# memoization

(algorithmic technique)

**Definition:**
Save (memoize) a computed answer for possible later reuse, rather than recomputing the answer.

**See also**
*dynamic programming*.

*Note:
The term comes from "memo": "A short note written as a reminder." [The American Heritage Dictionary of the English Language, © 1970, American Heritage Publishing]
*

* A naive program to compute **Fibonacci numbers* is

* fib(n) {*

if n is 1 or 2, return 1;

return fib(n-1) + fib(n-2);

}

* Because fib() is recomputed over and over for the same argument, run time for the above is **Ω*(1.6^{n}). If instead we memoize (save) the value of fib(n) the first time we compute it, the run time is *Θ*(n).
allocate array for memo;

set all elements of memo to zero;

fib(n) {

if n is 1 or 2, return 1;

if memo[n] is not zero, return memo[n];

memo[n] = fib(n-1) + fib(n-2);

return memo[n];

}

* Of course, computing Fibonacci numbers can be easily done in **logarithmic* time (see *Fibonacci numbers*), but this illustrates memoization.

Author: PEB

## Implementation

Mark Nelson's tutorial to using C++ Hash Table Memoization: [for] Simplifying Dynamic Programming (C++).

Go to the
Dictionary of Algorithms and Data
Structures home page.

If you have suggestions, corrections, or comments, please get in touch
with Paul Black.

Entry modified 14 August 2008.

HTML page formatted Tue Jan 16 10:34:44 2018.

Cite this as:

Paul E. Black, "memoization", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 14 August 2008. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/memoize.html