Memoization vs Tabulation
The two main DP implementation strategies have different trade-offs.
Memoization (Top-Down)
- Recursive approach.
- Start from the desired solution and go down to base cases.
- Store results in a cache (e.g., array or hash map) to avoid recomputation.
- Easier to code, especially for complex state transitions.
- May cause stack overflow for deep recursion.
Tabulation (Bottom-Up)
- Iterative approach.
- Start from base cases and build up to the desired solution.
- Usually uses an array (DP table).
- More efficient (no recursion overhead) and avoids stack overflow.
- Sometimes harder to derive the order of computation.
Example: Fibonacci numbers
// Memoization (top-down)
int[] memo = new int[n+1];
int fibMemo(int n) {
if (n <= 1) return n;
if (memo[n] != 0) return memo[n];
memo[n] = fibMemo(n-1) + fibMemo(n-2);
return memo[n];
}
// Tabulation (bottom-up)
int fibTab(int n) {
int[] dp = new int[n+1];
dp[0] = 0; dp[1] = 1;
for (int i = 2; i <= n; i++) dp[i] = dp[i-1] + dp[i-2];
return dp[n];
}
Two Minute Drill
- Memoization: recursion + caching. Easier to implement.
- Tabulation: iterative DP table. More efficient, avoids stack.
- Both have same time complexity, but tabulation often uses less overhead.
- Choose based on problem nature and constraints.
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