Time and Space Complexity of Ternary Search Last Updated : 15 Feb, 2024 Comments Improve Suggest changes Like Article Like Report The time complexity of Ternary Search is O(log3 N), where N is the size of the array. In terms of space complexity, ternary search requires only O(1) auxiliary space, as it operates directly on the given array without creating any additional data structures. Feature Ternary Search Time Complexity O(log3N) Auxiliary Space O(log3 N) Let's explore the detailed time and space complexity of the Ternary Search: Time Complexity of Ternary Search:Best Case Time Complexity: O(1) When the target element is found at the midpoint of the search interval.Average Case Time Complexity: O(log3 n) When the target element is not found at the midpoint, but is found within the search interval. This is the average case because, on average, the search interval will be divided into three equal parts, and the target element will be found within one of these parts.Worst Case Time Complexity: O(log3 n) When the target element is not found within the search interval. In this case, the search interval will be repeatedly divided into three equal parts until it becomes empty. The worst case occurs when the target element is not in the array, and the search interval is divided into three equal parts at each step.Auxiliary Space of Ternary Search:The auxiliary space of ternary search is O(log3 N), where N is the number of elements in the ternary search tree. This complexity is primarily due to the recursive call stack. Recursive Calls Stack: O(log3 N) Ternary search uses recursion to traverse the ternary search tree. Each recursive call creates a new stack frame, which requires additional memory space. The maximum depth of the recursion is equal to the height of the ternary search tree, which can be as large as O(log3 N). Comment More infoAdvertise with us Next Article Time and Space Complexity of Ternary Search T tarunsarawgi_gfg Follow Improve Article Tags : Algorithms Analysis of Algorithms Searching DSA Ternary Search +1 More Practice Tags : AlgorithmsSearching Similar Reads Time and Space Complexity of Depth First Search (DFS) The Depth First Search (DFS) algorithm is used to traverse a graph. It starts with a given source node and explores as far as possible along each branch before backtracking. It mainly traverses all vertices reachable through one adjacent, then it goes to the next adjacent.C++DFS(graph, root): create 2 min read Time and Space Complexity of Breadth First Search (BFS) The Breadth First Search (BFS) algorithm is used to traverse a graph. It starts at a node of the graph and visits all nodes at the current depth level before moving on to the nodes at the next depth level.Although there are other methods for graph traversal, BFS is commonly used for its level-wise e 4 min read Time and Space Complexity of Insertion Sort What is Insertion Sort?Insertion sort is a simple sorting algorithm that works similarly to the way you sort playing cards in your hands. The array is virtually split into a sorted and an unsorted part. Values from the unsorted part are picked and placed in the correct position in the sorted part. T 2 min read Time Complexity and Space Complexity Many times there are more than one ways to solve a problem with different algorithms and we need a way to compare multiple ways. Also, there are situations where we would like to know how much time and resources an algorithm might take when implemented. To measure performance of algorithms, we typic 13 min read Time and Space Complexity Analysis of Binary Search Algorithm Time complexity of Binary Search is O(log n), where n is the number of elements in the array. It divides the array in half at each step. Space complexity is O(1) as it uses a constant amount of extra space. Example of Binary Search AlgorithmAspectComplexityTime ComplexityO(log n)Space ComplexityO(1) 3 min read Like