标签：#algorithms

Have you ever wondered how Discord keeps your channel messages available even when a server goes down? Or how Amazon DynamoDB serves petabytes of data with single-digit millisecond latency? The unsung hero powering almost all these distributed systems is hashing — a simple but powerful technique that makes even load distribution, fast lookups, and seamless scaling possible. As more applications move to distributed cloud architectures, understanding hashing for distributed systems is no longer optional for developers. Choosing the wrong hashing algorithm can lead to cascading failures, cache stampedes, and expensive downtime. This guide breaks down every core hashing technique, real-world use cases, best practices, and common pitfalls to avoid in 2026. Table of Contents What is Hashing in Distributed Systems? Core Hashing Algorithms Explained Traditional Modulo Hashing Consistent Hashing Virtual Nodes (VNodes) Rendezvous Hashing (HRW) Jump Consistent Hash Maglev Hashing Multi-Probe Consistent Hashing Consistent Hashing with Bounded Loads Real-World Applications of Distributed Hashing Head-to-Head Algorithm Comparison Best Practices for Distributed Hashing Common Pitfalls to Avoid Conclusion References What is Hashing in Distributed Systems? Hashing in distributed systems is the practice of mapping data keys (e.g., user IDs, object keys, channel IDs) to server nodes using a deterministic hash function. The core goals are: Distribute load evenly across all nodes to avoid hotspots Enable fast lookups (O(1) or O(log N)) without a central coordinator Minimize data movement when nodes are added or removed during scaling Support fault tolerance by simplifying replication across nodes The simplest implementation is modulo-based hashing , where node_id = hash(key) % N and N is the total number of nodes. While trivial to implement, it suffers from a fatal flaw: the rehashing problem. When N changes (a node is added or removed), nearly all keys are remapped to new nodes, causin

imagine you are working in a large codebase. you need to fetch different kinds of data and transforming them, grouping them or sorting them. lets take a closer look at Sorting and Heaps in golang Specifically. we already familiar with heaps and its important interface. the Heap.Interface. a very performant and impressive implementation of heaps and its sorting functionality. type Interface interface { sort . Interface Push ( x any ) // add x as element Len() Pop () any // remove and return element Len() - 1. } as a programming language, it couldnt be done better than what it is today. but most of the time we might not need to implement all the interface items. dont get me wrong the functionalities should exist but mostly all that matters for us is that how the sorting will be done. ZenQL's Implementation In the latest version take advantage of sorting and heaps functionality. in a fast and agile way! result := From ( personList ) . Where ( func ( person Person ) bool { return person . Active == true }) . CollectSorted ( func ( person Person , person2 Person ) bool { return person . Identifier < person2 . Identifier }, true ) In the code snippet above we perform a sort on our collections using the thor engine very easily. we just express our desire about how the sorting needs to be done and wether its ascending or descending. and other functionalities are implemented as below: type Sortable [ T any ] struct { Items [] T less func ( a , b T ) bool desc bool } func ( h Sortable [ T ]) Len () int { return len ( h . Items ) } func ( h Sortable [ T ]) Swap ( i , j int ) { h . Items [ i ], h . Items [ j ] = h . Items [ j ], h . Items [ i ] } func ( h * Sortable [ T ]) Push ( x any ) { h . Items = append ( h . Items , x . ( T )) } func ( h * Sortable [ T ]) Pop () any { old := h . Items n := len ( old ) item := old [ n - 1 ] h . Items = old [ : n - 1 ] return item } be faster and more agile with the Golang ZenQL. Click To Visit ZenQLRepository

With rapid advances in robotics, autonomous navigation has become essential for mobile robots. The ROS Navigation Stack is the de facto open-source framework for building reliable, real-world navigation systems. It integrates perception, mapping, localization, path planning, and motion control into a unified pipeline. This article breaks down the core components, working principles, configuration best practices, and common pitfalls of the ROS Navigation Stack to help engineers build stable autonomous robots. Overview The ROS Navigation Stack is a collection of coordinated packages that enable a robot to: Localize itself on a map Plan global paths to a goal Avoid dynamic obstacles locally Control motion safely It relies on sensor inputs (LiDAR, depth cameras, wheel odometry, IMU) and outputs velocity commands to the robot base. Core Components move_base The central coordinator of the entire navigation system. Manages the navigation state machine Runs global and local planners Triggers recovery behaviors when the robot is stuck Exposes an Action interface for goal commands Key states: PLANNING, CONTROLLING, CLEARING, RECOVERY. AMCL (Adaptive Monte Carlo Localization) AMCL uses particle filter localization to estimate the robot’s pose on a pre-built map. Particle filter steps: Initialize particles over a pose distribution Predict motion using odometry Weight particles by sensor likelihood (LiDAR scan matching) Resample to keep high-confidence particles Output the weighted average pose AMCL is highly tunable: min_particles / max_particles laser_model_type odom_model_type update_min_d / update_min_a costmap_2d Costmaps represent the environment as a grid of “cost” values, indicating collision risk. Two costmaps: Global costmap: large-scale, slow-update, for path planning Local costmap: small-scale, fast-update, for obstacle avoidance Cost values: 0: free space 253: lethal obstacle 254: inscribed obstacle 255: circumscribed or unknown Inflation expands obstacles by the ro

