Merge pull request TheAlgorithms#151 from DTBUday/master

Added Ternary Search Algorithm

Author: harshildarji

searches/ternary_search.py

@@ -0,0 +1,112 @@
+'''
+This is a type of divide and conquer algorithm which divides the search space into
+3 parts and finds the target value based on the property of the array or list 
+(usually monotonic property).
+
+Time Complexity  : O(log3 N)
+Space Complexity : O(1)
+'''
+
+import sys
+
+# This is the precision for this function which can be altered.
+# It is recommended for users to keep this number greater than or equal to 10.
+precision = 10
+
+# This is the linear search that will occur after the search space has become smaller.
+def lin_search(left, right, A, target):
+    for i in range(left, right+1):
+        if(A[i] == target):
+            return i
+
+# This is the iterative method of the ternary search algorithm.
+def ite_ternary_search(A, target):
+    left = 0
+    right = len(A) - 1;
+    while(True):
+        if(left<right):
+            
+            if(right-left < precision):
+                return lin_search(left,right,A,target)
+
+            oneThird = (left+right)/3+1;
+            twoThird = 2*(left+right)/3+1;
+            
+            if(A[oneThird] == target):
+                return oneThird
+            elif(A[twoThird] == target):
+                return twoThird
+            
+            elif(target < A[oneThird]):
+                right = oneThird-1
+            elif(A[twoThird] < target):
+                left = twoThird+1
+            
+            else:
+                left = oneThird+1
+                right = twoThird-1
+        else:
+            return None
+
+# This is the recursive method of the ternary search algorithm.
+def rec_ternary_search(left, right, A, target):
+    if(left<right):
+        
+        if(right-left < precision):
+            return lin_search(left,right,A,target)
+
+        oneThird = (left+right)/3+1;
+        twoThird = 2*(left+right)/3+1;
+
+        if(A[oneThird] == target):
+            return oneThird
+        elif(A[twoThird] == target):
+            return twoThird
+        
+        elif(target < A[oneThird]):
+            return rec_ternary_search(left, oneThird-1, A, target)
+        elif(A[twoThird] < target):
+            return rec_ternary_search(twoThird+1, right, A, target)
+        
+        else:
+            return rec_ternary_search(oneThird+1, twoThird-1, A, target)
+    else:
+        return None
+
+# This function is to check if the array is sorted.
+def __assert_sorted(collection):
+    if collection != sorted(collection):
+        raise ValueError('Collection must be sorted')
+    return True
+
+
+if __name__ == '__main__':
+    
+    # For python 2.x and 3.x compatibility: 3.x has not raw_input builtin
+    # otherwise 2.x's input builtin function is too "smart"
+    
+    if sys.version_info.major < 3:
+        input_function = raw_input
+    else:
+        input_function = input
+
+    user_input = input_function('Enter numbers separated by coma:\n')
+    collection = [int(item) for item in user_input.split(',')]
+
+    try:
+        __assert_sorted(collection)
+    except ValueError:
+        sys.exit('Sequence must be sorted to apply the ternary search')
+
+    target_input = input_function(
+        'Enter a single number to be found in the list:\n'
+    )
+    target = int(target_input)
+    result1 = ite_ternary_search(collection, target)
+    result2 = rec_ternary_search(0, len(collection)-1, collection, target)
+    
+    if result2 is not None:
+        print('Iterative search: {} found at positions: {}'.format(target, result1))
+        print('Recursive search: {} found at positions: {}'.format(target, result2))
+    else:
+        print('Not found')