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Impact of High Dimensionality in Covariance Matrix Estimation
Lecture notes on how high dimensionality distorts sample covariance spectra, including the Marchenko–Pastur law, the Tracy–Widom limit for the largest eigenvalue, and connections to modern random matrix theory.
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Paper review: Score-Based Generative Modeling through SDEs
A summary of Song et al. (2021) which generalizes DDPMs and Score Matching into a unified continuous-time SDE framework.
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Paper review: Denoising Diffusion Probabilistic Models
A summary of Ho et al. (2020) on high-quality image synthesis using diffusion models.
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Understanding Bonds and Their Role in Portfolios
An overview of bonds, valuation principles, and their strategic use in institutional investing and diversification.
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Fixed Income Quant
Notes on quantitative research, alpha generation, and risk management in fixed income markets.
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Summary: Why Market Correlation Matters
A summary of John Edwards' article on market correlation, portfolio diversification, and volatility.
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Field guide to macro and markets
A field guide to macroeconomics and market dynamics.
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Paper review: Targeted Maximum Likelihood Estimation Using Exponential Families
A review of Díaz and Rosenblum (2015) on constructing fluctuation submodels via exponential families for targeted maximum likelihood estimation.
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Paper review: Data Fusion for High-Resolution Estimation
A review of Guan et al. (2026) on fusing unbiased administrative data with biased survey data for high-resolution estimation.
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Paper review: Catastrophe Insurance: An Adaptive Robust Optimization Approach
A review of Bertsimas and Zeng (2024) on applying adaptive robust optimization to catastrophe insurance pricing.
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Paper review: Sensitivity Analysis for Inverse Probability Weighting Estimators via the Percentile Bootstrap
A review of Zhao, Small, and Bhattacharya (2019) on conducting robust sensitivity analysis for IPW estimators using marginal sensitivity models and the percentile bootstrap.
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Paper review: A Distributional Approach for Causal Inference Using Propensity Scores
A review of Tan (2006) on estimating average causal effects and improving upon propensity score methods using a distributional approach.
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Paper review: Adjusting for Nonignorable Drop-Out Using Semiparametric Nonresponse Models
A review of Scharfstein, Rotnitzky, and Robins (1999) on handling nonignorable missing data and conducting sensitivity analysis using semiparametric methods.
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Personal vs. Commercial Insurance
A comparison of personal and commercial lines of property-casualty insurance: coverage, pricing, and data structure.
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ISO Property Data: Loss Ratio Analysis by State and ZIP Code
Aggregating earned premium and loss+LAE from ISO property data to compute loss ratios and peril compositions across states and ZIP codes.
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Understanding Chain-of-Thought Prompting: Why LLMs Need to 'Think' Before They Speak
A pedagogical look at Chain-of-Thought (CoT) prompting, its theoretical foundations, and its impact on LLM reasoning.
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LLM Evaluation: Frameworks, Benchmarks, and Best Practices
A deep dive into how we measure the intelligence, reliability, and safety of Large Language Models.
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Policy Learning
Empirical Welfare Maximization, Policy Evaluation, and Regret Bounds
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Paper review: Performance Guarantees for Individualized Treatment Rules
A review of Qian and Murphy (2011) on formulating individualized treatment rules via conditional outcome maximization with performance guarantees.
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EE 588: Convex Sets
Foundational concepts of convex sets, including definitions, examples, and operations that preserve convexity.
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DSO 699 Week 1: Linear Models and Matrix Decompositions
Review of linear algebra foundations for statistical modeling, including projections, QR decomposition, and SVD.
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Paper Review: CASCADE for Spike Inference from Calcium Imaging
A summary of the CASCADE algorithm for noise-optimized, generalized spike inference from calcium imaging.
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Summer Sublease
Summer sublease at Garrett Gardens near USC
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Fine-Tuning an LLM for Critical Road Trip Planning
A quick guide to fine-tuning lightweight LLMs on a Tesla T4 GPU in under an hour for ISE-547.
