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Data Structures & Algorithms

Master core and advanced data structures and algorithms with production-grade implementations, hardware-conscious optimizations, and real-world system designs.

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Abhishek
AbhishekBegginer
Asked: September 11, 2026In: Data Structures & Algorithms

Next.js 15: Error: Route used “params” without awaiting it (Asynchronous Page Props Fix)

After upgrading my application to Next.js 15 (Release Candidate / Stable) and React 19, my dynamic routing pages crashed with the runtime error: Error: Route "/blog/[slug]" used `params.slug`. `params` should be awaited before ...Read more

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Abhishek
AbhishekBegginer
Asked: September 11, 2026In: Data Structures & Algorithms, Greedy & Resource Allocation

Gas Station Circular Tour: Mathematical proof of why a single pass in O(N) is sufficient

There are n gas stations along a circular route, where the amount of gas at the i-th station is gas[i]. It costs cost[i] of gas to travel from station i to i + 1. You begin the journey with an ...Read more

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abderahman
abderahman
Asked: September 11, 2026In: Data Structures & Algorithms, System-Scale & Probabilistic Structures

How does a Count-Min Sketch estimate heavy-hitter item frequencies under bounded RAM?

We are building a DDoS mitigation filter monitoring billions of network packets per minute. We need to count the frequency of each source IP address in real-time to detect anomalous spikes. Using a standard hash map of counters would require tens ...Read more

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Abhishek
AbhishekBegginer
Asked: September 11, 2026In: Data Structures & Algorithms, Stacks, Queues & Ring Buffers

Daily Temperatures: How to use an Index-Tracking Monotonic Stack for next warmer day in O(N)

Given an array of integers temperatures, we need to return an array answer such that answer[i] is the number of days you have to wait after the i-th day to get a warmer temperature. If there is no future day ...Read more

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aarav0
aarav0
Asked: September 11, 2026In: Bit Manipulation & Low-Level Computing, Data Structures & Algorithms

How to find the Single Number when all others appear 3 times using a Digital Logic State Machine?

When elements in an array appear twice except one, we can simply XOR all numbers together. But what if every element appears three times, except for a single number that appears once? The standard hash-map solution uses O(N) space. How can ...Read more

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Ahmedelkomy
Ahmedelkomy
Asked: September 11, 2026In: Data Structures & Algorithms, Graphs & Network Topologies

Why does standard std::priority_queue in Dijkstra cause memory bloating, and how to fix it?

When implementing Dijkstra’s algorithm for large road networks (millions of nodes and edges), the standard textbook approach pushes a new pair (new_dist, u) into a binary heap whenever a shorter path is found. This means old, obsolete distance pairs remain sitting ...Read more

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aarav0
aarav0
Asked: September 11, 2026In: Advanced DP: Bitmask & Tree DP, Data Structures & Algorithms

Traveling Salesperson Problem: How does Bitmask DP reduce (N – 1)! factorial to O(N^2 * 2^N)?

We are building an autonomous drone route planner that must visit N = 20 delivery drop points with minimum total travel distance. Brute-force testing all permutations is (N - 1)!. For N = 20, $19! pprox 1.21 imes 10^{17}$, which would ...Read more

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Ahmedelkomy
Ahmedelkomy
Asked: September 11, 2026In: Data Structures & Algorithms, Dynamic Programming: 1D, 2D & Grid

Why does Patience Sorting solve Longest Increasing Subsequence in O(N log N) instead of O(N^2)?

The standard DP solution for Longest Increasing Subsequence (LIS) uses two nested loops: for each element i, scan all previous elements j < i. That takes O(N^2) time, which times out when N = 100,000. Everyone says the optimal solution is ...Read more

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abderahman
abderahman
Asked: September 11, 2026In: Data Structures & Algorithms, Heaps & Task Schedulers

How to compute Running Median in continuous data streams with O(log N) per tick?

In our telemetry service, financial tick prices arrive at ~10,000 events/second. We need an online algorithm that can output the exact running median at any moment. Sorting the buffer on every tick is O(N log N), which is impossible at high ...Read more

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Abhishek
AbhishekBegginer
Asked: September 11, 2026In: Data Structures & Algorithms, Two Pointers & Sliding Window

Minimum Window Substring: Why an integer frequency array beats HashMap in low-latency parsers

Given two strings s and t, return the minimum window substring of s such that every character in t (including duplicates) is included in the window. Most tutorials use two hash maps (dict or unordered_map) to track character counts and compare ...Read more

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