Blog_Home Patterns

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Important data structures

# Heaps | Priority Queue

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Techniques

# Backtracking [31/10/2021]

Definition

Backtracking is a method of solving any algorithmic problem that involves going through all the possible combinations of a solution and picking the valid ones. Best example to think of in visual terms is Depth first search in a Binary tree.

Note: Recursion is usually involved in backtracking

All backtracking type of problems generally will involve two steps:

1. generating all possible subsets/candidates for solution.
2. finding/extracting valid solutions out of it.

Optional: Optimization involves remiving unnecessary branches created under generation subset step.

_Examples_ :

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

• Given a directed acyclic graph (DAG) of n nodes labeled from 0 to n - 1, find all possible paths from node 0 to node n - 1 and return them in any order. [Learned]

  Note: When processing DAG, remember that everything will point to an empty location with no further nodes, i.e: [] element, also remember, no cycles in the graph.

• You have n tiles, where each tile has one letter tiles[i] printed on it.

  Return the number of possible non-empty sequences of letters you can make using the letters printed on those tiles. [Learned]

• A happy string is a string that:

  • consists only of letters of the set ['a', 'b', 'c'].
  • s[i] != s[i + 1] for all values of i from 1 to s.length - 1 (string is 1-indexed).

  For example, strings "abc", "ac", "b" and "abcbabcbcb" are all happy strings and strings "aa", "baa" and "ababbc" are not happy strings.

  Given two integers n and k, consider a list of all happy strings of length n sorted in lexicographical order.

  Return the kth string of this list or return an empty string if there are less than k happy strings of length n. [Solved]

• Given a string s, we can transform every letter individually to be lowercase or uppercase to create another string.

  Return a list of all possible strings we could create. You can return the output in any order. [Solved]

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

• 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. [Learned]

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

• In a gold mine grid of size m x n, each cell in this mine has an integer representing the amount of gold in that cell, 0 if it is empty.

  Return the maximum amount of gold you can collect under the conditions:

  • Every time you are located in a cell you will collect all the gold in that cell.
  • From your position, you can walk one step to the left, right, up, or down.
  • You can't visit the same cell more than once.
  • Never visit a cell with 0 gold.
  • You can start and stop collecting gold from any position in the grid that has some gold.

• 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. [Learned]

• Find all valid combinations of k numbers that sum up to n such that the following conditions are true:

  • Only numbers 1 through 9 are used.
  • Each number is used at most once.

  Return a list of all possible valid combinations. The list must not contain the same combination twice, and the combinations may be returned in any order. [Solved]

• Given an array of strings nums containing n unique binary strings each of length n, return a binary string of length n that does not appear in nums. If there are multiple answers, you may return any of them. [Solved but may need to optimize]

• You are given an integer array jobs, where jobs[i] is the amount of time it takes to complete the ith job.

  There are k workers that you can assign jobs to. Each job should be assigned to exactly one worker. The working time of a worker is the sum of the time it takes to complete all jobs assigned to them. Your goal is to devise an optimal assignment such that the maximum working time of any worker is minimized.

  Return the minimum possible maximum working time of any assignment. [Learned]

  Note: Creating all possible combinations of valid scenarios is the key. optimization involves removing unnecessary branches.

  This is a NP-complete problem, i.e solution is obtained in polynomial time.

• Given an integer array nums and an integer k, return true if it is possible to divide this array into k non-empty subsets whose sums are all equal. [Learned]

  Note: need different type of optimization here because the result is a binary form of either true or false and not a collection from k^n to k*2^n

• [1774. Closest Dessert Cost] You would like to make dessert and are preparing to buy the ingredients. You have n ice cream base flavors and m types of toppings to choose from. You must follow these rules when making your dessert:

  • There must be exactly one ice cream base.
  • You can add one or more types of topping or have no toppings at all.
  • There are at most two of each type of topping.

  You are given three inputs:

  • baseCosts, an integer array of length n, where each baseCosts[i] represents the price of the ith ice cream base flavor.
  • toppingCosts, an integer array of length m, where each toppingCosts[i] is the price of one of the ith topping.
  • target, an integer representing your target price for dessert.

  You want to make a dessert with a total cost as close to target as possible.

  Return the closest possible cost of the dessert to target. If there are multiple, return the lower one.

• [494. Target Sum] You are given an integer array nums and an integer target.

  You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.

  • For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression "+2-1".

  Return the number of different expressions that you can build, which evaluates to target. Solved

• [37. Sudoku Solver] Write a program to solve a Sudoku puzzle by filling the empty cells.

  A sudoku solution must satisfy all of the following rules:

  1. Each of the digits 1-9 must occur exactly once in each row.
  2. Each of the digits 1-9 must occur exactly once in each column.
  3. Each of the digits 1-9 must occur exactly once in each of the 9 3x3 sub-boxes of the grid.

  The '.' character indicates empty cells.

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# Sliding Window [16/11/2021]

Definition

As its name suggests, this technique involves taking a subset of data from a given array or string, expanding or shrinking that subset to satisfy certain conditions, hence the sliding effect.

