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This change gives the following algorithm (for a zero-based array). -- To shuffle an array a of n elements (indices 0..n-1): for i from n−1 down to 1 do j ← random integer such that 0 ≤ j ≤ i exchange a[j] and a[i] An equivalent version which shuffles the array in the opposite direction (from lowest index to highest) is:
The simplest form goes through the whole list each time: procedure cocktailShakerSort(A : list of sortable items) is do swapped := false for each i in 0 to length(A) − 1 do: if A[i] > A[i + 1] then // test whether the two elements are in the wrong order swap(A[i], A[i + 1]) // let the two elements change places swapped := true end if end for if not swapped then // we can exit the outer loop ...
Doing permutations(l+1, A) will in each iteration i of the for-loop, first do permutations(l, A) (rotating the first l elements of A by 1 position since l is even) and then, swap the elements in positions 0 and l (the last position) in A. Rotating the first l elements and then swapping the first and last elements is equivalent to rotating the ...
The reversal algorithm is the simplest to explain, using rotations. A rotation is an in-place reversal of array elements. This method swaps two elements of an array from outside in within a range. The rotation works for an even or odd number of array elements. The reversal algorithm uses three in-place rotations to accomplish an in-place block ...
Using the XOR swap algorithm to exchange nibbles between variables without the use of temporary storage. In computer programming, the exclusive or swap (sometimes shortened to XOR swap) is an algorithm that uses the exclusive or bitwise operation to swap the values of two variables without using the temporary variable which is normally required.
Suppose we want to swap the ith and the jth element. Clearly, inversions formed by i or j with an element outside of [i, j] will not be affected. For the n = j − i − 1 elements within the interval (i, j), assume v i of them form inversions with i and v j of them form inversions with j.
Recursively divide the list into sublists of (roughly) equal length, until each sublist contains only one element, or in the case of iterative (bottom up) merge sort, consider a list of n elements as n sub-lists of size 1. A list containing a single element is, by definition, sorted. Repeatedly merge sublists to create a new sorted sublist ...
For example, in a program, two variables may be defined thus (in pseudocode): data_item x := 1 data_item y := 0 swap (x, y); After swap() is performed, x will contain the value 0 and y will contain 1; their values have been exchanged.