##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
##### ###### ##### ### # # ### # # ###### ## ## ## ## ## ## ## # # # # # ## ##### #### ##### # # # # # # # #### ## # ## ## ## ## # # # # # ## ## # ###### ## ### # ### # ######
Discrete items block
In / knapsack, items are indivisible. Greedy by ratio fails.
Example: items = [(60,10), (100,20), (120,30)], W = . Greedy: take item (ratio P2), item (ratio P4). Total weight: , value: . Item does not fit.
But items + : weight = , value = . Better! The discrete constraint causes blocking. Use DP for / knapsack.
