The Fractional Knapsack Problem is solved optimally by a greedy algorithm that selects items based on decreasing ratios of profit to size (value density). This approach relies on the exchange argument, which proves that replacing any portion of an item with lower value-density in favor of one with higher value-density strictly increases total profit without violating capacity constraints. In contrast, optimal code construction for prefix-free codes utilizes a greedy strategy derived from Huffman coding principles, where symbols are merged iteratively based on their frequencies to minimize average codeword length while satisfying the Kraft inequality.
The Fractional Knapsack Problem is solved optimally by a greedy algorithm that selects items based on decreasing ratios of profit to size (value density). This approach relies on the exchange argumen…