Imagine you’re walking along a path that has treasure chests and traps. Some chests have gold coins, and some traps take away coins. You want to find the part of the path where you can get the most coins. The key idea: It is a dynamic programming algorithm for finding the maximum contiguous sum subarray in a given array. It is a simple and efficient algorithm that works by maintaining two variables: ...
Preface Facing the Dynamic Programming Challenge Like many others, I initially found Dynamic Programming (DP) on LeetCode daunting and perplexing. However, this challenging journey led to profound insights. My initial misconception was that DP was all about complexity, but I learned it’s fundamentally about simplifying complex problems into manageable segments. Here’s my journey into understanding DP and why it’s a crucial tool in a programmer’s toolkit. Unraveling Dynamic Programming The Essence of DP ...
Overview Recursion is a way of solving a problem by breaking it down into smaller problems of the same type. The smaller problems are then solved recursively, until a base case is reached. The base case is a simple problem that can be solved without recursion. Imagine you have a big box of toy blocks, and each block represents a problem you need to solve. Some blocks are big (complex problems), and some are tiny (simple problems). To solve a big problem, you take apart the big block to find smaller blocks inside, and then, if needed, you take apart those smaller blocks to find even tinier blocks inside them, and so on, until you reach the tiniest blocks that you can easily understand and solve. ...
Overview The union-find algorithm is a data structure and algorithm that maintains a collection of disjoint sets. A disjoint set is a set of elements that are not connected to each other. The union-find algorithm can be used to perform the following operations: Find: Find the set that an element belongs to. Union: Merge two sets together. The union-find algorithm is often used to solve problems that involve graph connectivity. For example, the union-find algorithm can be used to determine whether two nodes in a graph are connected, or to find all of the connected components in a graph. ...
Overview It is not easy to summarize the pattern of Two Pointers, but most likely it is used for list and linked list and the required time complexity is O(N) - the underlying pattern allows us to use Two Pointers to go through the list once to get the results. Common usage: Linear Structure: Typically applied to a sorted array or linked list. Two pointers might move in the same direction or in opposite directions. Classic Patterns: a. Converging Pointers (often used in sorted arrays): - Start one pointer at the beginning (left) and another at the end (right). - Move them toward each other until they meet or until some condition is satisfied. - Example: Checking if a sorted array has two numbers that sum up to a target. b. Sliding Window: - Use two pointers to represent the start and end of a window, then “slide” the window through the array/sequence. - Example: Finding the longest substring without repeating characters. c. Fast and Slow Pointers (often used in linked lists): - One pointer moves twice (or more times) as fast as the other. - Useful for detecting cycles in a linked list (Floyd’s Cycle Detection Algorithm) or finding the middle element. Usage Scenarios: Finding a Pair with a Given Sum/Target: Given a sorted array, determine if there’s a pair that sums up to a target. Move the left and right pointers based on the sum comparison to the target. Removing Duplicates: Two pointers can be used to remove duplicates from a sorted array or linked list, with one pointer iterating through and another pointing to the last non-duplicate item. Palindrome Checking: To determine if a string or linked list is a palindrome, you can use two pointers moving from the two ends towards the center. Max/Min Subarray/Sublist: Using the sliding window variant, find the subarray with the maximum/minimum sum or other properties. Advantages: Efficiency: The two-pointer technique can sometimes convert a brute force solution with time complexity O(n^2) to a more efficient O(n) solution. Space: This method is in-place and typically uses O(1) extra space. Example Questions 88. Merge Sorted Array You are given two integer arrays nums1 and nums2, sorted in non-decreasing order, and two integers m and n, representing the number of elements in nums1 and nums2 respectively. ...
Overview The Divide-n-Conquer strategy often employs recursion, as it relies on applying the same method to reduce the problem size by half and subsequently combining the outcomes for the ultimate solution. I view Divide-n-Conquer in a light similar to MapReduce, particularly when the task involves transformation. MapReduce breaks down a large problem into more manageable, independent sub-problems. Since each of these sub-problems operates autonomously, we can address them sequentially and still integrate their solutions. Key to this approach is ensuring the main problem can be independently segmented and the derived solutions can be seamlessly merged. ...
Overview In one word, binary search is to search for a target in a sorted array. The idea is to shrink the search space to empty. It must be sorted because we can be sure how to shrink the search space and we normally reduce the search space by half so the time complexity is O(logN) where N is the size of entire search space. One common problem to understand Binary Search is how to identify the boundary of the search space. ...