Binary search

Binary Search searches by exploiting the ordering in a sequence in splitting it in half each time.

A real-life example of Binary Search would be if you were to look for the name "Larry" in a phonebook, you would first go to the middle of the phonebook, if "Larry" is before the middle entry, you rip and throw away the latter half, and then do the same thing.

Binary Search is an example of divide and conquer paradigm. It runs in $$O(log n)$$ time on an array of length $$n$$.

Pseudo-code
Recursively: /* Searches value 'x' in sorted array a[left], a[left+1], ..., a[right]. Returns the index of 'x' in array, or -1 if it cannot be found. */ search(a, left, right, x)   if left > right then return -1 mid := floor((left + right) / 2) if a[mid] = x then return mid else if a[mid] > x then return search(a, left, mid-1, x)   else return search(a, mid+1, right, x)

Iteratively (in C): /* Search value 'x' in array a[0],a[1],...,a[n-1] */ int search(int a[], int n, int x) { int l, r, c;   for (l = 0, r = n-1; l <= r;) { c = (l + r) / 2; if (a[c] > x)           r = c - 1; else if (a[c] < x)           l = c + 1; else return c;   } return -1; }