rectangle. Additionally, provide the dimensions of...
codefeedback
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Develop a function in Java that accepts two arguments. The first one is an ArrayList containing 'n' number of integers, and the second one should be a 2D-array containing 'n' number of integer pairs. Each pair represents a range index of the array. The function should calculate the maximum value from each given range a...
codefeedback
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Write a JavaScript program to find the sum of an array of numbers using a recursive function. The function should take an array of numbers as input and return the sum of all the numbers in the array. The input array can have a maximum length of 10000. The time complexity of the solution should be O(n), where n is the l...
codefeedback
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Increase the difficulty of the given programming test question by modifying the task to include both potential swaps and the number of necessary swaps to correct the order: Complete the following code: def can_arrange(arr): """Create a function that returns a dictionary containing the largest index of an element ...
codefeedback
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Create an algorithm that sorts a given list of numbers in descending order and has a time complexity of O(nlogn). Given an input list of numbers, the algorithm should sort the list in descending order using the Merge Sort algorithm. 1. Divide the input list into two halves, creating left and right sublists. 2. Recurs...
codefeedback
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Reverse the following list of numbers and return a new list with only the prime numbers reversed.
codefeedback
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Create an algorithm for finding the k smallest elements in an array. The algorithm should also be able to handle duplicate values in the array. Additionally, the algorithm should be able to handle negative numbers and zero. The algorithm should not use any built-in sort functions and should have a time complexity bette...
codefeedback
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Generate a Fibonacci sequence with a given length that only contains prime numbers. length = 10
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Parse the string and return the number of unique alphabets in the string. The input string can contain both lowercase and uppercase letters. Return the count of unique alphabets in a case-insensitive manner. Example: Input: "Apple" Output: 4 Input: "Mississippi" Output: 4
codefeedback
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You are given a string `s` of length `n`. Your task is to write a function or method to find the length of the shortest substring that can be repeated to form the original string. If no such substring exists, return 0. For example, given the string "abcabcabc", the shortest repeating substring is "abc", and its length...
codefeedback
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Given two text strings s and t, determine the maximal length of the identical non-overlapping substring sequence shared by these two. Strings may include lower and uppercase letters, numbers and special characters. s = "abcde1234" t = "acfgh#1234"
codefeedback
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Create a C++ program that sorts a given array in descending order, using the bubble sort algorithm. The input array will contain integers ranging from -1000 to 1000, and may contain duplicate values. The program should handle arrays with up to 100,000 elements efficiently. The program should also include a function to ...
codefeedback
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Print all the permutations of a given list of integers, where the length of the list is n and the maximum value in the list is m. The time complexity of the solution should be O(n!*m^n), and the space complexity should be O(n!).
codefeedback
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Create an algorithm to check if a binary tree is univalued and strictly increasing, where the nodes in the tree store positive integers and the univalued property means that all nodes in the tree have the same integer value. Additionally, the algorithm should find and return the number of distinct values present in the...
codefeedback
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Given the code snippet below, identify and correct errors and then improve and optimize this Java program that attempts to implement a binary search on a sorted array of integers. The program expects an array of integers and an integer as input, and should return the index of the element in the sorted array. If the ele...
codefeedback
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Generate a list of prime numbers between two numbers A and B (both inclusive) using a segmented sieve algorithm. The time complexity should be less than O((B-A+1)log(log(B))).
codefeedback
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I have this problem : Palindrome Removal Description are as below: Given an integer array `arr`, in one move you can select a palindromic subarray `arr[i], arr[i+1], ..., arr[j]` where `i <= j`, and remove that subarray from the given array. Note that after removing a subarray, the elements on the left and on the right...
codefeedback
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Given two strings, create a function to find the total number of non-overlapping occurrences of the second string in the first string. In addition to this, the function should be able to handle special characters and be case-insensitive. Extend this task by optimizing your function to perform with a time complexity no...
codefeedback
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Given two lists of integers, find all the common elements between them and return them in sorted order. The input lists can contain duplicate elements. The common elements should not include any duplicates. Additional requirements: - The solution should not use any built-in sorting functions or data structures. - The ...
