The document discusses data structures and algorithms. It defines data structures as organized ways of storing data to allow efficient processing. Algorithms manipulate data in data structures to perform operations like searching and sorting. Big-O notation is introduced to analyze algorithms' time complexity as the problem size increases. Common time complexities like O(1), O(log n), O(n), O(n log n), O(n^2), O(n^3) and O(2^n) are defined. An example algorithm to find the minimum element in an array is analyzed, showing it has O(n) time complexity. Selection sort is analyzed and shown to have O(n^2) time complexity.

1. Data Structures and Algorithms Lecture # 1 Book: Fundamentals of Data Structures in c++ Horwitz, Sahani, and Mehta

15. Abstraction Vs. Implementation Two dimensional array User’s view (abstraction) System’s view (implementation) 54 345 106 0 99 82 76 22 64 38 2 3 6 3 5 1 54 345 106 0 99 82 76 22 64 38 2 3 6 3 5 1

25. found=false; while (( ! Found) && (low<= high)) { mid = (low + high)/2; if( A[mid]==key) found=true; else if ( A[mid] > key) high = mid – 1; else low = mid +1; } Key=29 73 55 50 48 47 32 29 28 22 15 12 10 7 5 3 2 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

31. Example 1 – Summing of a list of numbers (Step count Table) 2n+3 Total 0 0 0 } 1 1 1 return temp; N n 1 temp+=list[i] ; n + 1 n + 1 1 for (i=0;i<n; i++) 0 0 0 int i ; 1 1 1 float temp=0; 0 0 0 { 0 0 0 Float sum (float list[],int n) Total Steps Frequency S/e Statement

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