Remember that one “Guess the Number” game? Let’s look at the following scenario by applying the Binary Search algorithm in order for you to understand how Binary Search works.

The Guessing Game

Pick a number from 0 – 100 and depending on your guess, I’ll either say Correct, Higher, or Lower. What would you choose?

0

1

…

49

50

51

…

99

100

Well, 50 of course! Why? Best case you get it correct. Worst case you’ll either get a “Higher” or “Lower”. Now think about the following, if you got “Higher” you eliminated 0-49, or 51-100 if “Lower”, in other words, you eliminate HALF the possibilities.

50

51

…

74

75

76

…

99

100

Well, let’s say it was “Higher”. What would you guess after? 75. Since it’s in between 50 – 100. If you didn’t guess correctly, you’ll be facing the similar scenario as before. You’ll end up eliminating half the possibilities!

Binary Search Algorithm

The following is the recursive implementation.

int binarysearch(vector  vec, int low, int high, int key)
{
    //Not found
    if ( low > high )
    {
          return -1;
    }

    //Finding the middle index between high and low
    int mid = (low + high)/2;

    //Returning the index if key is found
    if ( vec[mid] == key )
    {
          return mid;
    }
    //If middle index value is larger than our key, we search the lower half of the vector
    //else we search the upper half of the vector
    else if ( vec[mid] > key )
    {
          return binarysearch(vec, low, mid-1, key);
    }
    else
    {
          return binarysearch(vec, mid+1, high, key);
    }
}

Example of Binary Search

Let’s say our container held the values 0-100 in its respective index values. Let’s say the value we are looking for is 57.

First iteration

50 < 57, so search through the upper half of our vector.

Second iteration

75 > 57, so search through the lower half of our vector.

Third iteration

63 > 57, so search through the lower half of our vector.

Fourth iteration

57 == 57!

Introduction

Without the use of a data structure, how would you store multiple variables? Let’s say we wanted to store 5 names into strings. How would this be done?

string name1,name2,name3,name4,name5;
cin >> name1 >> name2 >> name3 >> name4 >> name5;

That looks a bit ugly doesn’t it? What if we wanted to store the number of names the user wanted to input? That is where the vector comes in.

The Vector

#include  //You need to include this library to use the vector

//Syntax:
vector  name;

To populate our vector with 5 names, we would simply do the following:

vector  names;

string input;
for ( int i = 0; i < 5; i++ ) {
     cin >> input;
     names.push_back(input);
}

In other words, we simply ask the user five times with our for loop, to type in the terminal a name, and it will be push_back‘ed onto our vector. Every single time we use the push_back member function of the vector, we simply push the newly inserted element to the back. Let’s use the following visual example of a vector.

vector  names;
names.push_back("Joe");
names.push_back("Beth");
names.push_back("Mary");
names.push_back("Jon");
names.push_back("Sue");

How would we access and print out a variable?

Printing out elements of the vector

To print out an element we would simply do the following:

cout << names[0];

This allows us to print out the value that is contained in position zero. Therefore, "Joe".


To find out the size of our vector we would simply do:

cout << names.size();

This would print out 5 since our vector contains 5 elements.


To remove an element from our vector we would simply do:

names.pop_back();

This would remove "Sue" from our vector, giving it a size of 4.

Doing more with the vector

Challenge 1: Populate a vector with 5 integer values, and print them all out.
Challenge 2: Print out all the elements of a vector using a for loop.

What now?

Join our forums and discuss your newly discovered vector! Remember, there is still so much more to learn with how to use a vector, this is simply a tutorial for beginners and isn't meant for advanced users.