Let say a=[A, B, C, D], each element has a weight w, and is set to 1 if selected, 0 if otherwise. I'd like to generate permutation in the below order 1,1,1,1 1,1,1,0 1,1,0,1 1,1,0,0 1,0,1,1 1,0,1,0 1,0,0,1 1,0,0,0 Let's w=[1,2,3,4] for item A,B,C,D ... and max_weight = 4. For each permutation, if the accum weight has exceeded max_weight, stop calculation for that permutation, move to next permutation. For eg. 1,1,1 --> 6 > 4, exceeded, stop, move to next 1,1,1 --> 6 > 4, exceeded, stop, move to next 1,1,0,1 --> 7 > 4 finished, move to next 1,1,0,0 --> 3 finished, move to next 1,0,1,1 --> 8 > 4, finished, stop, move to next 1,0,1,0 --> 4 finished, move to next 1,0,0,1 --> 5 > 4 finished, move to next 1,0,0,0 --> 1 finished, move to next [1,0,1,0] is the best combination which does not exceeded max_weight 4 My questions are What's the algorithm which generate the required permutation? Or any suggestion I could generate the permutation? As the number of element can be up to 10000, and the calculation stop if the accum weight for the branch exceeds max_weight, it is not necessary to generate all permutation first before the calculation. How can the algo in (1) generate permutation on the fly?