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Comparative Analysis of Chain-of-Thought Reasoning in Large Language Models
Assignment examining different Chain-of-Thought (CoT) prompting strategies in LLMs.
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Tutorial on Lagrangean Decomposition: Theory and Applications
A comprehensive guide to the theory of Lagrangean Relaxation and Decomposition, with deep-dive applications in process systems engineering.
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Homework 3: Synthetic Data Generation and Classical Machine Learning
HW3 for USC ISE-547 2026 spring
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Window Functions in SQL and Pandas
A practical guide to window functions—ranking, aggregation, and offset operations computed over a sliding frame—demonstrated side-by-side in SQL and Python's pandas library.
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LeetCode 1204: Last Person to Fit in the Bus
Solving the 'Last Person to Fit in the Bus' problem using window functions in both SQL and pandas. A perfect application of running totals to real-world scenarios.
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Cleaner pandas: Beyond Redundant Boolean Indexing
Stop repeating your DataFrame name! A guide to using .query() and lambda functions for more readable, efficient, and 'fluent' pandas code.
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The Fundamental Theorem of Linear Programming
A quick intuition and justification of why linear programming optima occur at extreme points.
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Notes: Lagrangian Relaxation and Decomposition
An overview of Lagrangian relaxation, decomposition techniques, subgradient methods, and their applications in large-scale optimization.
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Paper Review: Convexification of multi-period quadratic programs with indicators
A deep dive into the recent paper by Lee, Gómez, and Atamtürk on constructing tight convex relaxations for multi-period quadratic optimization problems with logical indicators.
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Summary: Challenges in Experimentation (Lyft)
A summary of the Lyft Engineering blog post 'Challenges in Experimentation' by John Kirn.
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A/B Testing Metrics
A comprehensive guide to selecting and evaluating metrics in A/B testing and online experimentation.
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Leetcode 938: Range Sum of BST
Calculating the sum of all nodes in a given range by traversing a Binary Search Tree.
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Leetcode 202: Happy Number
Determining if a number is a happy number using Hash Set and Two Pointers techniques.
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Leetcode 160: Intersection of Two Linked Lists
Finding the node at which the intersection of two singly linked lists begins using the Two Pointers technique.
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Computing CDF by trapezoidal rule
A numerical integration approach to calculating the Cumulative Distribution Function directly from the Probability Density Function.
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Evaluating LLM Hallucination with TruthfulQA
HW2 for USC ISE-547 2026 spring
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k-means Clustering
Formulating and implementing k-means clustering as a mixed-integer optimization problem.
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The Illustrated Transformer
A visual explanation of the Transformer model, its components, and how it works.
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embedding
Understanding embeddings: representing language in vector space.
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Hyperparameter Tuning for Best Subset Selection
Exploring methods for determining the optimal subset size k in best subset selection problems.
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JUST WHAT IS A LANGUAGE MODEL?
An introduction to language models: prediction, generation, and probabilities.
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ML-guided Predict + Search for Mixed-Integer Programming Problems
A hybrid framework combining machine learning with traditional optimization solvers for MIP problems.
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Facility Location Problem with Outliers and Capacity Constraints
Exploring a variant of the Facility Location Problem incorporating outlier rejection and capacity constraints.
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Quick and Dirty Sample Size Calculation
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Potential Outcome Framework and Matching Estimators
An introduction to the Neyman-Rubin causal model and matching methods
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Case Study: Diagnosing and Addressing a Metric Drop
An end-to-end framework for investigating MAU drops, targeting at-risk users, and making data-driven 'ship' decisions.
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Paper review: Building Representative Matched Samples With Multi-Valued Treatments in Large Observational Studies
A review of Magdelena Bennett et al. (2020) on using mixed-integer optimization to create representative matched samples for multi-valued treatments.
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Paper review: Improving randomized controlled trial analysis via data-adaptive borrowing
A deep dive into how machine learning and adaptive lasso can enhance RCTs by selectively borrowing information from external controls.
