1.1 Data Structure and Algorithm Lecture 1 Array Record Sequential Search Binary Search Bubble Sort Recursion Complexity Topics

1.2 Data Structure and Algorithm Array An array is a sequence of elements. All the elements of an array must be of the same type (e.g. integer). Each elements can be selected by specifying its position index int list[10] Dhaka index char city[5]

1.3 Data Structure and Algorithm Record A record/structure is a collection of one or more variables, possibly of different types. An array is a sequence of elements all having the same type and size, whereas a record or structure is a sequence of elements having different types and sizes. Each element of a record is its member. Employee: Record name:char[20] address:char[50] salary: real struct employee{ char name[20]; char address[50]; float salary; }; Fig: C Convention

1.4 Data Structure and Algorithm Sequential Search [ Find the location where list array keeps the value of k ] sequential_search(k) returns integer Begin i = 0 while i k do i = i+1 if i<array_size then return i else return -1 End

1.5 Data Structure and Algorithm “C” implementation of Sequential Search #include int list[10] = {5,6,1,3,4,1,7,2,0,3}; int array_size = 10; int sequential_search(int k){ int i = 0; while ( (i<array_size) && ( list[i] != k) ) i++; if (i<array_size) return i; else return -1; } void main(){ int pos = sequential_search(2); printf(“The position is:%d”,pos); }

1.6 Data Structure and Algorithm Binary Search [ Find the location where sorted table array keeps the value of k ] binary_search(k): returns integer BEGIN l = 0 h = array_size found = 0; while l<h and found = 0 do m= (l+h)/2 //find the middle element xm = table[m] case xm<k: l = m+1 xm>k: h = m-1 xm=k: found = 1 if found then return m else return -1 END

1.7 Data Structure and Algorithm “C” Implementation of Binary Search #include int table[10] = {1,5,8,12,15,20,34,40,55,67}; int array_size = 10; int binary_search(int k){ int l =0; int h = array_size; int found =0,m,xm; while ( (l<h) && (found == 0) ){ m = (l+h)/2; xm = table[m]; if (xm<k) l = m+1; else if (xm>k) h = m-1; else found = 1; } if (found) return m; else return -1; } void main(){ int pos = binary_search(20); printf("The position is:%d",pos); }

1.8 Data Structure and Algorithm Recursive Binary Search [ Find the location where sorted table array keeps the value of k ] binary_search(l,h,k) BEGIN if l>h index = -1 else m= (l+h)/2 //find the middle element xm = table[m] case xm<k: binary_search(m+1,h) xm>k: binary_search(l,m-1) xm=k: index=m END

1.9 Data Structure and Algorithm Bubble Sort For i=0 to n-2 do BEGIN For j = i+1 to n-1 do BEGIN if list[i] > x[j] then swap list[i] and list[j] END

1.10 Data Structure and Algorithm Complexity Generally the complexity of an algorithm is measured by the two factors:  Time complexity  Space complexity Sequential search : O(n) Binary search: O(log 2 n) Bubble sort: O(n 2 )