Search Problem

Algorithm

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Search Problems can be divided as Sequential Search, Binary Search, Interpolation

1. Sequential Search

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2. Binary Search

Please Check:

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3. Interpolation Search

Interpolation Equation:

$$index = \frac{(target - arr[low])}{(arr[high]- arr[low])}*{(high-low)}$$

On average the interpolation search makes about log(log(n)) comparisons (if the elements are uniformly distributed), where n is the number of elements to be searched. In the worst case (for instance where the numerical values of the keys increase exponentially) it can make up to O(n) comparisons.

    public int interpolationSearch(int[] nums, int key) {       
        int l = 0, r = nums.length-1;
        while(l<r){
            int m = l+(r-l)*(key - nums[l])/(nums[r]-nums[l]);
            if(nums[m]<key)
                l = m+1;
            else if(nums[m]>key)
                r = m;
            else
                return m;
        }   
        return -1;
    }

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4. Fibonacci Search