Advanced Algorithms and Programming Techniques

Explore greedy algorithms through classic problems like the activity selection problem and Kadane's algorithm for maximum subarray sums, including interval scheduling and pairing examples.

Explore the knight's path on an n-by-n chessboard, visiting every square exactly once using a backtracking C++ approach with a move matrix and recursive search.

Apply dynamic programming to count non-attacking rooks on an imaginary board using the R[i][j] recurrence, then count non-attacking bishops on a chessboard.

Learn how to count word occurrences in a letter grid using dynamic programming, including prefix-based layering, and compare with Boggle’s backtracking approach that prohibits revisiting squares.

Explore Catalan numbers, definitions and recurrences for counting correctly paired parentheses, and apply them to equivalent problems and a C++ program computing C[n] modulo 1000000007.

Explore dynamic programming techniques to compute probabilities for independent events, sample space definitions, and practical applications such as night moves on a chessboard, tennis match outcomes, and rainy weather.

Learn dynamic programming techniques through games with numbers, greed on parks, and matrix path problems, with DP formulations, examples, and a C++ implementation.

Learn matrix exponentiation and its properties, including the product of two matrices and efficient A^p, using the Q matrix for Fibonacci numbers and adjacency matrices for directed graphs.

Apply the sliding window technique to compute minimum and maximum values in 1D and 2D arrays, solve trapped water problems, and find subarray minima in linear time.

Master advanced dynamic programming techniques for problems with overlapping subproblems, including dynamic programming on states, high-dimensional arrays, dynamic programming on trees and games, with memoization and hashing.

Explore dynamic programming for computational geometry problems, including optimal triangulation of convex polygons and selecting a convex polygon with the maximum number of vertices from a set of points.