Introduction to Algorithms : Analysis of Insertion Sort
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  • Step 1: The for loop executed n times, for i values from 2, 3, .....n+1
  • Step 2, 3, and 7: Each executed once for each iteration of the for loop. That is, each n-1 times.
  • Step 4: The while loop is executed at most i times, for i = 2, 3, .............., n. That is, .
  • step 5 and 6: Each instruction executed i-1 times, for each i. Hence, for each instruction.
  • Total number of instruction executed in the worst case is . Hence the time complexity of the algorithm is in .

    Similarly, we can analyze space required for the algorithm also. The Insertion sort algorithm has to store all n inputs and using three more variables. So, the space complexity of the algorithm is in .
 
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