Mastering Dynamic Programming: A Comprehensive Guide to All Patterns

Pattern 1: 1D Dynamic Programming

1D Dynamic Programming is often the starting point for beginners. Here, you deal with problems where the solution can be represented as a linear progression, often involving sequences or simple state transitions.

• Climbing Stairs: A classic problem that demonstrates how each step depends on the previous one or two steps.

  • URL: Climbing Stairs (LeetCode)

• Frog Jump: Similar to climbing stairs but with varying jump lengths.

  • URL: Frog Jump (LeetCode)

• Frog Jump with K: Extends the basic Frog Jump problem to allow jumps of up to K steps.

  • URL: Frog Jump with K Steps (GeeksforGeeks)

• Maximum Sum of Non-Adjacent Elements: Find the maximum sum possible by selecting elements that are not adjacent in an array.

  • URL: House Robber (LeetCode)

• House Robber: A variant of the above problem where you're a robber trying to maximize your loot without robbing two adjacent houses.

  • URL: House Robber (LeetCode)

• Ninja's Training 2: A more complex problem where each action affects future decisions.

  • URL: Ninja's Training (Coding Ninjas)

Key Takeaway: These problems teach you to think in terms of cumulative solutions, where the current state is determined by previous decisions.