中南林业大学校赛 I 背包问题 ( 折半枚举 || 01背包递归写法 )

题目链接

题意 : 中文题

分析 : 

价值和重量都太过于大，所以采用折半枚举的方法，详细可以看挑战的超大背包问题

由于 n <= 30 那么可以不必直接记录状态来优化，面对每个用例

直接采用递归回溯的方法来写这个 DP 即可

#include<bits/stdc++.h>
#define LL long long
#define ULL unsigned long long

#define scs(i) scanf("%s", i)
#define sci(i) scanf("%d", &i)
#define scd(i) scanf("%lf", &i)
#define scl(i) scanf("%lld", &i)
#define scIl(i) scanf("%I64d", &i)
#define scii(i, j) scanf("%d %d", &i, &j)
#define scdd(i, j) scanf("%lf %lf", &i, &j)
#define scll(i, j) scanf("%lld %lld", &i, &j)
#define scIll(i, j) scanf("%I64d %I64d", &i, &j)
#define sciii(i, j, k) scanf("%d %d %d", &i, &j, &k)
#define scddd(i, j, k) scanf("%lf %lf %lf", &i, &j, &k)
#define sclll(i, j, k) scanf("%lld %lld %lld", &i, &j, &k)
#define scIlll(i, j, k) scanf("%I64d %I64d %I64d", &i, &j, &k)

#define lson l, m, rt<<1
#define rson m+1, r, rt<<1|1
#define lowbit(i) (i & (-i))
#define mem(i, j) memset(i, j, sizeof(i))

#define fir first
#define sec second
#define ins(i) insert(i)
#define pb(i) push_back(i)
#define pii pair<int, int>
#define mk(i, j) make_pair(i, j)
#define all(i) i.begin(), i.end()
#define pll pair<long long, long long>
using namespace std;
int v[35];

int DP(int n, int m)
{
    if(n < 0 || m < 0) return 0;
    if(n == 0 || m == 0) return 1;
    return DP(n-1, m-v[n]) + DP(n-1, m);
}

int main(void)
{
    int n;
    while(~sci(n)){
        int m;
        sci(m);
        for(int i=1; i<=n; i++) sci(v[i]);
        printf("%d\n", DP(n, m));
    }
    return 0;
}

递归DP

#include<bits/stdc++.h>
#define LL long long
#define ULL unsigned long long
 
#define scs(i) scanf("%s", i)
#define sci(i) scanf("%d", &i)
#define scd(i) scanf("%lf", &i)
#define scl(i) scanf("%lld", &i)
#define scIl(i) scanf("%I64d", &i)
#define scii(i, j) scanf("%d %d", &i, &j)
#define scdd(i, j) scanf("%lf %lf", &i, &j)
#define scll(i, j) scanf("%lld %lld", &i, &j)
#define scIll(i, j) scanf("%I64d %I64d", &i, &j)
#define sciii(i, j, k) scanf("%d %d %d", &i, &j, &k)
#define scddd(i, j, k) scanf("%lf %lf %lf", &i, &j, &k)
#define sclll(i, j, k) scanf("%lld %lld %lld", &i, &j, &k)
#define scIlll(i, j, k) scanf("%I64d %I64d %I64d", &i, &j, &k)
 
#define lson l, m, rt<<1
#define rson m+1, r, rt<<1|1
#define lowbit(i) (i & (-i))
#define mem(i, j) memset(i, j, sizeof(i))
 
#define fir first
#define sec second
#define ins(i) insert(i)
#define all(i) i.begin(), i.end()
#define pb(i) push_back(i)
#define pii pair<int, int>
#define mk(i, j) make_pair(i, j)
#define pll pair<long long, long long>
using namespace std;
const int maxn = 30 + 2;
int n;
LL m, v[maxn];
vector<LL> arr;
 
int main(void)
{
    while(cin>>n>>m){
        arr.clear();
        for(int i=0; i<n; i++) scl(v[i]);
        for(int i=0; i<(1<<(n/2)); i++){
            LL sum = 0;
            for(int j=0; j<n/2; j++)
                if((i & (1<<j)))
                    sum += v[j];
            arr.pb(sum);
        }
 
        sort(all(arr));
 
        int ans = 0;
        for(int i=0; i<(1<<(n-n/2)); i++){
            LL sum = 0;
            for(int j=0; j<(n-n/2); j++)
                if((i & (1<<j)))
                    sum += v[j+n/2];
            ans += upper_bound(all(arr), m-sum) - arr.begin();
        }
 
        cout<<ans<<endl;
    }
    return 0;
}

折半枚举