Dynamic programming sounds advanced, but the first idea is approachable: if a program solves the same smaller problem many times, save the answer and reuse it. That can turn very slow recursive solutions into efficient ones.
Look for repeated subproblems
A recursive Fibonacci method is the classic example. It repeatedly recomputes the same values. Memoization stores those values after the first computation.
public static int fib(int n, int[] memo)
{
if (n <= 1)
return n;
if (memo[n] != 0)
return memo[n];
memo[n] = fib(n - 1, memo) + fib(n - 2, memo);
return memo[n];
}Memoization vs tabulation
Memoization starts with recursion and adds storage. Tabulation builds a table from small cases upward. Both approaches use stored answers to avoid repeated work.
Common mistakes
- Trying dynamic programming before defining the state clearly.
- Storing answers using the wrong index or key.
- Forgetting to initialize base cases.
- Using DP when a simpler greedy or sorting solution is enough.
Practice idea
Start with small counting problems: number of ways to climb stairs, best score up to each position, or longest increasing pattern in a small list. Write the state in plain English before writing code.