01 backpack TEMPLATE 1 2 Summary

Item quality W [0] W [1] W [2] ...... W [N] backpack capacity C t

Item value V [0] V [1] V [2] ...... V [N] item type N

 

(1) set dp (x, y)First x itemsLoadY-sized backpackThe maximum value of an item.

First x items (0 ---- X-1, x) to installBackpack with size of Y

 

| -------- 0 when x = 0 or Y = 0

DP (x, y) | dp (x-1, Y) without the X

| Dp (x-1, Y-W [x]) + V [x] Y-W [x]> = 0 x

 

 

 

 

 

 

 

 

 

(2) Set dp (x, y)Item X startsToItem nLoading an itemY-sized backpack.

SlaveItem XOpenStart(X, x + 1, x + 2, x + 3,... n)

 

 

 

 

 

| -------- 0 when x = m + 1 or Y = 0

DP (x, y) | dp (x + 1, Y) without the X

| Dp (x + 1, Y-W [x]) + V [x] Y-W [x]> = 0 x

 

 

 

Idea 1 of Dynamic Planning Algorithm:

M [I] [J] is used to represent the maximum value of a backpack loaded with J in the former I item area.

Where the range of I is 0 to n, where the range of J is 0 to C, and the solution to the program is m [N] [C].

There are three possible situations:

① M [0] [J]: The value of all J values is 0 (the item type is 0 ), M [I] [0] All I values are 0 (volume is 0)

② When the current volume J is greater than or equal to W [I], M [I] [J] is the maximum of the following two quantities: M [I-1] [J] (not loaded) and M [I-1] [J-W [I-1] + V [I] (assembly)

③ When the current volume J is less than W [I], M [I] [J] is equal to M [I-1] [J]

 

 

 

 

 

 

 

 

 

 

 

Dynamic Planning Algorithm concept 2:

Set M [I] [J] to indicate the maximum value obtained by loading an item into a J-sized backpack from item I to item n.

The range of I is 0 to n-1, where the range of J is 0 to C, and the solution to the program is m [0] [C].

It can be divided:

① M [n-1] [J] When J> = 0 and j <W [n-1] is equal to 0 (cannot be loaded); otherwise, it is equal to V [n-1] (can be installed)

② When the current volume J is greater than or equal to W [I], M [I] [J] is the maximum of the following two quantities: M [I + 1] [J] and M [I + 1] [J-W [I] + V [I]

③ When the current volume J is less than W [I], M [I] [J] equals m [I + 1] [J]