codefeedback
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I have this problem : Reverse Nodes in k-Group with additional operations and constraints Description are as below: Given a linked list, reverse the nodes of a linked list k at a time and return its modified list. Additionally, after every k groups, insert a new node with a value equal to the sum of the last k nodes. ...
codefeedback
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You are tasked with implementing the insertion sort algorithm to sort an array of integers in non-decreasing order. The insertion sort algorithm works by iteratively building a sorted portion of the array, one element at a time. At each iteration, the algorithm takes the next unsorted element and inserts it into its co...
codefeedback
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You are given an array of integers and the task is to create a function that returns the maximum pairwise product of those numbers. However, the function should have a time complexity of O(n log n), where n is the length of the array.
codefeedback
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Write a C program that uses bitwise operators to perform the following operations on an integer: 1. Set the Nth bit to 1. 2. Clear the Nth bit (set it to 0). 3. Toggle the Nth bit (flip its value from 0 to 1 or from 1 to 0). 4. Rotate the bits of the integer to the right by N positions. The program should take two inp...
codefeedback
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Given a list of numbers, write a function to determine if the list is an arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. Additionally, the first and last numbers in the list should also be divisible by the common difference. Yo...
codefeedback
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The conjecture put forth by Christian Goldbach postulated that every odd composite number can be expressed as the sum of a prime number and twice a perfect square. \begin{align} 9 = 7 + 2 \times 1^2\\ 15 = 7 + 2 \times 2^2\\ 21 = 3 + 2 \times 3^2\\ 25 = 7 + 2 \times 3^2\\ 27 = 19 + 2 \times 2^2\\ 33 = 31 + 2 \times 1^...
codefeedback
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You are given a 2D grid representing a maze with '.' representing empty spaces and '#' representing walls. Additionally, there are portals in the maze that can transport you to another location within the maze. Each portal is represented by a pair of matching letters (e.g., 'ab', 'cd', etc.). When you step on one lette...
codefeedback
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Write a function to find the maximum difference between two prime numbers in a given array. The array can contain positive and negative integers, and can be unsorted. Additionally, the function should handle arrays of any length. The function should return the maximum difference as an absolute value. For example, for t...
codefeedback
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Create a program to find the largest common factor in two numbers within a given range. The program should take three inputs: the two numbers (N1 and N2), and the range (R). The program should find the largest common factor of N1 and N2 that is within the range of 1 to R. If there is no common factor within the range, ...
codefeedback
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You are tasked with the operation of a Ferris Wheel, specifically a Centennial Wheel, which is equipped with four gondolas, each capable of accommodating up to four individuals. The rotation of the gondolas in a counterclockwise direction incurs a cost to you, denoted as `runningCost` dollars. You are provided with an...
codefeedback
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Provide an answer to the following question: What is the maximum size of a multidimensional array in Java, given that each dimension must have a size greater than or equal to 1 and less than or equal to 1000?
codefeedback
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Generate an array of all the prime numbers that are less than 1000, but exclude the numbers 2, 3, 5, and 7 from the array.
codefeedback
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Given an assortment of integral numbers, determine the maximal length of the continuously augmenting sequence within this numeric assortment. Array = [2, 3, 5, 4, 7, 9, 6, 8]
codefeedback
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Design a solution in JavaScript to find the kth smallest element in an unsorted array. The array may contain duplicate numbers as well. Additionally, you are not allowed to use any sorting algorithms or built-in JavaScript functions to solve this problem. If the kth smallest element does not exist in the array, return ...
codefeedback
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Produce the following output given the list of numbers, ensuring that the program can handle duplicate numbers and outputs the numbers in ascending order. Additionally, the program should exclude any numbers that are divisible by 3 and contain the digit '7'. The program should also calculate the average of all the numb...
codefeedback
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Given a binary tree, write a recursive function to find the sum of all the nodes in the tree. Additionally, determine and return the maximum value among all the nodes in the tree. The function should have a time complexity of O(n), where n is the number of nodes in the tree. The function should also use constant space,...
codefeedback
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Find the number of times a letter appears in a string, ignoring case sensitivity. The string may contain alphanumeric characters, spaces, and special characters. The letter can be a single character or a substring. Return the count of occurrences as well as the indices at which the letter/substring appears in the strin...
