Hacker be mitigated. White hats are usually employed by the target system's owner and are typically paid (sometimes quite well) for their work. Their work is not illegal because it is done with the system owner's consent. Black hats or crackers are hackers with malicious intentions. They often steal, exploit, and sell data, and are usually motivated by personal gain. Their work is usually illegal. A cracker is like a black hat hacker, but is specifically someone who is very skilled and tries via hacking to make profits or to benefit, not just to vandalize. Crackers find exploits for system vulnerabilities
Prefix sum runs in linear time for integer keys that are smaller than the number of items, and is frequently used as part of radix sort, a fast algorithm for sorting integers that are less restricted in magnitude. List ranking, the problem of transforming a linked list into an array that represents the same sequence of items, can be viewed as computing a prefix sum on the sequence 1, 1, 1, ... and then mapping each item to the array position given by its prefix sum value; by combining list ranking, prefix sums, and Euler tours, many important problems on trees may