Searching and Hashing

It is important to understand what search is and when it is appropriate. This page explains sequential and binary search, and their implementation. There is also the matter of hashing as a storage and search technique. In so doing, we introduce the unordered map and how to implement a map abstract data type using hashing. Read Sections 6.1-6.5. You may also find Sections 6.6-6.11 useful for practice.

2. Searching

In the next two chapters we will turn our attention to some of the most common problems that arise in computing: searching and sorting. In this chapter we will study searching and return to sorting in the next chapter.

Searching is the algorithmic process of finding a particular item in a collection of items. A search typically answers either True or False as to whether the item is present. On occasion it may be modified to return where the item is found. For our purposes here, we will simply concern ourselves with the question of membership.

In many languages, libraries provide very easy ways to ask whether an item is in a container of items. In Python one uses the in operator on a list:

>>> 15 in [3,5,2,4,1]
>>> 3 in [3,5,2,4,1]

In C++, the STD vector library provides the find command which works on vectors and even on arrays (although much more awkwardly.) Here is an example using a vector:

>>> #include <vector>
>>> int myints<int> = {3, 5, 2, 4, 1};
>>> cout << find(myints.begin(), myints.end(), 15);
>>> cout << find(myints.begin(), myints.end(), 3);

How does this work? Even though this is easy to write, an underlying process must be carried out to do the search.

A function can be created for C++ arrays by passing in the array, the size of the array, and the value to search for as arguments.

bool isIn(int alist[], int size, int value) {
    for (unsigned i=0; i<size; i++) {
        if (alist[i] == value) {
            return true;
    return false;

int main() {
    int myarr[] = {3, 5, 2, 4, 1};

    cout<<isIn(myarr, 5, 15)<<endl;
    cout<<isIn(myarr, 5, 3)<<endl;

    return 0;

This works, but it is not the only way to search! It turns out that there are multiple different ways to search for the item. What we are interested in here is how these algorithms work and how they compare to one another.