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Design and Analysis of Algorithms Lab program

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1. i. Implement Insertion Sort (The program should report the number of comparisons)
ii. Implement Merge Sort(The program should report the number of comparisons)

2. Implement Heap Sort(The program should report the number of comparisons)

3. Implement Randomized Quick sort (The program should report the number of comparisons)

4. Implement Radix Sort

5. Create a Red-Black Tree and perform following operations on it:
i. Insert a node ii. Delete a node
iii. Search for a number & also report the color of the node containing this number.

6. Write a program to determine the LCS of two given sequences

7. Implement Breadth-First Search in a graph

8. Implement Depth-First Search in a graph

9. Write a program to determine the minimum spanning tree of a graphFor the algorithms at S.No 1 to 3 test run the algorithm on 100 different inputs of sizes varying from30 to 1000. Count the number of comparisons and draw the graph. Compare it with a graph ofnlogn

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