Ternary search code added

Author: me-shaon

Searching/Ternary Search/README.md

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+# Ternary Search
+
+ **Ternary search** algorithm is a technique in computer science for finding the minimum or maximum of a [unimodal](https://en.wikipedia.org/wiki/Unimodality) function. A ternary search determines either that the minimum or maximum cannot be in the first third of the domain or that it cannot be in the last third of the domain, then repeats on the remaining two-thirds.
+ Unimodal functions are functions that, have a single highest value.
+
+
+#### Binary Search vs. Ternary Search
+Binary search looks a zero or a specific value in case of monotonic(Non-increasing or non-decreasing) input; ternary search is used to locate an extremum for unimodal(Having a single extremum) inputs.
+
+
+#### Complexity Analysis
+- Average Case - O(logn)
+
+
+### More on this topic
+- https://en.wikipedia.org/wiki/Ternary_search
+- https://www.hackerearth.com/practice/algorithms/searching/ternary-search/tutorial/

Searching/Ternary Search/search.py

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+def simpleTernarySearch(item_list):
+    """
+    Find the maximum value in a strictly increasing and then strictly decreasing list
+    N.B.- This method won't work if the list does not represent an unimodal function
+    e.g. if the maximum value present in the first or last index of the list
+    """
+    left, right = 0, len(item_list) - 1
+
+    found = False
+
+    while left <= right:
+        if (right - left) < 3: #Here 3 is the smallest range to divide the left and right value
+            found = True
+            break
+
+        leftThird = left + (right - left) // 3
+        rightThird = right - (right - left) // 3
+
+        #To find the minimum in an unimodal function change the following comparison to >
+        if item_list[leftThird] < item_list[rightThird]:
+            left = leftThird
+        else:
+            right = rightThird
+
+    return (left + right) // 2
+
+
+def ternarySearch(func, left, right, absolutePrecision):
+    """
+    Find maximum of unimodal function func() within [left, right]
+    To find the minimum, reverse the if/else statement or reverse the comparison.
+    """
+    while True:
+        #left and right are the current bounds; the maximum is between them
+        if abs(right - left) < absolutePrecision:
+            return (left + right)/2
+
+        leftThird = left + (right - left)/3
+        rightThird = right - (right - left)/3
+
+        if func(leftThird) < func(rightThird):
+            left = leftThird
+        else:
+            right = rightThird
+
+
+def ternarySearchRecursive(func, left, right, absolutePrecision):
+    """
+    left and right are the current bounds. the maximum is between them
+    """
+    if abs(right - left) < absolutePrecision:
+        return (left + right)/2
+
+    leftThird = (2*left + right)/3
+    rightThird = (left + 2*right)/3
+
+    if func(leftThird) < func(rightThird):
+        return ternarySearch(func, leftThird, right, absolutePrecision)
+    else:
+        return ternarySearch(func, left, rightThird, absolutePrecision)

Searching/Ternary Search/test.py

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+from search import *
+
+def main():
+    # This list must be sorted. If it is not given as sorted, sort it first, then call the binarySearch method
+    testlist = [1, 50, 20, 10, 2, 1]
+    index = simpleTernarySearch(testlist)
+    print(testlist[index])
+
+    result = ternarySearch(func, 0, 1, 1e-6)
+    print(func(result))
+
+    result = ternarySearchRecursive(func, 0, 1, 1e-6)
+    print(func(result))
+
+
+def func(x):
+    return -1*1*x*x + 2*x +3 # (-a*x*x + b*x + c) is an unimodal function, here a = 1, b = 2, c = 3
+
+if __name__ == '__main__':
+    main()