We have a 0-1 knapsack in which the increasing order of items by weight is the same as the decreasing order of items by value. Design a greedy algorithm and prove that the greedy choice guarantees an optimal solution.
Given the two orders I imagined that we could just choose the first k elements from either sequence and use them to fill knapsack until it was full. This would be similar to choosing the items with the greatest ratio of value to weight. But I don't think that is an optimal solution.
So what I need help with is whether or not this solution is optimal. And how would I prove the correctness of a greedy algorithm.