I'm looking for an intuitive, real-world example of a problem that takes (worst case) exponential time complexity to solve for a talk I am giving.
Here are examples for other time complexities I have come up with (many of them taken from this SO question):
- O(1) - determining if a number is odd or even
- O(log N) - finding a word in the dictionary (using binary search)
- O(N) - reading a book
- O(N log N) - sorting a deck of playing cards (using merge sort)
- O(N^2) - checking if you have everything on your shopping list in your trolley
- O(infinity) - tossing a coin until it lands on heads
Any ideas?
- O(10^N): trying to break a password by testing every possible combination (assuming numerical password of length N)
p.s. why is your last example is of complexity O(infinity) ? it's linear search O(N) .. there are less than 7 billion people in the world.
The brute force solution of the traveling salesman problem is O(n!) which is approximately O(N^N)
A brute-force and naive n-queens problem's solution.
You have to place n queens on a n*n board without them to be taken by others.
while there are untried configs,
go to next solution and
test it
Assuming every queen is on a given row, there are n possibilities for the queen to be placed and n for the (n-1) other queens (because duplicate rows are not checked).
Therefore, you've got a O(n^n) complexity
What about finding a subset of integers within a set such that their sum is a designated value X?
I believe this has complexity O(2^(n/2))
来源：https://stackoverflow.com/questions/7055652/real-world-example-of-exponential-time-complexity