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Lecture 16: Canonical Gradient and Efficient Influence Curve
Notes by Rachael Phillips for PB HLTH 290, Spring 2019
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Vibe Coding Report: Advanced Recursive Maze Solver
A report on generating an Advanced Recursive Maze Solver (BFS with Teleports) using AI prompts.
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Vibe Coding Report: Recursive Maze Solver
A report on generating a Recursive Maze Solver using AI prompts and iterative refinement.
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Vibe Coding Report: Group Anagrams
A report on generating a Group Anagrams script using AI prompts and iterative refinement.
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Vibe Coding Report: Palindrome Checker
A report on generating a Palindrome Checker using AI prompts and iterative refinement.
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Vibe Coding Report 1: Word Frequency Analyzer
A report on generating a Word Frequency Analyzer using AI prompts and iterative refinement.
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Prompting for Vibe Coding
Strategies for effective AI-assisted coding: Structure, Iteration, and Meta-Prompting.
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Retrieval-Augmented Generation (RAG)
Understanding RAG: Connecting frozen LLMs to external dynamic knowledge.
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Multi-period MILP and Dynamic Lot Sizing Problem
An introduction to the Dynamic Lot Sizing Problem and its key assumptions.
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Best Subset Selection via a Modern Optimization Lens
Lecture summary for 02-04-2026 on Best Subset Selection
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Large Neighborhood Search (LNS) for Mixed-Integer Linear Programming (MILP)
An overview of Large Neighborhood Search (LNS) heuristics for solving complex Mixed-Integer Linear Programs (MILP), exploring core concepts, 'destroy and repair' methods, and popular frameworks like RINS and Local Branching.
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An Overview of Constraint Programming (CP)
Exploring the fundamentals of Constraint Programming (CP), how it differs from MILP, and its powerful constraint propagation mechanisms for solving complex combinatorial problems.
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Time Series Operations in Pandas
A collection of useful pandas snippets for time series analysis, including date filtering, period conversion, and merging by nearest match.
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pandas merge and groupby
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pandas Basic
A practical guide to window functions—ranking, aggregation, and offset operations computed over a sliding frame—demonstrated side-by-side in SQL and Python's pandas library.
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Augmented IPW and Double Robustness
AIPW estimator, double robustness, and cross-fitting
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FWL Theorem
Frisch-Waugh-Lovell theorem
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Deriving the IPW Estimator: From One RCT to Infinite RCTs under Unconfoundedness
An intuitive derivation of the Inverse Probability Weighting (IPW) estimator from a single RCT to multiple RCTs and observational data.
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Paper review: Statistical Challenges in Online Controlled Experiments
A review of Larsen et al. (2024) on the statistical landscape and challenges of A/B testing in large-scale online environments.
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Case Study: Causal Effect of ETA Reduction
A practical case study on measuring the causal effect of reducing Estimated Time of Arrival (ETA) in a ridesharing marketplace.
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Case Study: Causal Effect of ETA Reduction
A practical case study on measuring the causal effect of reducing Estimated Time of Arrival (ETA) in a ridesharing marketplace.
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Synthetic Control and Experimentation Culture
When standard experiments fail: utilizing Synthetic Controls, managing experimentation culture, and understanding various treatment effects.
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Switchback Experiments
An overview of switchback (time-split) experiments: what they are, why they are used to solve network interference, and their trade-offs.
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Violation of SUTVA in A/B Testing: network interference
A summary of the Lyft Engineering blog post 'Interference Across a Network' detailing how naive A/B testing can bias effect estimates in ridesharing.
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Causal Inference vs Causal Estimation
A deep dive into confidence intervals—what they are, how to interpret them, some caveats, and oft-encountered issues in online experimentation.
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Causal Assumption: SUTVA and Ignorability
Understanding SUTVA and ignorability, fundamental assumptions in causal inference, what they mean, and what happens when they are violated.
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Causal Inference Overview
Understanding SUTVA and ignorability, fundamental assumptions in causal inference, what they mean, and what happens when they are violated.
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Methods of Finding Interval Estimators: Inverting a Test Statistic
A discussion on finding interval estimators by inverting test statistics, exploring the strong correspondence between hypothesis testing and interval estimation.
