Question

Problem 3: (5 2 points) Design an algorithm that takes an array of positive integers A of length n and a positive integer T as an input and finds the largest N < T such that N can be written as a sum of some elements of A and returns such a representation of N. The complexity of the algorithms has to be O(nT). For example, for A 3,7, 10 and T 19, the output is 17 7+10, because we can make 17 out of elements of A (7+10) but we cannot make 18 or 19. So the largest N T that can be made from A is 17

Answer 1

Hi,
Given question doesnt put any restrictions over the elements order which makes it even simpler,

here is the pseduo code for the algorithm
def fun(A,T)
sum=0;
end=0
i=0
max=0
for i<A.size

if(sum>max && sum<=T)
max=sum
if(sum+A[end]<T && end<A.size)
sum=sum+A[end]
end++
else
sum=sum-i
i++

end.
We are basically maintaining 2 pointers, and moving them together based on how the sum is varying, i,e
like in this example for input [3,7,10]
first sum becomes 3,
then adding 10 becomes it becomes 13 and max sum will be 13
then adding 17 takes it to else(since >T), where max sum will be after subtracting from end, therefore 3 will be subtracted, and then 17 will be returned
Since we are only looping through the list one time, the order is O(n) only

Thumbs up if this was helpful, otherwise let me know in comments