Ternary Search
I haven’t yet encountered a problem where this is needed. It is very similar to Binary Search , except that it reduces the time complexity even more, (log base 3).

Unimodality
We are given a function $f(x)$ which is Unimodal Function on an interval $[l,r]$ .

In this article, we will assume the first scenario. The second scenario is completely symmetrical to the first.

The task is to find the maximum of function f(x) on the interval [l,r].

double ternary_search ( double l , double r ) {
double eps = 1 e- 9 ; //set the error limit here
while (r - l > eps) {
double m1 = l + (r - l) / 3 ;
double m2 = r - (r - l) / 3 ;
double f1 = f (m1); //evaluates the function at m1
double f2 = f (m2); //evaluates the function at m2
if (f1 < f2)
l = m1;
else
r = m2;
}
return f (l); //return the maximum of f(x) in [l, r]
}

// Function to perform Ternary Search (iteratively)
int ternarySearch ( int l , int r , int key , int ar [])
{
while (r >= l) {
// Find the mid1 and mid2
int mid1 = l + (r - l) / 3 ;
int mid2 = r - (r - l) / 3 ;
// Check if key is present at any mid
if (ar[mid1] == key) {
return mid1;
}
if (ar[mid2] == key) {
return mid2;
}
// Since key is not present at mid,
// check in which region it is present
// then repeat the Search operation
// in that region
if (key < ar[mid1]) {
// The key lies in between l and mid1
r = mid1 - 1 ;
}
else if (key > ar[mid2]) {
// The key lies in between mid2 and r
l = mid2 + 1 ;
}
else {
// The key lies in between mid1 and mid2
l = mid1 + 1 ;
r = mid2 - 1 ;
}
}
// Key not found
return - 1 ;
}
// Driver code
int main ()
{
int l, r, p, key;
// Get the array
// Sort the array if not sorted
int ar[] = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 };
// Starting index
l = 0 ;
// length of array
r = 9 ;
// Checking for 5
// Key to be searched in the array
key = 5 ;
// Search the key using ternarySearch
p = ternarySearch (l, r, key, ar);
// Print the result
cout << "Index of " << key << " is " << p << endl;
// Checking for 50
// Key to be searched in the array
key = 50 ;
// Search the key using ternarySearch
p = ternarySearch (l, r, key, ar);
// Print the result
cout << "Index of " << key << " is " << p;
}