Factorial
The factorial of a nonnegative integer n, written n!, is the product of all positive integers from 1 through n, with 0! equal to 1.
Statistics Every Programmer Needs
A factorial is the product of all positive integers from a given natural number down to one.
- How it is used
- Uses factorials to count ordered selections when replacement is not allowed.
- How deep it goes
- Defines factorials, works through numerical examples, derives a permutation formula, and implements it in Python.
- Examples
- Uses 5!, 3!, five runners competing for three positions, and Python results for 60 permutations.
- What you can do after
- Apply factorials via Python's math.factorial to calculate permutation counts without replacement.
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Classic Computer Science Problems in Swift: Essential techniques for practicing programmers
A factorial is the product of all positive integers from one through a given nonnegative integer.
- How it is used
- Uses factorial to quantify the search space of brute-force traveling-salesman permutations.
- How deep it goes
- Defines factorial through permutation growth and stops short of deriving its formula or analyzing factorial algorithms.
- Examples
- Uses five, six, and seven cities to show how factorially many traveling-salesman paths expand.
- What you can do after
- Evaluate whether exhaustive permutation search is practical and recognize when near-optimal methods are preferable.
Related concepts
- sine functionused by · The sine function is a periodic trigonometric function that maps a real number or angle to a value between −1 and 1.
- recursionimplemented by · Recursion is a computational technique in which a definition or procedure refers to or invokes the same definition or procedure, directly or indirectly.
- permutationmeasures · A permutation is a bijective rearrangement of the elements of a finite set, equivalently an ordering in which each element appears exactly once.
- conditional logicuses · Conditional logic is a programming technique that selects execution paths, actions, or result values according to evaluated conditions.
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