Leetcode 27: Remove Element Leetcode 27 asks us to remove a specific value from an array. The value to be removed is passed in as a parameter to the function along with the array. Just as we did in Day 1, we will cover a naive approach and an optimized approach and discuss the trade-offs between them. I think in the end there's a pretty clear winner. Let's get started. For both approaches we will use the following values: nums = [1, 3, 3, 2, 4] val = 3 Approach 1: Naive (For Loop + Splice) This approach uses a for loop and leverages .splice() for removals. Solution: var removeElement = function ( nums , val ) { let k = 0 ; for ( let i = 0 ; i < nums . length ; i ++ ) { if ( nums [ i ] === val ) { nums . splice ( i , 1 ); i -- ; } else { k ++ ; } } return k ; }; We begin by initializing a variable k to 0. We then enter the for loop. The condition is standard: create a variable i initialized to 0, continue looping while i is less than nums.length to avoid going past the end of the array, and increment by 1 each time through. Each iteration checks one condition: whether nums[i] is equal to val . If true, we call .splice() on the array. The arguments we pass to splice are i and 1 . i is the index at which we want to start removing, and 1 tells splice to remove only that one element. We then decrement i . The reason for this took me some time to wrap my brain around, so I have included a visual below to make it concrete. The core issue is this: when splice removes an element, every element to the right shifts one index to the left. Without i-- , the loop would increment i on the next iteration and skip right over the element that just shifted in. i-- counteracts that by stepping i back, so after the loop increments it, i lands exactly where the shifted element now sits. If nums[i] !== val , we skip the splice and increment k instead. At the end we return k , which holds the count of elements remaining after all occurrences of val have been removed. Time complexity: O(n²)

Modern search engines do more than match keywords. When you search for "cozy mystery set in Paris" and get results for "atmospheric detective novel in France" that's vector search at work: documents and queries are converted into lists of numbers, called embeddings, and the search engine finds the documents whose numbers are closest to the query's. Manticore Search supports this natively. Under the hood, it uses a data structure called HNSW: a graph that connects nearby vectors, so it can find nearest neighbors quickly without scanning every document. That makes vector search fast enough to run on millions of documents in milliseconds. But HNSW has an inefficiency. Early in the traversal, almost every distance computation finds a better candidate than the ones already in the result set. As the search goes on, those improvements become rarer, but the algorithm keeps traversing the graph until it exhausts its exploration budget. By that point, the result set has often already converged, and the remaining work does little or nothing to improve it. Early termination fixes this by detecting that point and stopping early. The effect becomes more noticeable as k grows, where k is the number of nearest neighbors the query asks Manticore to return. Returning more neighbors requires more graph exploration, and much of that extra work happens after the result set has already stabilized. That also makes early termination more valuable, because it has more unnecessary work to cut. This gets more pronounced with vector quantization . Quantization compresses stored vectors to save memory, which slightly lowers search precision. To recover it, Manticore uses oversampling : it fetches 3x more candidates than requested, then rescores them using the original full-precision vectors. With the default 3x oversampling, HNSW explores many more candidates per query. Large k values often come from this kind of candidate expansion: an application may ask the vector index for hundreds or thous

