We want to modify our pseudo-polynomial time algorithm for the knapsack problem so that it solves the multiknapsack problem. We can write a slightly modified version of our algorithm for the knapsack problem as follows: We change the arrasy so that its first index runs from 0 to n rather than 1 to n.

We want to modify our pseudo-polynomial time algorithm for the knapsack problem so that it solves the multiknapsack problem. We can write a slightly modified version of our algorithm for the knapsack problem as follows: We change the arrasy so that its first index runs from 0 to n rather than 1 to n. we set Ali,wJexists to True if w-0 and False if w>0 we set AU.val-O for all j and w. For j 1 to n do For w-1 to w-1 do Alj,w].exists-Alj-1,w].exists Alj,w].val-AUj-1,w].val For w-w, to W do Ali,w].exists Ali-1,w].exists OR Ai-1,w-w].exists IF Ali,.exists then If Ali-1.exists then Ali,w].val:= Ali-1,w].val If Ai-1,w-wl.exists AND Ai,w-w].valtv >Ali,w].val then Ali,w].val:= Ali-1,w-w i].val+y For w:= 1 to w do: If A[n,w].val>v* Then vA[n,w].val Return (v* 2V) Our version for the multi-knapsack problem will look like very similar. We set it out below with a (*) in front of the lines which are different from the old version: For some values of i and x it will be: We want to modify our pseudo-polynomial time algorithm for the knapsack problem so that it solves the multiknapsack problem. We can write a slightly modified version of our algorithm for the knapsack problem as follows: We change the arrasy so that its first index runs from 0 to n rather than 1 to n. we set Ali,wJexists to True if w-0 and False if w>0 we set AU.val-O for all j and w. For j 1 to n do For w-1 to w-1 do Alj,w].exists-Alj-1,w].exists Alj,w].val-AUj-1,w].val For w-w, to W do Ali,w].exists Ali-1,w].exists OR Ai-1,w-w].exists IF Ali,.exists then If Ali-1.exists then Ali,w].val:= Ali-1,w].val If Ai-1,w-wl.exists AND Ai,w-w].valtv >Ali,w].val then Ali,w].val:= Ali-1,w-w i].val+y For w:= 1 to w do: If A[n,w].val>v* Then vA[n,w].val Return (v* 2V) Our version for the multi-knapsack problem will look like very similar. We set it out below with a (*) in front of the lines which are different from the old version: For some values of i and x it will be