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Fundamentals of Diffusion Map Embedding
Principles and practice of nonlinear dimensionality reduction popularly used in neuroscience.
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Fundamentals of Matching and Weighting Estimator for Causal Inference
Principles and practice of matching and weighting estimator for causal inference.
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FDR control: Storey's procedure
Review of Storey's procedure for FDR control.
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Data Analysis Detail: Subsequent Analysis for Biological Interpretation
Principle and practice of mapping the brain's functional architecture into a low-dimensional space.
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Fundamentals of Functional Connectivity and Gradients
Principle and practice of mapping the brain's functional architecture into a low-dimensional space.
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Wavelet Basis & Function Spaces: Besov vs. Hölder
Understanding Nonparametric Regression, Haar Wavelets, and Smoothness Norms
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Data Analysis Detail: Mouse Behavioral Study
Details for the data analysis section of the Nature Communications paper 'In-vivo integration of soft neural probes through high-resolution printing of liquid electronics on the cranium'
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Fundamentals of Phase Locking
Distinguishing Spike-Field Locking from Inter-Trial Phase Locking
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Fundamentals of Neural Signal Decomposition
Spikes, LFPs, and frequency bands
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Nonlinear Mixed-Effects Modeling
An overview of Nonlinear Mixed-Effects Models (NLME), their structure, and workflow using SimBiology.
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Fundamentals of the Filter-Hilbert Method
Decoupling filtering from the analytic signal for better frequency control
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Fundamentals of Continuous Wavelet Transform
Time-frequency decomposition using Analytic and Complex Morlet Wavelets
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Fundamentals of Fourier Transform
From neural oscillations to frequency domain analysis
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Fundamentals of Convolution
Inner product and convolution in signal processing and statistics
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Fundamentals of Neural Recording
Non-invasive, invasive, intracellular, extracellular, and single-unit recording methods
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Data Structure: Stack
An introduction to the Last-In-First-Out (LIFO) stack data structure and its common algorithmic patterns.
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Introduction to Two Pointers
A comprehensive guide to the two-pointer algorithmic pattern
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Data Structures: Binary Search Tree
A node-based binary tree data structure with properties that make it highly efficient for searching, inserting, and deleting elements.
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Leetcode 914: X of a Kind in a Deck of Cards
Grouping elements by checking the Greatest Common Divisor (GCD) of their frequencies.
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Leetcode 141: Linked List Cycle
Detecting a cycle in a linked list using Floyd's Tortoise and Hare algorithm.
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Leetcode 1: Two Sum
Finding a pair of numbers that add up to a target dynamically using a one-pass Hash Map.
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Leetcode 242: Valid Anagram
Checking if two strings are anagrams of each other using a Hash Map.
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Leetcode 169: Majority Element
Finding the majority element in an array using a Hash Map frequency table.
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Leetcode 1134: Armstrong Number
Determining if a number is an Armstrong number by extracting its digits.
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Leetcode 69: Sqrt(x)
Computing the integer square root of a number using Binary Search.
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Leetcode 121: Best Time to Buy and Sell Stock
Iteratively updating minimums and maximum profits in a single pass
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Data Structures: Hash Table
A foundational dictionary data structure allowing for $O(1)$ average associative lookups.
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Leetcode 70: Climbing Stairs
Solving the Climbing Stairs problem using recursion, recursion tree analysis, and memoization.
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Leetcode 704: Binary Search
A foundational $O(\log n)$ search algorithm for sorted arrays.
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Leetcode 13: Roman to Integer
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Leetcode 977: Squares of a Sorted Array
A two-pointer inward traversal approach to square each number and sort the array in O(n) time
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Leetcode 125: Valid Palindrome
A two-pointer approach to check if a string is a valid palindrome
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Leetcode 392: Is Subsequence
A two-pointer approach to check if one string is a subsequence of another
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Leetcode 283: Move Zeroes
A two-pointer approach to move all non-zero elements to the front of an array
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Techniques
Techniques