# Algorithms and Flowchart Binary Search

## Binary Search

**Q) Explain the binary search with an algorithm.**

- Binary search is an efficient search as compared to a linear search. it is used to search elements from a sorted array.
- In the search middle element of an array is compared with the item, if they are equal then a search is successful.
- Otherwise, it item > middle element then perform searching in the upper half or if item<middle element then perform searching in the lower half.

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### Working Binary Search

- Initially set beg = 1 and end = size of the array, then find the middle of an array using mid= (beg+end)/2.
- Compare array[mid] with the item to be searched, if they are equal the search is successful and the process is stopped.
- When the value of item > array[mid] then proceed to search in the upper half using beg = mid + 1. Otherwise, when the value of item < array [mid] then proceeds to search in the lower half using end = mid - 1.
- The same steps are repeated in the respective half until the element is found or beg <= end.

**Algorithm: Binary_Serach[Data[], lb, ub, item, loc]**

- This the algorithm for linear search
- Data[]- Array of an element,
- lb- lower bound,
- ub - upper bound,
- beg -beginning position,
- end - end position,
- mid - middle position,
- item - element to be search,
- loc - location.

step 1: start

step 2 : [initialize variable]

Set beg=lb, end=ub,loc=0

step 3 : Repeat steps4, 5 and 6 until beg <= end and data[mid] != item

step 4 : [find middle]

mid=(beg+end)/2

step 5 : [compare data[mid] and item]

if data [mid] == itme the

set loc=mid

End if

step 6 : [jump in respective half]

if item >data[mid]then

beg = mid + 1

else

end = mid - 1

step 7 : if loc == 0 then

Print "item is not found"

else

Print "item is found at loc"

step 8 : Stop

### Example Binary Search

Consider the following example containing 8sorted array elements.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|

11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 |

Element to be searched is:

**55**set

**beg = 1**and

**end = 8**

**Pass 1**

Find mid

mid = (ben+end)/2

mid = (1+8)/2

mid = 4

compare A[mid] with 55

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|

11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 |

Red is mid

As A[mid] != 55 &

55 > A[mid] Proceed searching in the Upper half

Set beg = mid + 1

beg = 4 + 1

beg = 5

**Pass 2**

Find mid

mid = (beg+end)/2

mid = (5+8)/2

mid = 6

compare A[mid] with55

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|

11 | 22 | 33 | 5 | 55 | 66 | 77 | 88 |

Red is mid

As A[mid] != 55 &

55 < A[mid] Proceed searching in the lower half

Set end = mid - 1

end = 6 - 1

end = 5

**Pass 3**

Find mid

mid = (beg+end)/2

mid = (5+5)/2

mid = 5

compareA[mid] with 55

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|

11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 |

Red is mid

As A[mid] = 55

Print "Search is Successful"

**Result:**Given element 55 is found ar 5th position.

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