CODEWITHSUNDEEP
algorithmsearch
nerd
nerd

Reputation: 31

Ternary search recursion isn't correct

I learned about ternary search from Wikipedia. I'm not sure what they mean by the parameter absolute precision. They didn't elaborate. But here is the pseudocode:

def ternarySearch(f, left, right, absolutePrecision):
    #left and right are the current bounds; the maximum is between them
    if (right - left) < absolutePrecision:
        return (left + right)/2

    leftThird = (2*left + right)/3
    rightThird = (left + 2*right)/3

    if f(leftThird) < f(rightThird):
        return ternarySearch(f, leftThird, right, absolutePrecision)

    return ternarySearch(f, left, rightThird, absolutePrecision)

I want to find max value from a unimodal function. That means I want to print the border point of the increasing and decreasing sequence. If the sequence is

1 2 3 4 5 -1 -2 -3 -4

then I want to print 5 as output.

Here is my attempt. It isn't giving output. Can you please help or give me link that contains good tutorial on ternary search for self learning?

#include<iostream>

using namespace std;
int ternary_search(int[], int, int, int);
int precval = 1;

int main()
{
    int n, arr[100], target;
    cout << "\t\t\tTernary Search\n\n" << endl;
    //cout << "This program will find max element in an unidomal array." << endl;
    cout << "How many integers: "; 
    cin >> n;
    for (int i=0; i<n; i++)
        cin >> arr[i];
    cout << endl << "The max number in the array is: ";
    int res = ternary_search(arr,0,n-1,precval)+0;
    cout << res << endl;
    return 0;
}

int ternary_search(int arr[], int left, int right, int precval)
{
    if (right-left <= precval)
        return (arr[right] > arr[left]) ? arr[right] : arr[left];
    int first_third = (left * 2 + right) / 3;
    int last_third = (left + right * 2) / 3;
    if(arr[first_third] < arr[last_third])
        return ternary_search(arr, first_third, right, precval);
    else
        return ternary_search(arr, left, last_third, precval);
}

Thank you in advance.

Upvotes: 2

Views: 1669

Answers (2)

lijie
lijie

Reputation: 4871

Absolute precision means the maximum error between the returned result and the true result i.e. max | returned_result - true_result |. In that context, f is a continuous function.

Since you are looking at a discrete function, you can't do much better than get to the point where right - left <= 1. Then, just compare the two resultant values and return the value corresponding to the larger one (since you're looking for max).

EDIT

The first partition point, being mathematically 2/3*left + right/3, should be discretized to ceil(2/3*left + right/3) (so that the relationship is left < first_third <= last_third < right

So first_third = (left*2+right)/3 should be changed to first_third = (left*2 + right + 2)/3.

Upvotes: 2

Liberius
Liberius

Reputation: 148

Try Golden Section search (or Fibonacci search for discrete functions). It has a smaller number of recursions AND a 50% reduction in evaluations of f, compared to the above ternary search.

Upvotes: 0

Related Questions