Mastering Dynamic Programming#

Dynamic programming (DP) is a method for solving complex problems by breaking them down into simpler subproblems. It is one of the most commonly tested topics in technical interviews.

The Two Key Properties#

A problem is a good candidate for DP if it has:

Optimal substructure — the optimal solution contains optimal solutions to subproblems
Overlapping subproblems — the same subproblems are solved multiple times

Top-Down vs. Bottom-Up#

Top-Down (Memoization)#

Start with the main problem and recursively solve subproblems, caching results.

python

def fib(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 1:
        return n
    memo[n] = fib(n - 1, memo) + fib(n - 2, memo)
    return memo[n]

Bottom-Up (Tabu#

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Mastering Dynamic Programming: From Recursion to Optimization