hdu2844 Multiple Backpack templates

01 Backpack

There are n different items, each item has two attributes, size volume, value value, now to a backpack with a capacity of W, ask the most can take away how much value of the goods.

int f[w+1];   // F[x] Indicates the maximum value  when the backpack capacity is X  for (int i=0; i<n; i++)        for (int j=w; j>=size[i]; j--)           // Reverse

Full backpack

If the item does not count as many items as there are countless pieces, change it slightly.

 for (int i=0; i<n; i++)        for (int j=size[i]; j<=w; j + +)           = Max (F[j], f[j-size[i]]+value[i]);  // Positive Order

Multiple backpacks are both a certain weight W and value V for each object, and a certain amount of CNT, set m for the backpack can contain weight;

#include <iostream>#include<map>#include<math.h>#include<algorithm>#include<vector>#include<cstdlib>#include<cstdio>#include<cstring>#include<Set>using namespacestd;intn,m,a[ the],num[ the],dp[100005];voidCOMDP (intWintv) {    inti;  for(i=w; i<=m; i++) Dp[i]=max (dp[i],dp[i-w]+v);}voidZeroOne (intWintv) {    inti;  for(i=m; i>=w; i--) Dp[i]=max (dp[i],dp[i-w]+v);}voidMULTIDP (intWintVintCNT)//Start multiple backpacks at this time, Dp[i] indicates the maximum value that is included in the backpack weight of I {if(cnt*w>=m)//this is equivalent to an unlimited number of items. Complete Backpack{COMDP (w,v); return; }    intk=1;//Otherwise, the multi-backpack, the code under the mathematical theorem can be     while(k<=CNT) {ZeroOne (k*w,k*v); CNT-=K; K*=2; } zeroone (CNT*w,cnt*v); return ;}

Theorem: A positive integer n can be decomposed into 1,2,4,..., 2^ (k-1), n-2^k+1 (k is the largest integer that satisfies n-2^k+1>0), and all integers within 1~n can be uniquely represented as 1,2,4,..., 2^ (k-1), n-2^k+ 1 in the form of a certain number of numbers.

The proof is as follows:

(1) Sequence 1,2,4,..., 2^ (k-1), and the N of all elements in n-2^k+1, so the range of several elements is: [1, N];

(2) If the positive integer t<= 2^k–1, then T must be able to use 1,2,4,..., 2^ (k-1) Some number of the and expression, this is easy to prove: We put the binary representation of T, it is obvious that T can be expressed as n=a0*2^0+a1*2^1+...+ak*2^ (k-1), where ak=0 or 1, indicates that the AK bit of T is a binary number 0 or 1.

(3) If t>=2^k, set s=n-2^k+1, then t-s<=2^k-1, so T-S can be expressed as 1,2,4,..., 2^ (k-1) in the form of some number of, and then T can be expressed as 1,2,4,..., 2^ (k-1), The form of a certain number of numbers in S and (Addend must contain s).

(Certificate of Completion!) ）

hdu2844 Multiple Backpack templates