Dynamic Programming Algorithms Master Course

Learn how to implement factorial using recursion, identify base and recursive cases, explore call stack dynamics, and analyze time and space complexity O(N).

Learn to determine if an array is sorted using recursion, with base cases and two implementation approaches: pointer arithmetic with n-1 and index-based checks in C++.

Learn to derive recurrences for tiling a 4x n board with 4x1 tiles using recursion, considering vertical and horizontal placements and the F(n)=F(n-1)+F(n-4) base cases.

Count the ways n friends go solo or pair up using f(n)=f(n-1)+(n-1)f(n-2) with base cases, and see how dynamic programming and memorization reduce time from exponential to linear.

Explore counting all n-queen configurations by extending backtracking to accumulate every valid arrangement, using base cases that return one and summing results across rows and columns.

Learn to implement a sudoku solver using backtracking and brute-force search, filling empty cells with 1–9 while upholding row, column, and 3x3 subgrid rules.

Explore dynamic programming fundamentals by forming states, deriving recursive relations, and solving 26 problems using bottom-up (tabulation) and top-down (memorization) approaches, with optimal substructure and overlapping subproblems.

Master dynamic programming by comparing tabulation and memorization through a Fibonacci example. See how memorization reduces calls and how bottom-up tabulation builds solutions, guiding you to start top-down.

Explore how dynamic programming solves a Zonal Computing Olympiad scheduling problem, weighing greedy ideas, and building DP states, base cases, and transitions for optimal substructure and overlapping subproblems.

Explore the rod cutting problem via dynamic programming, treating it as a partitioning task and using a recurrence to maximize price by cutting the rod into subpieces.

Explore rod cutting with dynamic programming, using a recursive relation and memoization to maximize revenue from given prices. Consider base cases and one-dimensional structure to analyze DP time complexity.

Explore the house robber problem and solve it with dynamic programming, presenting two-state and one-dimensional approaches, with recurrence relations and space optimization.

Learn subset sum with tabulation in dynamic programming by building a table that shows sums achievable with or without each element, then optimize memory.

Explore memory optimization in the subset sum dynamic programming solution by using two-row and one-row techniques to reduce space complexity while maintaining time efficiency.

Trace back approaches in dynamic programming to reconstruct a subset by choosing include or exclude decisions, using an index-based base case and a print-subset routine to follow the solution path.

Explore the knapsack problem through zero-one and unbounded variants, compare greedy approaches with dynamic programming insights, and learn why greedy can fail for optimal value.

Use a dynamic programming approach to the colorful knapsack, selecting exactly one stone from each color within capacity, and maximize the total weight via a dp table.

Compute the minimum painting cost for adjacent houses by iterating colors, initializing base cases, and updating dynamic programming arrays to track costs, ensuring no two adjacent houses share a color.

Apply dynamic programming to the plates problem, using two stacks and a dp state to pick exactly p top plates for maximum beauty.

Learn a dynamic programming approach to palindromic partitioning, using memoization to compute the minimum number of palindromic partitions in a string, with palindrome checks and dynamic programming states.