Backtracking

Given an integer array nums of unique elements, return all possible subsets (the power set). The solution set must not contain duplicate subsets. Return the solution in any order.

Given an integer num, repeatedly add all its digits until the result has only one digit, and return it.

You are painting a fence of n posts with k different colors. You must paint the posts following these rules: Every post must be painted exactly one color. There cannot be three or more consecutive posts with the same color. Given the two integers n and k, return the number of ways you can paint the fence.

RandomizedCollection is a data structure that contains a collection of numbers, possibly duplicates (i.e., a multiset). It should support inserting and removing specific elements and also reporting a random element. Implement the RandomizedCollection class: RandomizedCollection() Initializes the empty RandomizedCollection object. bool insert(int val) Inserts an item val into the multiset, even if the item is already present. Returns true if the item is not present, false otherwise. bool remove(int val) Removes an item val from the multiset if present. Returns true if the item is present, false otherwise. Note that if val has multiple occurrences in the multiset, we only remove one of them.

Given the API rand7() that generates a uniform random integer in the range [1, 7], write a function rand10() that generates a uniform random integer in the range [1, 10]. You can only call the API rand7(), and you shouldn't call any other API. Please do not use a language's built-in random API. Each test case will have one internal argument n, the number of times that your implemented function rand10() will be called while testing. Note that this is not an argument passed to rand10().

Suppose you have n integers labeled 1 through n. A permutation of those n integers perm (1-indexed) is considered a beautiful arrangement if for every i (1 <= i <= n), either of the following is true: perm[i] is divisible by i. i is divisible by perm[i]. Given an integer n, return the number of the beautiful arrangements that you can construct.

There is a group of n members, and a list of various crimes they could commit. The ith crime generates a profit[i] and requires group[i] members to participate in it. If a member participates in one crime, that member can't participate in another crime. Let's call a profitable scheme any subset of these crimes that generates at least minProfit profit, and the total number of members participating in that subset of crimes is at most n. Return the number of schemes that can be chosen. Since the answer may be very large, return it modulo 109 + 7.

You are installing a billboard and want it to have the largest height. The billboard will have two steel supports, one on each side. Each steel support must be an equal height. You are given a collection of rods that can be welded together. For example, if you have rods of lengths 1, 2, and 3, you can weld them together to make a support of length 6. Return the largest possible height of your billboard installation. If you cannot support the billboard, return 0.

Return the number of permutations of 1 to n so that prime numbers are at prime indices (1-indexed.) (Recall that an integer is prime if and only if it is greater than 1, and cannot be written as a product of two positive integers both smaller than it.) Since the answer may be large, return the answer modulo 10^9 + 7.

No-Zero integer is a positive integer that does not contain any 0 in its decimal representation. Given an integer n, return a list of two integers [a, b] where: a and b are No-Zero integers. a + b = n The test cases are generated so that there is at least one valid solution. If there are many valid solutions, you can return any of them.

Design an algorithm that accepts a stream of integers and retrieves the product of the last k integers of the stream. Implement the ProductOfNumbers class: ProductOfNumbers() Initializes the object with an empty stream. void add(int num) Appends the integer num to the stream. int getProduct(int k) Returns the product of the last k numbers in the current list. You can assume that always the current list has at least k numbers. The test cases are generated so that, at any time, the product of any contiguous sequence of numbers will fit into a single 32-bit integer without overflowing.

Write an API that generates fancy sequences using the append, addAll, and multAll operations. Implement the Fancy class: Fancy() Initializes the object with an empty sequence. void append(val) Appends an integer val to the end of the sequence. void addAll(inc) Increments all existing values in the sequence by an integer inc. void multAll(m) Multiplies all existing values in the sequence by an integer m. int getIndex(idx) Gets the current value at index idx (0-indexed) of the sequence modulo 109 + 7. If the index is greater or equal than the length of the sequence, return -1.

Given an m x n matrix, return a new matrix answer where answer[row][col] is the rank of matrix[row][col]. The rank is an integer that represents how large an element is compared to other elements. It is calculated using the following rules: The rank is an integer starting from 1. If two elements p and q are in the same row or column, then: If p q then rank(p) > rank(q) The rank should be as small as possible. The test cases are generated so that answer is unique under the given rules.

You are given an n x n integer matrix grid. Generate an integer matrix maxLocal of size (n - 2) x (n - 2) such that: maxLocal[i][j] is equal to the largest value of the 3 x 3 matrix in grid centered around row i + 1 and column j + 1. In other words, we want to find the largest value in every contiguous 3 x 3 matrix in grid. Return the generated matrix.

Given two positive integers num1 and num2, find the positive integer x such that: x has the same number of set bits as num2, and The value x XOR num1 is minimal. Note that XOR is the bitwise XOR operation. Return the integer x. The test cases are generated such that x is uniquely determined. The number of set bits of an integer is the number of 1's in its binary representation.

You are given two positive integers n and target. An integer is considered beautiful if the sum of its digits is less than or equal to target. Return the minimum non-negative integer x such that n + x is beautiful. The input will be generated such that it is always possible to make n beautiful.

Given an array of distinct integers candidates and a target integer target, return a list of all unique combinations of candidates where the chosen numbers sum to target. You may return the combinations in any order. The same number may be chosen from candidates an unlimited number of times. Two combinations are unique if the frequency of at least one of the chosen numbers is different. The test cases are generated such that the number of unique combinations that sum up to target is less than 150 combinations for the given input.

Given a collection of candidate numbers (candidates) and a target number (target), find all unique combinations in candidates where the candidate numbers sum to target. Each number in candidates may only be used once in the combination.

Given an array nums of distinct integers, return all the possible permutations. You can return the answer in any order.

Given an integer array nums that may contain duplicates, return all possible subsets (the power set). The solution set must not contain duplicate subsets. Return the solution in any order.

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

Given an m x n grid of characters board and a string word, return true if word exists in the grid. The word can be constructed from letters of sequentially adjacent cells, where adjacent cells are horizontally or vertically neighboring. The same letter cell may not be used more than once.

Given a string s, partition s such that every substring of the partition is a palindrome. Return all possible palindrome partitioning of s.

Given a string containing digits from 2-9 inclusive, return all possible letter combinations that the number could represent. Return the answer in any order. A mapping of digits to letters (just like on the telephone buttons) is given below. Note that 1 does not map to any letters.

The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other. Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order. Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space, respectively.