Dynamic Programming Made Simple: Divide‑and‑Conquer and Redundancy Elimination

Many people feel algorithms are difficult and think interview questions are just a showcase of intelligence, but the author argues that each algorithm has a simple core idea that can be expressed in one or two sentences; once that idea is grasped, memorization is unnecessary.

Core idea 1: advanced recursion (divide‑and‑conquer) – Any seemingly complex problem can be reduced to a collection of sub‑problems. No matter how large the original problem, if a solution exists it can be broken into n smaller, independent sub‑problems that resemble the original. These are solved recursively and their solutions are merged to obtain the final answer. This view treats dynamic programming as an optimized form of recursion.

Core idea 2: memoization – While solving the n sub‑problems, intermediate results are stored so that the same sub‑problem is not recomputed. By reusing previously computed answers, the algorithm avoids wasted computation and eliminates redundant work.

The author extends the analogy to business management: a boss decomposes a performance target into sub‑tasks (e.g., marketing, product, operations), lets each department recursively handle its part, and then integrates the results. The boss also looks for duplicated effort across project teams and creates a shared technical platform to provide standard solutions, mirroring memoization’s role in avoiding redundant work.

In summary, dynamic programming’s essence is the combination of divide‑and‑conquer thinking and the elimination of redundancy through memoization. This strategy is applicable to any optimization problem whose sub‑problem tree contains many repeated sub‑problems, and mastering it enables programmers to tackle a wide range of complex, real‑world challenges.