01背包方案数（变种题）Stone game--The Preliminary Contest for ICPC Asia Shanghai 2019

Posted 2022-11-07 --hpy-7m

题意：https://nanti.jisuanke.com/t/41420

给你n个石子的重量，要求满足（Sum<=2*sum<=Sum+min)的方案数，min是你手里的最小值。

思路：

从最大重量的石子开始背包，每次ans+=dp【j-v【i】】就行了。

  1 #define ios ios_base::sync_with_stdio(0); cin.tie(0);
  2 #include <cstdio>//sprintf islower isupper
  3 #include <cstdlib>//malloc  exit strcat itoa system("cls")
  4 #include <iostream>//pair
  5 #include <fstream>//freopen("C:\\Users\\13606\\Desktop\\草稿.txt","r",stdin);
  6 #include <bitset>
  7 //#include <map>
  8 //#include<unordered_map>
  9 #include <vector>
 10 #include <stack>
 11 #include <set>
 12 #include <string.h>//strstr substr
 13 #include <string>
 14 #include <time.h>//srand(((unsigned)time(NULL))); Seed n=rand()%10 - 0~9;
 15 #include <cmath>
 16 #include <deque>
 17 #include <queue>//priority_queue<int, vector<int>, greater<int> > q;//less
 18 #include <vector>//emplace_back
 19 //#include <math.h>
 20 //#include <windows.h>//reverse(a,a+len);// ~ ! ~ ! floor
 21 #include <algorithm>//sort + unique : sz=unique(b+1,b+n+1)-(b+1);+nth_element(first, nth, last, compare)
 22 using namespace std;//next_permutation(a+1,a+1+n);//prev_permutation
 23 #define rint register int
 24 #define fo(a,b,c) for(rint a=b;a<=c;++a)
 25 #define fr(a,b,c) for(rint a=b;a>=c;--a)
 26 #define mem(a,b) memset(a,b,sizeof(a))
 27 #define pr printf
 28 #define sc scanf
 29 #define ls rt<<1
 30 #define rs rt<<1|1
 31 typedef long long ll;
 32 void swapp(int &a,int &b);
 33 double fabss(double a);
 34 int maxx(int a,int b);
 35 int minn(int a,int b);
 36 int Del_bit_1(int n);
 37 int lowbit(int n);
 38 int abss(int a);
 39 const double E=2.718281828;
 40 const double PI=acos(-1.0);
 41 //const ll INF=(1LL<<60);
 42 const int inf=(1<<30);
 43 const double ESP=1e-9;
 44 const int mod=(int)1e9+7;
 45 const int N=(int)1e6+10;
 46 
 47 int v[N],dp[N];
 48 void Init(int _[],int n)
 49 
 50     for(int i=1;i<=n;++i)
 51         _[i]=0;
 52 
 53 
 54 void PR(int _[],int n)
 55 
 56     for(int i=1;i<=n;++i)
 57         pr("%d ",_[i]);
 58     pr("\n");
 59 
 60 
 61 bool J(int sum,int x,int min_)
 62 
 63     return 2*x>=sum&&2*x<=sum+min_;
 64 
 65 
 66 int main()
 67 
 68     int T;
 69     sc("%d",&T);
 70     while(T--)
 71     
 72         int n,sum=0;
 73         sc("%d",&n);
 74         for(int i=1;i<=n;++i)
 75             sc("%d",&v[i]),sum+=v[i];
 76         sort(v+1,v+1+n);
 77         Init(dp,sum);
 78 
 79         ll ans=0;
 80         dp[0]=1;
 81         for(int i=n;i>=1;--i)
 82         
 83             for(int j=sum;j>=v[i];--j)
 84                 if(dp[j-v[i]])
 85                 
 86                     dp[j]+=dp[j-v[i]];
 87                     dp[j]%=mod;
 88                     ans+=J(sum,j,v[i])?dp[j-v[i]]:0;
 89                     ans%=mod;
 90                 
 91         
 92         pr("%lld\n",ans);
 93     
 94     return 0;
 95 
 96 
 97 /**************************************************************************************/
 98 
 99 int maxx(int a,int b)
100 
101     return a>b?a:b;
102 
103 
104 void swapp(int &a,int &b)
105 
106     a^=b^=a^=b;
107 
108 
109 int lowbit(int n)
110 
111     return n&(-n);
112 
113 
114 int Del_bit_1(int n)
115 
116     return n&(n-1);
117 
118 
119 int abss(int a)
120 
121     return a>0?a:-a;
122 
123 
124 double fabss(double a)
125 
126     return a>0?a:-a;
127 
128 
129 int minn(int a,int b)
130 
131     return a<b?a:b;
132