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Practice › LeetCode › LeetCode (archived) › LeetCode 02xx ›

LeetCode 265: Paint House II

Problem Restatement We are given n houses and k colors. The painting cost is stored in: costs[i][j] which means: Cost to paint house i using color j . Adjacent houses cannot use the same color. We need to return the minimum total painting cost. Unlike LeetCode 256, the number of colors is not fixed to 3 . The constraints are: 1 <= n <= 100 1 <= k <= 20...
leetcode dynamic-programming array optimization May 10, 2026
Maths ›

90. Operations Research, Mathematical Programming

This volume studies decision-making under constraints using mathematical models. It integrates optimization, stochastic models, and algorithmic methods. Part I. Foundations Chapter 1. Optimization Models 1.1 Decision variables 1.2 Objective functions 1.3 Constraints 1.4 Feasible regions 1.5 Examples Chapter 2. Linear Programming 2.1 Standard form 2.2 Feasible solutions 2.3 Geometry of solutions 2.4 Applications 2.5 Examples Chapter 3. Duality 3.1 Dual problems 3.2 Weak and strong duality 3.3 Complementary slackness 3.4...
optimization operations-research May 2, 2026
Maths ›

49. Calculus of Variations and Optimal Control; Optimization

This volume studies optimization of functionals and systems. It connects analysis, geometry, control theory, and computation. Part I. Foundations of Optimization Chapter 1. Optimization Problems 1.1 Definitions and examples 1.2 Objective functions and constraints 1.3 Local and global optima 1.4 Existence of solutions 1.5 Examples Chapter 2. Convexity 2.1 Convex sets 2.2 Convex functions 2.3 Properties 2.4 Jensen’s inequality 2.5 Applications Chapter 3. Optimality Conditions 3.1 First-order conditions 3.2 Second-order...
analysis calculus-of-variations optimization May 2, 2026
Wiki › Algorithms › 01. Searching and Sorting › 1. Linear and Sequential Search ›

Pairwise Min Max Search

Pairwise Min Max Search Pairwise min max search improves over the basic min max scan by reducing the number of comparisons. It processes elements in pairs, comparing them with each other first, then updating global minimum and maximum. This reduces comparisons from about $2n$ to about $1.5n$. Problem Given a sequence $A$ of length $n$, find indices $i$ and $j$ such that $$ A[i] = \min_{0 \le k < n}...
algorithms searching optimization
Wiki › Algorithms › 01. Searching and Sorting › 2. Binary Search and Ordered Search ›

Parametric Search

Parametric Search Parametric search solves an optimization problem by repeatedly asking whether a candidate parameter value is feasible. It replaces direct optimization with a sequence of decision problems. The most common practical form is binary search on answer. The broader idea is that an unknown optimal value can be found by using a decision procedure whose result changes monotonically with the parameter. Problem Given a parameter $p$ and a feasibility...
algorithms searching parametric-search optimization decision-problem
Wiki › Algorithms › 01. Searching and Sorting › 2. Binary Search and Ordered Search ›

Continuous Ternary Search

Continuous Ternary Search Continuous ternary search finds the maximum or minimum of a unimodal function defined over a real interval. It applies when the domain is continuous and the function has a single peak or valley. Unlike the discrete version, there is no final scan. The algorithm stops when the interval becomes sufficiently small. Problem Given a function $f(x)$ defined over a real interval $[l, r]$, find a point $x$...
algorithms searching ternary-search optimization continuous
Wiki › Algorithms › 01. Searching and Sorting › 2. Binary Search and Ordered Search ›

Discrete Ternary Search

Discrete Ternary Search Discrete ternary search finds the maximum or minimum of a unimodal function defined over integer indices. A function is unimodal if it strictly increases up to a point and then strictly decreases, or the reverse. Unlike binary search, which relies on a monotone predicate, ternary search relies on a unimodal shape. Problem Given a function $f(i)$ defined on integer indices $i \in [0, n-1]$, find an index...
algorithms searching ternary-search optimization
Wiki › Algorithms › 01. Searching and Sorting › 2. Binary Search and Ordered Search ›

Binary Search on Answer

Binary Search on Answer Binary search on answer finds an optimal numeric value by searching over possible answers instead of searching over array indices. It is used when a direct formula is difficult, but a candidate answer can be tested efficiently. The method requires a monotone feasibility condition. For minimization problems, the predicate often has the form: $$ false, false, false, true, true, true $$ For maximization problems, it often...
algorithms searching binary-search optimization monotone-predicate