Dynamic Programming: Concepts to Code

Solve 1D DP problems where state `dp[i]` depends on previous states `dp[j]` for `j < i` (e.g., House Robber).

Solve the Coin Change problem by defining state as the target amount.

Solve the Longest Increasing Subsequence problem by searching over previous optimal subproblems.

Optimize memory in 1D DP by reducing state storage (e.g., from O(N) to O(1)).

Solve 2D grid traversal problems (e.g., Unique Paths, Minimum Path Sum).

Solve the 0/1 Knapsack problem using a 2D state representing items and capacity.

Compute the length of the Longest Common Subsequence (LCS) of two strings.

Compute the Edit Distance between two strings.

Reconstruct the optimal solution for a DP problem (e.g., the items in the knapsack, the LCS) by backtracking through the computed DP table.

Adapt reconstruction logic for different problem types, such as pathing versus subset selection.

Identify interval substructure where the state `dp[i][j]` represents a solution for a contiguous range `[i...j]`.

Solve the Matrix Chain Multiplication problem using an interval DP formulation.

Solve a partitioning problem (e.g., Palindrome Partitioning) using interval DP.

Given a novel problem, determine if DP is applicable and classify its likely structural pattern (e.g., 1D sequence, 2D, interval).

Systematically derive a DP solution: define state, write the recurrence, identify base cases, and determine the final answer's location.

Debug a DP implementation by validating state transitions, base cases, and boundary conditions.