From Memo to Table

The same DP as a loop instead of recursion: same array, base cases first, loop so that what you need is already filled, copy the recurrence. Then save memory with two variables.

11 min 1 video Quiz Pro

Memo works from the top down: start from the big question and let recursion reach the small ones. A table works from the bottom up: fill the small answers first in a loop. Same answers, same speed.

When to bother:

The recursion can be very deep (thousands of calls): use a table.
The question asks you to save memory: use a table plus two variables.
Otherwise memo is fine in a test. Get the memo right first.

The 5 steps

Step	Do
1	Same array, same size as the memo
2	Write the base-case answers into it
3	Loop so that the values you need are already filled
4	Copy the recurrence, with `f(x)` replaced by `dp[x]`
5	The answer is `dp` at the first call’s state

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Inside: 4 sections · 1 video · quiz.

The 5 steps
Example: Frog Jump
2-D tables
Save memory

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Item 21 of 44 · updated 2026-10-13