Discrete math Blocks consisting of successive Os or Is are called run. (such as 000, 1, 11, 00) With a run test, we test whether a password consisting of 0 and 1 is randomly generated as follows: Total number of runs in a n-bit array is (n + 1) /2: The number of runs with a length of 1 is (n + 1) /22; The number of runs with length of k is (n + 1) / 2*+1. For example, for z = 1101000 running password n is 7, and the expected number of runs: 4 according to formula. -The number of runs with a length of 1: (n + 1) /22= 2. - The number of runs with a length of 2: (n + 1) / 23= 1. - Number of runs with a length of 3: (n + 1) /24=0.5 3 1. Indeed, 4 runs for this password is obtained as follows; - Runs with a length of 1: 0 and 1 (2) - Run length 2; 11 (1) - Run with a length of 3; 000 (1) Accordingly, create a flowing password that passes the 15-bit long run test.

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Counting sort

The counting sort algorithm sorts an array’s contents by counting the repetition of each element that occurs in the array. A counting sort algorithm is a stable algorithm that works the best when the range of elements in the array is small, say for example from 0 to 9. The count which is the number of repetitions of an element in the array is mapped to an index of an auxiliary array, which is then saved in an auxiliary array. The counting sort algorithm has a stable time complexity of the order of O(size of array + size of auxiliary array). Let’s discuss the algorithm in detail as follows.