ExponentialSearch (TheAlgorithms#14)

mered, ignoring CI failure for macOS-latest

src/searches/exponential_search.jl

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+"""
+# Exponential Search
+It works in O(Log n) time
+Exponential search involves two steps:  
+- Find range where element is present
+- Do Binary Search in above found range.
+### Time Complexity : 
+O(Log n) 
+### Auxiliary Space :
+The above implementation of Binary Search is recursive and requires O(Log n) space. With iterative Binary Search, we need only O(1) space.
+Applications of Exponential Search: 
+Exponential Binary Search is particularly useful for unbounded searches, where size of array is infinite. Please refer Unbounded Binary Search for an example.
+It works better than Binary Search for bounded arrays, and also when the element to be searched is closer to the first element.
+"""
+
+""" 
+	Binary Search 
+"""
+function binary_search(arr::AbstractArray{T,1}, l::T, r::T, x::T) where T <: Real
+	n = size(arr)[1]
+	if(r>=l)
+		mid = Int(ceil(l+(r-l)/2));
+		println(mid)
+		if(arr[mid] == x)
+			return "Element present at index $mid"
+		elseif(arr[mid] > x)
+			binary_search(arr, l, mid-1, x)
+		else
+			binary_search(arr, mid+1, r, x)
+		end
+	else 
+		return "Element not present in array"
+	end
+end
+
+"""
+	 exponential_search(arr::AbstractArray{T,1}, x::T) where {T <: Real}
+	
+Exponential Search in 1-D array
+Time Complexity:  O(Log n)
+"""
+function exponential_search(arr::AbstractArray{T,1}, x::T) where {T <: Real}
+	n = size(arr)[1]
+	if(arr[1] == x)
+		return "Elemenet present at index 1"
+	end
+
+	i = 1
+	while( i<n && arr[i]<=x)
+		i = i * 2
+	end
+	return binary_search( arr, Int(ceil(i / 2)), min(i, n), x)   
+end
+
+
+# Arguments
+arr = [1, 2, 3, 4, 13, 15, 20];
+x = 4;
+n = size(arr)[1]
+l = 1;
+r = n;
+
+exponential_search(arr, x)