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Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
For example, a procedure that adds up all elements of a list requires time proportional to the length of the list, if the adding time is constant, or, at least, bounded by a constant. Linear time is the best possible time complexity in situations where the algorithm has to sequentially read its entire input.
The problem of exponential time complexity in top-down parsers constructed as sets of mutually recursive functions has been solved by Norvig in 1991. [9] His technique is similar to the use of dynamic programming and state-sets in Earley's algorithm (1970), and tables in the CYK algorithm of Cocke, Younger and Kasami.
In software engineering, profiling ("program profiling", "software profiling") is a form of dynamic program analysis that measures, for example, the space (memory) or time complexity of a program, the usage of particular instructions, or the frequency and duration of function calls.
Link-time optimization (LTO) is a type of program optimization performed by a compiler to a program at link time. Link time optimization is relevant in programming languages that compile programs on a file-by-file basis, and then link those files together (such as C and Fortran), rather than all at once (such as Java's just-in-time compilation ...
Since the time taken on different inputs of the same size can be different, the worst-case time complexity () is defined to be the maximum time taken over all inputs of size . If T ( n ) {\displaystyle T(n)} is a polynomial in n {\displaystyle n} , then the algorithm is said to be a polynomial time algorithm.
A model of computation may be defined in terms of an abstract computer, e.g. Turing machine, and/or by postulating that certain operations are executed in unit time. For example, if the sorted list to which we apply binary search has n elements, and we can guarantee that each lookup of an element in the list can be done in unit time, then at ...
Most compilers have at least the following compiler phases (which therefore occur at compile-time): syntax analysis, semantic analysis, and code generation.During optimization phases, constant expressions in the source code can also be evaluated at compile-time using compile-time execution, which reduces the constant expressions to a single value.