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  2. Bit manipulation - Wikipedia

    en.wikipedia.org/wiki/Bit_manipulation

    To determine if a number is a power of two, conceptually we may repeatedly do integer divide by two until the number won't divide by 2 evenly; if the only factor left is 1, the original number was a power of 2. Using bit and logical operators, there is a simple expression which will return true (1) or false (0):

  3. List of NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/List_of_NP-complete_problems

    Dominating set, a.k.a. domination number [3]: GT2 NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem in line graphs. NP-complete variants include the connected dominating set problem and the maximum leaf spanning tree problem. [3]: ND2 Feedback vertex set [2] [3]: GT7

  4. P versus NP problem - Wikipedia

    en.wikipedia.org/wiki/P_versus_NP_problem

    For example, the problem of deciding whether a graph G contains H as a minor, where H is fixed, can be solved in a running time of O(n 2), [25] where n is the number of vertices in G. However, the big O notation hides a constant that depends superexponentially on H .

  5. Partition problem - Wikipedia

    en.wikipedia.org/wiki/Partition_problem

    The problem is known to undergo a "phase transition"; being likely for some sets and unlikely for others. If m is the number of bits needed to express any number in the set and n is the size of the set then / < tends to have many solutions and / > tends to have few or no solutions. As n and m get larger, the probability of a perfect partition ...

  6. Karp's 21 NP-complete problems - Wikipedia

    en.wikipedia.org/wiki/Karp's_21_NP-complete_problems

    In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...

  7. Integer programming - Wikipedia

    en.wikipedia.org/wiki/Integer_programming

    An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers.In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.

  8. Stable marriage problem - Wikipedia

    en.wikipedia.org/wiki/Stable_marriage_problem

    The hospitals/residents problem – also known as the college admissions problem – differs from the stable marriage problem in that a hospital can take multiple residents, or a college can take an incoming class of more than one student.

  9. Bitwise operation - Wikipedia

    en.wikipedia.org/wiki/Bitwise_operation

    For unsigned integers, the bitwise complement of a number is the "mirror reflection" of the number across the half-way point of the unsigned integer's range. For example, for 8-bit unsigned integers, NOT x = 255 - x , which can be visualized on a graph as a downward line that effectively "flips" an increasing range from 0 to 255, to a ...