If a problem is NP-hard, under the assumption that P ≠ NP there is no algorithm that is deterministic, exactly correct on all inputs all the time, and efficient on all possible inputs. If you absolutely need all of the above guarantees, then you’re pretty much out of luck. However, if you’re willing to settle … Read more
For k=4, space complexity O(n), time complexity O(n2 * log(n)) Sort the array. Starting from 2 smallest and 2 largest elements, calculate all lesser sums of 2 elements (a[i] + a[j]) in the non-decreasing order and all greater sums of 2 elements (a[k] + a[l]) in the non-increasing order. Increase lesser sum if total sum … Read more
This problem is NP-Complete! In a nutshell one needs to explore all possible combinations to find the list of acceptable solutions. Because of the variations in the circumstances in which the problem appears at various schools (for example: Are there constraints with regards to classrooms?, Are some of the classes split in sub-groups some of … Read more
I assume that you are looking for intuitive definitions, since the technical definitions require quite some time to understand. First of all, let’s remember a preliminary needed concept to understand those definitions. Decision problem: A problem with a yes or no answer. Now, let us define those complexity classes. P P is a complexity class … Read more