Brute force-algorithm

INTRODUCTION
The Maximum sub-array problem is the task of finding the contiguous sub-array
within a one dimensional array.
For Example:
Brute force algorithm is a step by step procedure for solving a problem so it is
consider as a straight forward approach usually based on the problem statement.
1 -3 2 -5 7 6 -1 -4 11 -23
0 1 2 3 4 5 6 7 8 9

PSEUDO CODE
Max-Sub-array-Brute-Force (A)
n = A.length
max-so-far = -∞
For l = 1 to n
sum = 0
for h = l to n
sum = sum + A[h]
if sum > max-so-far
max-so-far = sum
low = l
high = h
Return (low , high)

IMPLEMENTATION
3 -2 5 -1
0 1 2 3
FOR EXAMPLE
:
1.
3
SUM:
-2 5 -1
3 -2 -15
MAX_SO_FA
R
3 3 5 5
2.
3 -2 -2 5 5 -1
SUM: 1
MAX_SO_FA
R
5
3
5 5
4
Taking one at a
time :
Taking two at a
time :

3.
3 -2 -2 5
SUM: 6
MAX_SO_FA
R
6
2
6
Taking three at a
time :
IMPLEMENTATION
5 -1
3 -2
SUM: 5
MAX_SO_FA
R
6
5
4. Taking four at a time
:
-1

IMPLEMENTATION
3 -2 5 -1
0 1 2 3
Maximum Sub-Array

Max-Sub-array-Brute-Force (A)
n = A.length
max-so-far = -∞
For l = 1 to n
sum = 0
for h = l to n
sum = sum + A[h]
if sum > max-so-far
max-so-far = sum
low = l
high = h
Return (low , high)
O(n)
O(n)
Time
Time Complexity
Overall time complexity :
O(n2)

CONCLUSION
 Brute force is a straight forward approach to problem solving , It is applicable to very wide variety of
problem.
 Brute force algorithm is useful for solving small size instance of problem.
 A brute force algorithm can serve an important theoretical or educational purpose.
 A brute force algorithm is often easier to implement than a more sophisticated one and , because of this
simplicity, sometime it can be more efficient.
 Brute force algorithm is used when the simplicity of implementation is more important than speed.
 Brute force algorithm can be applied only to problems where input size is small , otherwise it will be
not efficient .

Brute force-algorithm

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Brute force-algorithm