如何更改算法以获得更好的渐近复杂度？

Question

guys.

I have an algo with a good timing, i should change it to get better time, but i have no any idea.

Can u help me?

Here is time:

• real 0m0.164s
• user 0m0.021s
• sys 0m0.010s

Here is algo:

def algo2(A, B):
    x=0
    y=0
    for a in A:
          m=0
          for b in B:
                if a == b:
                      m += 1
          if m>y:
                x = a
                y = m
    return x;

Here is arrays for algo:
A = [1,2,3,4,5,6,7,8,9,0] B = [1,2,3,4,5,6,4,7,8,9,0]

Answer 1

Your algorithm is O(n*m). If the arrays are always sorted, you can do a straight merge (O(n+m)), as below. (Note that the code is not python ... I think you can get the idea and translate it)

ixA = 0
ixB = 0
maxVal = 0
maxCount = 0
workingVal = A[ixA]
workingCount = 0
while (ixA < A.length and ixB < B.length)
{
    if (workingVal == B[ixB])
    {
        workingCount += 1
    }
    else if (workingCount > maxCount)
    {
        maxCount = workingCount
        maxVal = workingVal
        workingCount = 0
        ixA += 1
        workingVal = A[ixA]
    }
    ixB += 1
}
// have to check the last one
if (workingCount > maxCount)
{
    maxCount = workingCount
    maxVal = workingVal
}

If the arrays aren't sorted, you can sort them first, then do the merge. That will be O(m log m) + O(n log n) + O(m+n). That's still better than your O(m*n).