I have to write polynomial time algorithm for the problem which should say accept or reject if the number(s) to the left don't match to the number on right. You can group the numbers also, examples are below
X & Y .......... & N = SUM
where X, Y, and N can be any integer
Case 1: 4 & 6 & 10 = 14 , accepts
So case 1 accepts because first number and the third number together sum up to 14.
Case 2: 4 & 6 & 10 = 8 rejects
Case 3: 4 & 6 & 10 = 6 , accepts
Case 4: 4 & 6 & 10 = 11 rejects
Some more test cases:
Case 1: 4 & 6 & 10 = 4 , accepts
Case 2: 4 & 6 & 10 = 21 rejects
Case 3: 4 & 6 & 10 = 20 , accepts
Case 4: 4 & 6 & 10 = 17 rejects
Case 5: 4 & 6 & 10 = 16 , accepts
Case 6: 4 & 6 & 10 = 200 rejects
Case 7: 4 & 6 & 10 = 111 , rejects
Case 8: 4 & 6 & 10 = 7 rejects
some more test cases
Case 1 : 1 & 1 & 1 = 3 accepts
Case 2 : 1 & 1 & 1 & 2 & 2 & 22 = 29 accepts
For this how can I write polynomial time algorithm? Is it NP Problem?
It seems to me too that this is the subset sum problem, which is NP-complete (meaning that a polynomial-time solution doesn't exist, unless P=NP) but can be solved in pseudo-polynomial time (i.e. time polynomial both in the number of numbers and the value of the sum) using dynamic programming.