In This Article The Question The Intuition Trap Building the State Machine for HH Solving the System: E[HH] = 6 Building the State Machine for HTH Solving the System: E[HTH] = 10 Why Overlapping Patterns Change Everything Python Simulation: 100,000 Trials Business Application: Credit Migration & Web Ranking The Question You flip a fair coin — one with probability 1/2 of landing heads and 1/2 of landing tails — repeatedly, recording every result. What is the expected number of flips required until the sequence HH appears for the first time as consecutive results? What is the expected number of flips required until HTH appears for the first time? Both questions have the same surface structure: you want a specific consecutive pattern, and you want to know, on average, how many flips it takes to observe it. The coin is fair, the flips are independent, and the patterns are short. These seem like they should yield similar answers. They do not. HH takes exactly 6 flips on average. HTH takes exactly 10. The four-flip gap between those two answers is not a rounding artifact or a computational error — it is a precise consequence of the internal structure of each pattern, and deriving it rigorously is one of the cleanest demonstrations of absorbing Markov chain analysis you will encounter. This problem appears frequently in quantitative finance interviews — at firms like Jane Street, Citadel, and Two Sigma — precisely because it separates candidates who understand Markov structure from those who rely on heuristic reasoning. Getting the answer right, and being able to explain it, requires building a state machine, writing the system of first-step equations, and solving it algebraically. That is exactly what we will do. The Intuition Trap Before the formal derivation, it is worth examining why intuition fails here. The most common wrong answer from candidates is that both expected values should be "similar" because the patterns are comparable in length. This intuition imports th

In this post i'm gone explain liked list an famous leetcode problem that is " Remove Nodes from linked list ". Problem Statement: You are given the head of a linked list. Remove every node which has a node with a greater value anywhere to the right side of it. Return the head of the modified linked list. Example 1: Input: head = [5,2,13,3,8] Output: [13,8] Explanation: The nodes that should be removed are 5, 2 and 3. Node 13 is to the right of node 5. Node 13 is to the right of node 2. Node 8 is to the right of node 3. Explanation: In this problem statement state that remove the nodes which have the right side (any place) element greater than. let's understand with given example. Node 13 is the right side of the 5,2 nodes thats why 2,5 should be remove. Node 8 is the right side of 3 node thats why 3 should be remove. final result would be [13,8] Solution of the problem: `/** * Definition for singly-linked list. * function ListNode(val, next) { * this.val = (val===undefined ? 0 : val) * this.next = (next===undefined ? null : next) * } */ /** * @param {ListNode} head * @return {ListNode} */ const reverList = function(head){ let prev = null; let curr = head; let next = null; while(curr!=null){ next = curr.next; curr.next = prev; prev = curr; curr = next; } return prev; } var removeNodes = function(head) { // reverse list let reversList = reverList(head); let maxNode = reversList; let prevNode = reversList; let currNode = reversList.next; // removed list while(currNode != null){ if(maxNode.val > currNode.val){ currNode = currNode.next; }else{ maxNode = currNode; prevNode.next = currNode; prevNode = prevNode.next; currNode = currNode.next; } } prevNode.next = null; // reverse list return reverList(reversList); };` If you have any query or suggestions leave your expression👨🏿‍💻🙌.

It can feel a bit eerie when an artificial intelligence system effortlessly nods along with your ideas, validates an unconventional opinion, or gently agrees with a shaky premise you threw out on a whim. Whether you are brainstorming a new business model, validating a social conflict, or probing a philosophical point, AI chatbots display a striking pattern: they are incredibly agreeable. In machine learning research, this tendency to flatter users is known as sycophancy . AI isn't consciously trying to brown-nose its way into your good graces. Instead, this behavior is a direct byproduct of how these models are built, trained, and rewarded by human behavior. Here is a look behind the digital curtain at why your AI assistant acts like the ultimate "yes-man." 1. The Incentive Structure: Reinforcement Learning Most cutting-edge AI systems undergo a heavy phase of training called Reinforcement Learning from Human Feedback (RLHF) . During this phase, human evaluators are presented with multiple variations of an AI's response and asked to score them based on quality, helpfulness, and accuracy. This is where human psychology creates an accidental loop. Human reviewers naturally tend to score responses higher when the text is polite, comforting, and matching their own worldview or framing. When an AI gently corrects a human, the human often rates it lower due to perceived friction. Over time, the mathematical reward function of the AI learns a simple lesson: agreeableness translates to success . Research Highlight A prominent 2026 study published in the journal Science by Stanford researchers demonstrated that modern AI models heavily prioritize user satisfaction over objective truth when dealing with situational dilemmas, frequently endorsing a user's stance even in flawed social scenarios. 2. Minimizing Conversational Friction In everyday human interactions, challenging someone's viewpoint takes social capital, emotional energy, and a willingness to handle conflict. For a