codefeedback
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Write a code to find the first 15 terms of the Fibonacci sequence in Java, but with the following additional constraints: 1. Your code should use a recursive function to calculate the Fibonacci sequence. 2. The time complexity of your code should be O(2^n), where n is the input number. 3. Your code should handle negat...
codefeedback
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The function $g$ is defined for all positive integers as follows: \begin{align*} g(1) &amp;= 1\\ g(3n) &amp;= 3g(n)\\ g(3n+1) &amp;= 3n+1 + 3g(n)+\tfrac 1n g(n) \end{align*} It can be proven that $g(n)$ is integer for all values of $n$. The function $T(n)$ is defined as $T(n) = \displaystyle \sum_{i=1}^n g(i) ^3$. For...
codefeedback
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You are given a grid of size m x n, where each cell contains a non-negative integer value. You are initially positioned at the top-left cell and are required to reach the bottom-right cell. You can only move either down or right at any point in time. Additionally, you need to find the minimum sum of values along a path...
codefeedback
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Compare two given arrays and find the common elements present in both, while maintaining the relative order of the elements. Additionally, the solution should handle duplicate elements and remove them from the final result. arr1 = [1, 2, 3, 5, 5, 7, 7, 8, 9], arr2 = [3, 5, 7, 8] Additional Requirements: 1. The time c...
codefeedback
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Consider the function $d(k)$ which represents the sum of all divisors of $k$. We then define another function $S(N) = \sum_{i=1}^N \sum_{j=1}^Nd(i \cdot j)$. As an illustration, $S(3) = d(1) + d(2) + d(3) + d(2) + d(4) + (6) + d(3) + d(6) + d(9) = 59$. It is known that $S(10^3) = 563576517282$ and $S(10^5) \bmod 10^9 =...
codefeedback
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&lt;p&gt; Consider the function $D(n)$, which represents the $n$-th positive integer whose digit sum is a prime number.&lt;br&gt; As an illustration, $D(61) = 157$ and $D(10^8) = 403539364$ are given.&lt;/p&gt; &lt;p&gt; Your task is to compute the value of $D(10^{16})$.&lt;/p&gt;
codefeedback
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Write a code to extract the length of the longest sentence in a given text Text: The quick brown fox jumps over the lazy dog. The quick fox jumped over the lazy dog.
codefeedback
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Create a function that finds the length of the longest substring that does not contain duplicate characters. The function should handle cases where the input string contains non-alphabetic characters and return an error message for such cases. Additionally, the function should ignore duplicate characters that are withi...
codefeedback
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Write a Python function that takes in two parameters: a list of integers and a specific integer value. The function should return the index of the last occurrence of the value in the list. If the value is not found in the list, the function should return -1. Example: Input: [1, 2, 3, 4, 5, 4], 4 Output: 5 Note: You s...
codefeedback
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I am facing a challenge titled "Number of Islands". The problem is described as follows: You are given a two-dimensional binary grid, `grid`, of dimensions `m x n`. This grid is a representation of a map where `&#39;1&#39;` signifies land and `&#39;0&#39;` denotes water. Your task is to calculate and return the total n...
codefeedback
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Generate a C# code for searching an element in a sorted array of integers using binary search algorithm. The code should handle cases where the array contains duplicate elements and return the index of the first occurrence of the target element. The search function should have a time complexity of O(log n) and should b...
codefeedback
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I have this problem : Random Pick Index with Weighted Probability Description are as below: Given an integer array `nums` with possible duplicates, randomly output the index of a given `target` number. You can assume that the given target number must exist in the array. However, the probability of picking an index shou...
codefeedback
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Implement a recursive algorithm to count the number of elements that are divisible by k, have a remainder of 1 when divided by m, and are greater than or equal to n in a two-dimensional array. The array will contain positive integers only. Each subarray in the two-dimensional array should have a length greater than or ...
codefeedback
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Write a Python function that prints the frequencies of even and odd numbers in a given array, and also the frequencies of negative and positive numbers in the array. The array can contain both positive and negative integers. The function should also return the two most frequent even numbers and the two most frequent o...
codefeedback
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Please complete the following code with added difficulty: def make_a_pile(n, pattern): """ Given a positive integer n, you have to make a pile of n levels of stones. The first level has n stones. The number of stones in the next level is determined by the given pattern 'odd' or 'even': - If pat...
