2. Sequential Search
O (n)
• A sequential search of a list/array begins at the beginning of the
list/array and continues until the item is found or the entire
list/array has been searched
Data Structures Using C++ 2
3. Sequential Search
bool LinSearch(double x[ ], int n, double item){
for(int i=0;i<n;i++){
if(x[i]==item) return true;
else return false;
}
return false;
}
Data Structures Using C++ 3
4. Search Algorithms
Data Structures Using C++ 4
Suppose that there are n elements in the array. The following expression
gives the average number of comparisons:
It is known that
Therefore, the following expression gives the average number of comparisons
made by the sequential search in the successful case:
6. Binary Search
O(log2 n)
•A binary search looks for an
item in a list using a divide-and-
conquer strategy
Data Structures Using C++ 6
7. Binary Search
• Binary search algorithm assumes that the items in the
array being searched are sorted
• The algorithm begins at the middle of the array in a
binary search
• If the item for which we are searching is less than the
item in the middle, we know that the item won’t be in
the second half of the array
• Once again we examine the “middle” element
• The process continues with each comparison cutting in
half the portion of the array where the item might be
Data Structures Using C++ 7
10. Binary Search
bool BinSearch(double list[ ], int n, double item, int&index){
int left=0;
int right=n-1;
int mid;
while(left<=right){
mid=(left+right)/2;
if(item> list [mid]){ left=mid+1; }
else if(item< list [mid]){right=mid-1;}
else{
item= list [mid];
index=mid;
return true; }
}// while
return false;
}
Data Structures Using C++ 10
15. Binary Search Tree
O(log2 n)
bool search(Node * root, int id) {
bool found = false;
if(root == NULL) return false;
if(root->data == id) {
cout<<" The node is found "<<endl;
found = true;
}
if(!found) found = search(root->left, id);
if(!found) found = search(root->right, id);
return found;
}
Data Structures Using C++ 15
![Sequential Search
bool LinSearch(double x[ ], int n, double item){
for(int i=0;i<n;i++){
if(x[i]==item) return true;
else return false;
}
return false;
}
Data Structures Using C++ 3](https://image.slidesharecdn.com/06-search-array-1-linearbinary-250227094049-e0b4b476/85/06-search-ar121r11111ay-1-LinearBinary-ppt-3-320.jpg)
![Binary Search
bool BinSearch(double list[ ], int n, double item, int&index){
int left=0;
int right=n-1;
int mid;
while(left<=right){
mid=(left+right)/2;
if(item> list [mid]){ left=mid+1; }
else if(item< list [mid]){right=mid-1;}
else{
item= list [mid];
index=mid;
return true; }
}// while
return false;
}
Data Structures Using C++ 10](https://image.slidesharecdn.com/06-search-array-1-linearbinary-250227094049-e0b4b476/85/06-search-ar121r11111ay-1-LinearBinary-ppt-10-320.jpg)
