# huge sparse array

(data structure)

**Definition:**
Let N be the number of items to store and R be the size of the *range* of *key* values; R >> N. Allocate, but don't initialize, two arrays: an item array I, where |I|≥N, and a location array L, where |L|=R. Initialize a variable, next, the number of items, to zero (with *0-based indexing*). To insert an item, put it in the next place in the item array and save where to find it in the location array.

I[next] = item;

L[item.key] = next;

next++;

To look up an item by key, get the index from the location array. If the index is invalid or refers to the wrong item, the item is not found. index = L[key];

if (index < 0 OR index >= next) return NOTFOUND;

if (I[index].key != key) return NOTFOUND;

return I[index];

Inserting N items takes *Θ(N)* total time, assuming allocation takes constant time. Retrieving an item by key (or responding "not found") takes constant time. Listing all items takes Θ(N) time using I.
**Generalization** (I am a kind of ...)

*array*.

**See also**
*sparse matrix*, *hash table*.

*Note:
Keys must be unique. Duplicate keys could be handled with **collision resolution schemes*. This data structure is usually impractical since the range is enormous.

*
* This effectively allocates a huge array without explicitly initializing it, at the cost of Θ(N) space and a little time for each access.

* This is what **hash tables* want to be: constant time for insertion and look up.

Author: PEB

## More information

**Historical Note**

Motivating problem first posed as exercise 2.12 in **Alfred V. Aho, John E. Hopcroft**, and **Jeffrey D. Ullman**, *The Design and Analysis of Computer Algorithms*, page 71, Addison-Wesley, 1974.

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.

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Cite this as:

Paul E. Black, "huge sparse array", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 14 August 2008. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/hugeSparseArray.html