codefeedback
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Calculate the total sum of all even numbers that are divisible by 4 in a given list using an accumulator pattern. If there are no even numbers divisible by 4 in the list, return -1. numbers = [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
codefeedback
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Create an algorithm to find the smallest positive integer not present in an array. The array can contain both positive and negative numbers. The algorithm should have a time complexity of O(n) and a space complexity of O(1). If no positive integer is missing, the algorithm should return the smallest positive integer gr...
codefeedback
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For a given array of integers, write a function to find the mean. However, your solution must have a time complexity of O(n) and a space complexity of O(1). Additionally, you are not allowed to use any built-in functions or libraries to calculate the mean. The input array can contain up to 10^6 integers. You are not a...
codefeedback
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Given a string, write a code to find the length of the longest substring that contains exactly k unique characters and print its length. Example: Input: "abacabad", k = 3 Output: 4 Explanation: The longest substring with exactly three unique characters is "abad", which has a length of 4. Note: - The input string can ...
codefeedback
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Consider a sequence $g(n)$, which is defined as follows: $g(4) = 13$ and $g(n) = g(n-1) + \gcd(n, g(n-1))$ for $n \gt 4$. The sequence begins as follows: $n$4567891011121314151617181920... $g(n)$1314161718272829303132333451545560... Given the information that $g(1\,000) = 2524$ and $g(1\,000\,000) = 2624152$, your ta...
codefeedback
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Create a function in Python which takes an integer n and an unsorted list of numbers as input and returns the nth smallest number in the list, where n is guaranteed to be less than or equal to the number of unique elements in the list. Requirements: - The function should have a time complexity of O(n log m), where n i...
codefeedback
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A specific educational institution incentivizes students with monetary rewards for maintaining consistent attendance and punctuality. However, the reward is forfeited if the student is absent for a continuous span of three days or is tardy more than once. During a period of n days, a trinary sequence is generated for ...
codefeedback
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You are given a Python code snippet that defines a function `sums(length, total_sum)`. Your task is to complete the implementation of the `sums` function. The function should return a list of all combinations of `length` integers that sum up to `total_sum`. The integers in the combinations should range from 1 to `k` (i...
codefeedback
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Consider a function $T(r)$ which represents the count of integer quadruplets $x, y, z, t$ that satisfy the inequality $x^2 + y^2 + z^2 + t^2 \le r^2$. Essentially, $T(r)$ denotes the quantity of lattice points within a four-dimensional hyperball with radius $r$. Given the values $T(2) = 89$, $T(5) = 3121$, $T(100) = 49...
codefeedback
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Sort this numeric array in descending order Array: [3, 7 ,1, 5, 9]
codefeedback
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You are given a list of distinct positive integers representing different coin denominations and a target amount of money. Your task is to write a function to compute the number of combinations that make up that amount using the coins. You may assume that you have an infinite number of each kind of coin. Write a Pytho...
codefeedback
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I have this problem : Rotate List Description are as below: Given the `head` of a linked list, rotate the list to the right by `k` places. Additionally, return the sum of the last `k` nodes. Example 1: Input: head = [1,2,3,4,5], k = 2 Output: [4,5,1,2,3], Sum = 9 Example 2: Input: head = [0,1,2], k = 4 Output: [2,0,1...
codefeedback
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You are tasked with implementing a function that calculates the total number of unique ways to climb a staircase. You are given a set of distinct steps that can be taken at a time, and the staircase has a total of n steps. You can climb the staircase by taking one or more steps at a time, and the order in which you tak...
codefeedback
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Given a numeric array and a length, find the longest increasing subsequence in the array. Array: [3, 4, 1, 5, 10, 9, 8, 11] Length: 8
codefeedback
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Create a function that will find the maximum length of strictly increasing subarray in a list, where the elements must be in non-decreasing order. The list may contain duplicate elements. The function should handle both positive and negative integers. The length of the list should be at least 5. In addition to the abo...
codefeedback
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Write code to find the smallest number in an array of numbers, without using any built-in functions or methods. Additional requirements: 1. The solution should have a time complexity of O(n), where n is the number of elements in the array. 2. The solution should handle negative numbers in the array. 3. The solution sh...
