The Road To Dynamic Programming: Java, JavaScript, & Python

Explore how dynamic programming optimizes the fibonacci sequence by replacing exponential recursive calls with base cases F(0)=0 and F(1)=1, using normalization and tabulation.

Switch from memorisation to tabulation for the fibonacci problem, using a bottom-up dynamic programming array to store values and avoid stack overflow.

The lecture demonstrates a dynamic programming approach to making change, using two nested loops to update the minimum number of bills for each amount by comparing current and new solutions.

Implement a Java dynamic programming solution that computes the minimum number of bills for a given amount using a dp array and update logic, returning -1 if impossible.

Write pseudocode to solve a dynamic programming coin change problem by iterating bills, updating the number of ways for each amount, and validating with an example before implementing.

implement a java dynamic programming approach to count ways to make an amount with given bills. initialize ways[0]=1, update with each bill, and validate with amount 5 and bills 1,2,3,4.

JavaScript programming to count ways to make a target amount with given bill denominations. Use a ways array, set ways[0] = 1, then update for each bill and return ways[amount].

Implement a Python function to compute the number of ways to make a target amount using given bills, updating a ways list with for loops and printing the results.

This lecture introduces the knapsack problem, compares fractional and discrete versions, and shows dynamic programming as the solution, including unlimited quantity and without repetition cases with weights and values.

Explore the knapsack problem with a dynamic programming approach, defining value and weight arrays and a dp table of size W+1, and implement the nested loops to update optimal solutions.

Explore implementing the knapsack problem in JavaScript with a dynamic programming approach. Build a knapsack function that processes weights and values to compute the maximum value for a given capacity.

Explore the knapsack without repetition problem and build a two-dimensional dynamic programming solution, contrasting it with the unlimited-quantity version, illustrated by a weight-10 example that yields 57.

Explore counting subsets that sum to a target using recursion, illustrated with [1,3,4,5] and target 9. Identify two subsets (1,3,5) and (4,5) and preview dynamic programming with memorization.

Implement a JavaScript dynamic programming function using a memo map to count the number of ways to reach a target total by including or excluding list elements.

This lecture demonstrates a dynamic programming tabulation approach to the longest common subsequence, building a 2d matrix with zeros and diagonal matches, with time complexity O(x*y).

Learn to implement the longest common subsequence length in Java using dynamic programming, including a public static function, a dp matrix, and the recurrence.

This video demonstrates optimizing a recursive approach with dynamic programming to compute the longest increasing subsequence, using a per-index array and nested loops with quadratic time and linear space.

Implement a JavaScript function to compute the longest increasing subsequence using dynamic programming, initialize arrays and indices, iterating i and j, and verify results on a sample data list.

Recap how we use Fibonacci sequence to define memorization and tabulation, draw trees and matrices with pseudocode, solve dynamic programming algorithms by hand, and implement in Java, JavaScript, and Python.