When can we use it ? Generally speaking, the sliding window technique is useful when you need to keep track of a contiguous sequence of elements, such as summing up the values in a subarray.

Note: Sometimes, in string matching and cases where finding longest repeating char with k replacements, idea should be checking the length of the current window minus the max char count and seeing if that's bigger than k. Keep track of maximum count of replacements in each substring.

Note: For string counting, maintaining a count map can be helpful as characters are only 26.

_Examples_:

• [1876. Substrings of Size Three with Distinct Characters] A string is good if there are no repeated characters.

  Given a string s, return the number of good substrings of length three in s.

  Note that if there are multiple occurrences of the same substring, every occurrence should be counted.

  A substring is a contiguous sequence of characters in a string. Solved

• [1343. Number of Sub-arrays of Size K and Average Greater than or Equal to Threshold] Given an array of integers arr and two integers k and threshold.

  Return the number of sub-arrays of size k and average greater than or equal to threshold. Solved

• [1004. Max Consecutive Ones III] Given a binary array nums and an integer k, return the maximum number of consecutive 1's in the array if you can flip at most k 0's. Learned

• [1358. Number of Substrings Containing All Three Characters] Given a string s consisting only of characters a, b and c.

  Return the number of substrings containing at least one occurrence of all these characters a, b and c.Learned

• [1493. Longest Subarray of 1's After Deleting One Element] Given a binary array nums, you should delete one element from it.

  Return the size of the longest non-empty subarray containing only 1's in the resulting array. Return 0 if there is no such subarray. Learned

• [1031. Maximum Sum of Two Non-Overlapping Subarrays] Given an integer array nums and two integers firstLen and secondLen, return the maximum sum of elements in two non-overlapping subarrays with lengths firstLen and secondLen.

  The array with length firstLen could occur before or after the array with length secondLen, but they have to be non-overlapping.

  A subarray is a contiguous part of an array.Need to come back for this

• [1052. Grumpy Bookstore Owner] There is a bookstore owner that has a store open for n minutes. Every minute, some number of customers enter the store. You are given an integer array customers of length n where customers[i] is the number of the customer that enters the store at the start of the ith minute and all those customers leave after the end of that minute.

  On some minutes, the bookstore owner is grumpy. You are given a binary array grumpy where grumpy[i] is 1 if the bookstore owner is grumpy during the ith minute, and is 0 otherwise.

  When the bookstore owner is grumpy, the customers of that minute are not satisfied, otherwise, they are satisfied.

  The bookstore owner knows a secret technique to keep themselves not grumpy for minutes consecutive minutes, but can only use it once.

  Return the maximum number of customers that can be satisfied throughout the day. Learned

• [992. Subarrays with K Different Integers] Given an integer array nums and an integer k, return the number of good subarrays of nums.

  A good array is an array where the number of different integers in that array is exactly k.

  For example, [1,2,3,1,2] has 3 different integers: 1, 2, and 3.Learned

• [718. Maximum Length of Repeated Subarray] Given two integer arrays nums1 and nums2, return the maximum length of a subarray that appears in both arrays. Learned Note: this is actually DP. Come back to this question again. Important concept to learn.

• [438. Find All Anagrams in a String] Given two strings s and p, return an array of all the start indices of p's anagrams in s. You may return the answer in any order.

  An Anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. Learned

  Note: this is string matching. technique involved should be similar to Rabin-Karp algorithm for pattern match. Trick is to remember different mechanisms to compare strings like:

  • ASCII pattern match
  • exact string match
  • Modulo hash value match Come back to it when coming for string related questions.

• [904. Fruit Into Baskets] You are visiting a farm that has a single row of fruit trees arranged from left to right. The trees are represented by an integer array fruits where fruits[i] is the type of fruit the ith tree produces.

  You want to collect as much fruit as possible. However, the owner has some strict rules that you must follow:

  • You only have two baskets, and each basket can only hold a single type of fruit. There is no limit on the amount of fruit each basket can hold.
  • Starting from any tree of your choice, you must pick exactly one fruit from every tree (including the start tree) while moving to the right. The picked fruits must fit in one of your baskets.
  • Once you reach a tree with fruit that cannot fit in your baskets, you must stop. Given the integer array fruits, return the maximum number of fruits you can pick. Learned

• [424. Longest Repeating Character Replacement] You are given a string s and an integer k. You can choose any character of the string and change it to any other uppercase English character. You can perform this operation at most k times.

  Return the length of the longest substring containing the same letter you can get after performing the above operations.Learned

• [3. Longest Substring Without Repeating Characters] Given a string s, find the length of the longest substring without repeating characters.Learned

• [862. Shortest Subarray with Sum at Least K] Given an integer array nums and an integer k, return the length of the shortest non-empty subarray of nums with a sum of at least k. If there is no such subarray, return -1.Learned

• [76. Minimum Window Substring] Given two strings s and t of lengths m and n respectively, return the minimum window substring of s such that every character in t (including duplicates) is included in the window. If there is no such substring, return the empty string "".Learned