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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.
For example, if the input is 123 456 789 and the hash table size 10 000, then squaring the key produces 15 241 578 750 190 521, so the hash code is taken as the middle 4 digits of the 17-digit number (ignoring the high digit) 8750. The mid-squares method produces a reasonable hash code if there is not a lot of leading or trailing zeros in the key.
The problem of determining if a given set of Wang tiles can tile the plane. The problem of determining the Kolmogorov complexity of a string. Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers.
Simon's problem considers access to a function : {,} {,}, as implemented by a black box or an oracle. This function is promised to be either a one-to-one function, or a two-to-one function; if is two-to-one, it is furthermore promised that two inputs and ′ evaluate to the same value if and only if and ′ differ in a fixed set of bits. I.e.,
While the chosen value is an invalid result for this operation, it might be a valid input to followup operations. For example in Python str.find returns −1 if the substring is not found, [2] but −1 is a valid index (negative indices generally start from the end [3]).
Python supports a wide variety of string operations. Strings in Python are immutable, so a string operation such as a substitution of characters, that in other programming languages might alter the string in place, returns a new string in Python. Performance considerations sometimes push for using special techniques in programs that modify ...
In computer science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting may also often be applied to sorting problems in which the keys are floating point numbers, rational numbers, or text strings. [1]
For example, factoring is a search problem where the instances are (string representations of) positive integers and the solutions are (string representations of) collections of primes. A search problem is represented as a relation consisting of all the instance-solution pairs, called a search relation. For example, factoring can be represented ...