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In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
In computer programming, foreach loop (or for-each loop) is a control flow statement for traversing items in a collection. foreach is usually used in place of a standard for loop statement.
Armstrong number, also known as a narcissistic number or a pluperfect digital invariant (PPDI), is a number that is equal to the sum of its own digits, ...
For-loops are typically used when the number of iterations is known before entering the loop. For-loops can be thought of as shorthands for while-loops which increment and test a loop variable. Various keywords are used to indicate the usage of a for loop: descendants of ALGOL use "for", while descendants of Fortran use "do".
In contrast, e.g. the property 0<=i && i<=n is a loop invariant for both the original and the optimized program, but is not part of the code, hence it doesn't make sense to speak of "moving it out of the loop". Loop-invariant code may induce a corresponding loop-invariant property.
The key insight in the algorithm is as follows. If there is a cycle, then, for any integers i ≥ μ and k ≥ 0, x i = x i + kλ, where λ is the length of the loop to be found, μ is the index of the first element of the cycle, and k is a whole integer representing the number of loops.
First, place the natural numbers along the top row. To determine a number in the table, take the number immediately to the left. Then use that number to look up the required number in the column given by that number and one row up. If there is no number to its left, simply look at the column headed "1" in the previous row.
A conditional loop has the potential to become an infinite loop when nothing in the loop's body can affect the outcome of the loop's conditional statement. However, infinite loops can sometimes be used purposely, often with an exit from the loop built into the loop implementation for every computer language , but many share the same basic ...