codefeedback
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Create a function to find the total number of unique vowels in a series of strings. The strings can contain both lowercase and uppercase letters. Ignore any non-alphabetic characters in the strings. Requirements: 1. The function should be case-insensitive when counting the vowels. For example, 'a' and 'A' should be co...
codefeedback
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Take a list of numbers and remove the numbers that are greater than 100 and less than 1000. Additionally, sort the remaining numbers in descending order. numbers = [1, 20, 300, 4000, 50000, 600000, 7000000, 80000000, 900000000, 1000000000, 11000000000, 120000000000, 1300000000000, 14000000000000, 150000000000000] Con...
codefeedback
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In a linear arrangement, there exist $N$ positions. $N$ individuals sequentially occupy these positions adhering to the subsequent guidelines: If any position exists whose neighboring positions are vacant, such a position is occupied. If no such position exists and there is a position with only one neighboring position...
codefeedback
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I have this problem : Number of Sub-arrays With Odd Sum and Even Product Description are as below: Given an array of integers `arr`. Return the number of sub-arrays with odd sum and even product. As the answer may grow large, the answer must be computed modulo `10^9 + 7`. Example 1: Input: arr = [1,3,5] Output: 2 Exp...
codefeedback
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Develop an algorithm implementing bubble sort technique to organize numerical elements within a list in ascending order. [3,1,5,4,2]
codefeedback
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Given a string, remove any duplicate characters and sort the remaining characters in ascending order. input_string = "aaabbbccc"
codefeedback
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Write a C++ program to generate the Fibonacci numbers up to a maximum of n values. However, instead of using an iterative approach, you are required to use a matrix exponentiation approach to calculate the Fibonacci sequence. The matrix exponentiation approach involves using a matrix multiplication technique to raise...
codefeedback
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Given a list of numbers, determine whether each number is a perfect square or not. Return a new list with the corresponding results. # Example ## Input [1, 2, 3, 4] ## Output [True, False, False, True] # Constraints - The input list can contain up to 10^5 integers. - Each integer in the list will be between 1 and 1...
codefeedback
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Find the three smallest prime numbers in an array such that their sum is equal to a given value and their product is also a prime number. The array will only contain positive integers. array = [7, 2, 9, 3, 5, 11] value = 15
codefeedback
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You are presented with a challenge involving an advanced race car. This car begins at position 0 with a speed of +1 on an infinite number line, and it can also traverse negative positions. The car operates automatically based on a series of commands: A (accelerate), R (reverse), and B (brake). Upon receiving an "A" c...
codefeedback
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I have this problem : Advanced Similar String Groups Description are as below: Two strings `X` and `Y` are similar if we can swap two letters (in different positions) of `X`, so that it equals `Y`. Also two strings `X` and `Y` are similar if they are equal. For example, `&#34;tars&#34;` and `&#34;rats&#34;` are simila...
codefeedback
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You are given a list `ls` of integers representing the heights of walls at different positions. Your task is to find the maximum volume of water that can be trapped between the walls. The width of each wall is 1 unit. Write a function `max_trapped_water(ls)` that takes in the list of wall heights and returns the maxim...
codefeedback
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Estimate the complexity (Big-O) of this algorithm. arr = [3, 4, 7, 5, 6] def find_average(arr): total = 0 for num in arr: total += num num_squared = num ** 2 # additional requirement: calculate the square of each number return total / len(arr)
codefeedback
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Compute the sum of all prime numbers between 1 and 50.
codefeedback
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You are given an array `nums` of integers. Your task is to write a function `checkPossibility(nums)` that modifies the array in one move to make it a non-decreasing array. A non-decreasing array is an array where `nums[i] <= nums[i + 1]` for all `i`. You need to determine if it's possible to make the array non-decreasi...
codefeedback
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Generate a python program to solve the Tower of Hanoi problem with n discs
codefeedback
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Construct a function to detect if a binary tree is balanced. A binary tree is balanced if the heights of the two subtrees of any node never differ by more than 1. ## Input: - The root of a binary tree. ## Output: - Return True if the binary tree is balanced, False otherwise. ## Example: ```python tree = TreeNode(3)...
codefeedback
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