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Looks like this would work. Seems like a pretty smart solution. The complexity seems like O(n) as it takes linear time to build a heap. So, to build 2 heaps of size n/2 will take will be O(n) as well.

Also discussed on stackoverflow. question id is 10657503

sivibasava, in your post you state that "if both heaps are of equal size peep top element from both the heaps, sum them and divide the sum by 2 and return" . This wil not work if you have the dynamically generated sequence 5, 5, 5, 5, 7, 7, 7, 7. According to your approach the median should be 6 which is not the case.

How did you build your heap. After processing all of your input
your heap ( if you followed the algo) should be

4 elements (5) in on heap and other 4 elements (7) in other heap. And once median is requested you will peep 5 & 7 and return 6.

heap max:   heap min   ramaing input       median
{}                {}                {5,5,5,5,7,7,7,7}       -1
{5}              {}                {5,5,5,7,7,7,7}          5
{5}              {5}              {5,5,7,7,7,7}             5
{5,5}           {5}              {5,7,7,7,7}                5 
{5,5}           {5,5}           {7,7,7,7}                   5 
{5,5}           {5,5,7}        {7,7,7,7}                   5 ret top ele frm max size heap
{5,5,5}        {5,7,7}        {7,7}                         5
{5,5,5}        {5,7,7,7}     {7,7}                         5
{5,5,5,5}     {7,7,7,7}     {}                              6

How did you build your heap. After processing all of your input
your heap ( if you followed the algo) should be

4 elements (5) in on heap and other 4 elements (7) in other heap. And once median is requested you will peep 5 & 7 and return 6.


heap max: heap min ramaing input median
{} {} {5,5,5,5,7,7,7,7} -1
{5} {} {5,5,5,7,7,7,7} 5
{5} {5} {5,5,7,7,7,7} 5
{5,5} {5} {5,7,7,7,7} 5
{5,5} {5,5} {7,7,7,7} 5
{5,5} {5,5,7} {7,7,7,7} 5 ret top ele frm max size heap
{5,5,5} {5,7,7} {7,7} 5
{5,5,5} {5,7,7,7} {7,7} 5
{5,5,5,5} {7,7,7,7} {} 6

According to wikipedia, if you have an even number of observations ,the median has several alternative definitions the choice being either 1) always the smallest one 2) always the largest one 3) randomly choose between the two. The advantages of 1) , 2) and 3) are that it is guaranteed that the the median is always a list element(e.g a list of integers will never have a fractional median) and it guarantees that the median exists for any ordinal valued data. sivabasava, how would you adapt your program to the alternative definitions of median?

In the even case: peep elements in both the heaps, let they be e1 and e2. In the solution I have given (e1+e2)/2 as my median, lets see how to attempt wikipedia cases.

Case 1: choose the smallest
simple return Math.min(e1,e2)
Case 2: always the largest one
simple return Math.max(e1,e2)
Case 3: randomly choose between the two
if random.randnextint(2) == 1 return e1 else e2
Hope this helps.

sivabasava, please let me know your professional opinion of the following SQLITE MEDIAN function. Thank you Cameron91

{{
CREATE TABLE BULBLIFE(HOURS INT)

INSERT INTO BULBLIFE VALUES(4)
INSERT INTO BULBLIFE VALUES(4)
INSERT INTO BULBLIFE VALUES(4)
INSERT INTO BULBLIFE VALUES(4)
INSERT INTO BULBLIFE VALUES(6)
INSERT INTO BULBLIFE VALUES(6)
INSERT INTO BULBLIFE VALUES(6)
INSERT INTO BULBLIFE VALUES(6)


Following is a SQLITE MEDIAN function solution credited to David Rozenshtein, Anatoly Abramovich, and Eugene Birger

SELECT x.hours median
FROM BULBLIFE x, BULBLIFE y
GROUP BY x.HOURS
HAVING
SUM(CASE WHEN y.HOURS <= x.HOURS
THEN 1 ELSE 0 END) >= (COUNT(*) + 1)/2 AND
SUM(CASE WHEN y.HOURS >= x.HOURS
THEN 1 ELSE 0 END) >=(COUNT(*) + 1)/2 + 1

SQLITE returns MEAN 4


}}

sivabasava, To handle data which is dynamically added at runtime. I modified the algorithm of the esteemed investment banking firm Goldman Sachs engineers --David Rozenshtein, Anatoly Abramovich , Eugene Birger in the following way

CREATE INDEX IDX_HOURS ON BULBLIFE(HOURS ASC)

Each time I insert data, INSERT INTO BULBLIFE VALUES(5 or 7). the SQLITE INDEX data structure gets modified

As a result when the Goldman Sachs' engineers' SQL statement is applied after each insert statement., the new median is accurately determined and changes if required. Please let me know if my modification is correct. Thank you Cameron Chang.

Hold on.

I guess the above code fails if there are odd distinct elements.
Example consider: x = { 1,2,3}

cond1: sum( y.hours<=x.hours) >= (count(*)+1)/2
cond2: sum( y.hours>=x.hours) >= (count(*)+1)/2+1
for element 1:
1 >= 2 -- false -no need to consider the other condition

for 2:
cond1: 2>= 2 true
cond2: 2 >= 3 -- false

for 3:
cond1: 3 >=2 true
cond2: 1>= 3 false

so, the median function fails. Let me know if i misunderstood.

sivabasava. I get the resut median = 2 for odd number of elements {1,2,3} if I run the following SQLITE statements:

CREATE TABLE BULBLIFE (HOURS INT);

CREATE INDEX IDX_HOURS ON BULBLIFE(HOURS ASC)


INSERT INTO BULBLIFE VALUES(1)
INSERT INTO BULBLFE VALUES(2)
INSERT INTO BULBLIFE VALUES(3)

SELECT X.HOURS median
     FROM BULBLIFE X,BULBLIFE Y
     GROUP BY X.HOURS
    HAVING
    SUM(CASE WHEN Y.HOURS <= X.HOURS
        THEN 1  ELSE 0 END) >= (COUNT(*) + 1) / 2 AND
    SUM(CASE WHEN Y.HOURS >= X.HOURS
        THEN 1 ELSE 0 END) >=(COUNT(*)/2) + 1

sibabasava, please run the  above sql statements and please let me know what you get. Thank you. Cameron.