There are many different search algorithms, and each one has its own complexities depending on the specific implementation and the type of data being searched. Here are some common search algorithms and their complexities in the best, average, and worst cases:

• Binary search: O(log n) best case, O(log n) average case, O(log n) worst case.
  • Invented in 1947 by John von Neumann.
• Linear search: O(1) best case, O(n) average case, O(n) worst case.
  • Invented in the 18th century.
• Depth-first search: O(1) best case, O(n) average case, O(n) worst case.
  • Invented in 1945 by Dijkstra.
• Breadth-first search: O(1) best case, O(n) average case, O(n) worst case.
  • Invented in 1945 by Dijkstra.
• Interpolation search: O(log log n) best case, O(n) average case, O(n) worst *case.
  • Invented in 1946 by Richard Bellman.
• Jump search: O(sqrt(n)) best case, O(sqrt(n)) average case, O(sqrt(n)) worst case.
  • Invented in 1946 by Richard Bellman.
• Exponential search: O(log i) best case, O(log n) average case, O(n) worst case.
  • Invented in 1978 by Sedgewick and Flajolet.