Please, please, I want a solution and explanation, as well as the analysis and design of algorithms

theoretical

Q1. Find the topological sorting problem for the given graph A and B. (2 Mark) Q2. Apply Merge sort and Quick to sort the list, U, N, I, V, R, S, I, T , Y in alphabetica order. (2 Mark) Q3. Explain Master Theorem.Using Master Theorem solved the following recurrence. relation a) T(n)=9T(2n/6)+n2 b) T(n)=6T(3n/27)+n5 (2 Mark) Q4. Write the Recursive algorithm for Quick Sort.Consruct the recurrence relation for recursive algorithm and solve using backward Subtution. (2 Mark) 25. Solve the following equations using Gaussian Elimination Method: 5x13x2+6x3=107x1+7x27x3=236x1+4x22x3=20 (2 Mark) Q1. Find the topological sorting problem for the given graph A and B. ( 2 Mark ) Q2. Apply Merge sort and Quick to sort the list, U,N,I,V,R,S,I,T,Y in alphabetical order. (2 Mark) Q3. Explain Master Theorem.Using Master Theorem solved the following recurrence. relation (2 Mark) a) T(n)=9T(2n/6)+n2 b) T(n)=6T(3n/27)+n5 Q4. Write the Recursive algorithm for Quick Sort.Consruct the recurrence relation for recursive algorithm and solve using backward Subtution. (2 Mark) Q5. Solve the following equations using Gaussian Elimination Method: (2 Mark) 5x13x2+6x3=107x1+7x27x3=236x1+4x22x3=20