Question

My first array M + N size and second array of size N.

let us say m=4,n=5
a[ ]= 1,3,5,7,0,0,0,0,0

b[ ]= 2,4,6,8,10

Now , how can i merge these two arrays without using external sorting algorithms and any other temporary array(inplace merge) but complexity should be o(n).Resultant array must be in sorted order.

Answer 1

Provided a is exactly the right size and arrays are already sorted (as seems to be the case), the following pseudo-code should help:

#    0 1 2 3 4 5 6 7 8
a = [1,3,5,7,0,0,0,0,0]
b = [2,4,6,8,10]
afrom = 3
bfrom = 4

ato = 8
while bfrom >= 0:
    if afrom == -1:
        a[ato] = b[bfrom]
        ato = ato - 1
        bfrom = bfrom - 1
    else:
        if b[bfrom] > a[afrom]:
            a[ato] = b[bfrom]
            ato = ato - 1
            bfrom = bfrom - 1
        else:
            a[ato] = a[afrom]
            ato = ato - 1
            afrom = afrom - 1
print a

It’s basically a merge of the two lists into one, starting at the ends. Once bfrom hits -1, there are no more elements in b so the remainder in a were less than the lowest in b. Therefore the rest of a can remain unchanged.

If a runs out first, then it’s a matter of transferring the rest of b since all the a elements have been transferred above ato already.

This is O(n) as requested and would result in something like:

[1, 2, 3, 4, 5, 6, 7, 8, 10]

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Understanding that pseudo-code and translating it to your specific language is a job for you, now that you’ve declared it homework 🙂