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The variant's value must decrease during each loop iteration but must never become negative during the correct execution of the loop. Loop variants are used to guarantee that loops will terminate. A loop invariant is an assertion which must be true before the first loop iteration and remain true after each iteration.
Loops implemented using a counter variable as typically found in data processing algorithms will usually terminate, demonstrated by the pseudocode example below: i := 0 loop until i = SIZE_OF_DATA process_data(data[i])) // process the data chunk at position i i := i + 1 // move to the next chunk of data to be processed
The test for i < len is still present, but it has been moved outside the loop, which now contains only a single test (for the value), and is guaranteed to terminate due to the sentinel value. There is a single check on termination if the sentinel value has been hit, which replaces a test for each iteration.
The loop counter is used to decide when the loop should terminate and for the program flow to continue to the next instruction after the loop. A common identifier naming convention is for the loop counter to use the variable names i, j, and k (and so on if needed), where i would be the most outer loop, j the next inner loop, etc. The reverse ...
After a function's value is computed for that parameter or set of parameters, the result is stored in a lookup table that is indexed by the values of those parameters; the next time the function is called, the table is consulted to determine whether the result for that combination of parameter values is already available. If so, the stored ...
first checks whether x is less than 5, which it is, so then the {loop body} is entered, where the printf function is run and x is incremented by 1. After completing all the statements in the loop body, the condition, (x < 5), is checked again, and the loop is executed again, this process repeating until the variable x has the value 5.
Therefore a loop possessing a variant will terminate after a finite number of iterations, as long as its body terminates each time. A while loop , or, more generally, a computer program that may contain while loops, is said to be totally correct if it is partially correct and it terminates.
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value.