4. Design and analysis of an Algorithm (25 points) A is an array of n data records to sort and that the key of each record has the value 0 or 1. Design an algorithm for sorting such a set of records possess the following desirable characteristics: The algorithm runs in O(n) time. The algorithm is stable. The algorithm returns A as output, i.e., A stores the final result. (1) (15 points) Pseudocode: Give an algorithm that satisfies the above criteria. The pseudocode should use the textbook conventions (2) (10 points) Analysis: Justify your algorithm runs in O(n) time and why it is stable. What is the space complexity of your algorithm? 7. To sort a set of data, the data must be compared and moved as necessary. The efficiency of these two operations depends on the size of the data set. for d = 1 to the position of the leftmost digit of the longest number distribute all numbers in data[ ] among queues through 9 according to the dth digit; put all integers in data[ ]; Figure 3: Pseudocode for sorting algorithm X. a) Based on pseudocodes in Figure 3, identify the name of the sorting algorithm. b) Identify the complexity for sorting algorithm X in Figure 3. (2 Marks) (2 Marks) [Total: 4 Marks]