HDU 2844 Coins
像下面代码直接利用二进制求解多重背包会超时
1 #include <iostream> 2 #include <cstdio> 3 #include <cstdlib> 4 #include <vector> 5 #include <algorithm> 6 7 using namespace std; 8 9 int main(){ 10 int n,m; 11 while(cin>>n>>m && n && m){ 12 vector<int> A(n),C(n); 13 for(int i = 0 ; i < n; i ++ ) cin >> A[i]; 14 for(int i = 0 ; i < n; i ++ ) cin >> C[i]; 15 vector<int> coin; 16 17 for(int i = 0; i < n; i ++ ){ 18 int tmp = 1; 19 while(C[i] > tmp){ 20 coin.push_back(tmp*A[i]); 21 C[i] -= tmp; 22 tmp <<=1; 23 } 24 coin.push_back(C[i]*A[i]); 25 } 26 27 vector<int> dp(m+1,0); 28 for(int i = 0 ; i < coin.size(); i ++ ){ 29 for(int j = m ; j >= coin[i]; j -- ){ 30 dp[j] = max(dp[j],dp[j-coin[i]] + coin[i]); 31 } 32 } 33 34 int cnt = 0; 35 for(int i = 1; i <= m ; i++) 36 if(dp[i] != dp[i-1]) cnt++; 37 cout<<cnt<<endl; 38 } 39 return 0; 40 }
参考背包九讲，对多重背包进行优化
1 #include <iostream> 2 #include <vector> 3 #include <algorithm> 4 #include <cstring> 5 6 #define MAX 100000 7 using namespace std; 8 9 int dp[MAX]; 10 11 void CompletePack(int val, int m){ 12 for(int j = val; j <= m; j ++ ) 13 dp[j] = max(dp[j],dp[j - val]+ val); 14 } 15 16 void ZeroOnePack(int val, int m){ 17 for(int j = m; j >= val; j -- ) 18 dp[j] = max(dp[j],dp[j - val]+ val); 19 } 20 21 void MultiplePack(int val,int num, int m){ 22 if(val*num >= m ){ //对于固定的m来说，相当于有无限个硬币， 23 CompletePack(val,m); //完全背包 24 return; 25 } 26 int k = 1; //利用二进制优化转化为01背包 27 while( k < num){ 28 ZeroOnePack(k*val,m); 29 num -= k; 30 k <<= 1; 31 } 32 ZeroOnePack(num*val,m); 33 } 34 35 int main(){ 36 int n,m; 37 while(cin>>n>>m && n && m){ 38 vector<int> A(n),C(n); 39 for(int i = 0 ; i < n; i ++ ) cin >> A[i]; 40 for(int i = 0 ; i < n; i ++ ) cin >> C[i]; 41 //vector<int> dp(m+1,0); 42 memset(dp,0,sizeof(dp)); 43 for(int i=0; i < n; i ++ ) 44 MultiplePack(A[i],C[i],m); 45 int cnt = 0; 46 for(int i = 1; i <= m ; i++) 47 if(dp[i] == i) cnt++; 48 cout<<cnt<<endl; 49 } 50 return 0; 51 }
