Question

I have given x and y items , I need to choose some x and some y with some constrain say x < 10 and y < 5 and the total number should be p.

How to solve such problem. Algorithm/ mathematical technique.

Answer 1

The trick is we only need to go through one array (e.g. the x_array), and we can work out y using p-x=y. Now we only need to ensure y is in the y_array and we know we have our answer. To ensure y is in the y_array, we make a set or binary search tree for fast look-ups.

Here is some python code:

p=13
xs=[1,3,99,9,18]
ys=[10,4,33]

y_set=set(ys)

#y=p-x
results=((x,p-x) for x in xs if x<10 and p-x<5 and p-x in y_set)

print "x=%s,y=%s,p=13" % results.next()
'x=9,y=4,p=13'