Question1 (b)Consider the followingalgorithmwhere Small is an array of ninteger values:   AlgorithmQ1 //Input: An array Smallcontaining ninteger values b = ∞ for h = 1 to n-1       for k = h + 1 to n           if (Small[h] –Small[k]) < b                       b = Small[h] –Small[k]                           return b   i.Explain what does this algorithm compute. ii.Findthe asymptotic bound/complexity ofthis algorithm. iii.Producean improved algorithm to Question1 (b) above with a better asymptotic complexity/running time. iv.Findthe asymptotic bound/complexity of the improvedalgorithmin Question 1(b)iii. above.

Prime numbers can also be generated by an algorithm known as the Sieve of Eratosthenes . The algorithm for this procedure is presented here. Write a program that implements this algorithm so as to find all prime numbers up to n = 150. Sieve of Eratosthenes Algorithm To Display All Prime Numbers Between 1 and n Step 1: Define an array of integers P . Set all elements P i to 0, 2 <= i <= n. Step 2: Set i to 2. Step 3: If i > n , the algorithm terminates. Step 4: If P i is 0 (value i is a prime number), then i is prime and display its value. Step 5: For all positive integer values of j , such that i * j ≤ n , set P i ∗ j to 1 (non - prime). Step 6: Add 1 to i and go to step 3

in java ecplise . Implement a program that randomly generates 10 integers from -100 to 100,stores them in a 1D array, and finds their maximum value. Calculate theexecution time of finding a maximum. Repeat the test for 10,000 and10,000,000 numbers. Provide your results in the form of a table below andprovide a small summary. Implement a Java program that will populate a 5x5 matrix with randomlygenerated integers from 0 to 100.(1) print your matrix in a table form.(2) modify your code to multiply all even numbers by 10 and print the matrix.Your output of questions (1) and (2) should match the format of the followingsample outputs:

The algorithm below searches for the maximum in an input array A. Assume A is a random sequence containing n distinguishable real numbers, what is the probability for line #4 to be executed exactly once? (The phrase "random sequence" here means the n numbers can appear in any order with equal chance.) mymax(A, n) { 1: max = A[1]; 2: for i = 2:n 3: if A[i] > max 4: max = A[i); 5: end; 6: end; 7: return max; }