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High Quality Content by WIKIPEDIA articles! The Steinhaus Johnson Trotter algorithm or Johnson Trotter algorithm is an algorithm that generates permutations by transposing elements.The algorithm is set up with the idea that only one set of neighbors needs to swap positions and that there need only be one swap to generate the next permutation. To accommodate this, there needs to be an extra data element added: direction of mobility (ie direction of the swap). This direction is either left or right, but is initialized to the left.An integer is said to be mobile if, in the direction of its mobility, the nearest integer is less than the current integer. Note that if an integer is to the far left and its mobility is to the left, it is not mobile. Similarly, if an integer is to the far right and its mobility is to the right, it is also not mobile.