P1441 砝码称重（01背包+枚举子集）

思路：
用$01$背包求$n$个数组成不同数的方案数，$dp[i]$代表组成能否组成$i$，然后用枚举子集求去掉$m$个数的状态集合，来枚举最大方案。

参考代码：

/*
 * @Author: vain
 * @Date: 2020
 * @LastEditTime: 2020-10-07 18:44:42
 * @LastEditors: sueRimn
 * @Description: 学不会 dp 的 fw
 * @FilePath: \main\demo.cpp
 */
#include <bits/stdc++.h>
#include <cstdio>
#include <algorithm>
#include <iostream>
#include <vector>
#include <map>
#include <queue>
#include <set>
#include <ctime>
#include <cstring>
#include <cstdlib>
#include <math.h>
#include <bitset>
//#include <unordered_map>
using namespace std;
typedef long long ll;
#define ll long long
//typedef unsigned long long uint;
const int N = 5000 + 20;
const int maxn = 1e5 + 20;
const int mod = 998244353;
int cnt, head[maxn], pos[maxn];

//typedef pair<ll, ll> p;
//priority_queue<p, vector<p>, greater<p>> q;
//int sum[maxn];
double Max(double a, double b) {
    
     return a > b ? a : b; }
int min(int a, int b) {
    
     return a < b ? a : b; }
int gcd(int a, int b) {
    
     return b ? gcd(b, a % b) : a; }
int lcm(int a, int b) {
    
     return a * b / gcd(a, b); }
void swap(int &x, int &y) {
    
     x ^= y, y ^= x, x ^= y; }
int lowbit(int x) {
    
     return (x) & (-x); }
//map<int, int> vis;
//unordered_map<int,int>vis;
ll ksm(ll a, ll b)
{
    
    
    ll res = 1;
    for (; b;)
    {
    
    
        if (b & 1)
            res = (res * a) % mod;
        b >>= 1, a = a * a % mod;
    }
    return res;
}
int read(int &v)
{
    
    
    int k = 1;
    v = 0;
    int c = getchar();
    while (c < '0' || c > '9')
    {
    
    
        if (c == '-')
            k = 0;
        c = getchar();
    }
    while (c >= '0' && c <= '9')
        v = (v << 3) + (v << 1) + (c - 48), c = getchar();
    if (k == 0)
        v = -v;
    return c;
}
int n, dp[2005], m, a[25], st[maxn * 10], ns, Maxs;
ll ans;
void init()
{
    
    
    for (int i = 0; i < (1 << n); i++)
    {
    
    
        int sum = 0;
        for (int j = 0; j < n; j++)
        {
    
    
            if ((i >> j) & 1)
                sum++;
        }
        if (sum == m)
            st[ns++] = i;
    }
}
void slove(int x)
{
    
    
    memset(dp, 0, sizeof dp);
    dp[0] = 1;
    ll Ma = 0;
    for (int i = 0; i < n; i++)
    {
    
    
        if ((x >> i) & 1)
            continue;
        for (int j = Maxs; j >= a[i]; j--)
        {
    
    
            if (dp[j - a[i]] && (!dp[j]))
                dp[j] = 1, Ma++;
        }
    }
    if (Ma > ans)
        ans = Ma;
}
int main()
{
    
    
    read(n), read(m);
    init();
    for (int i = 0; i < n; i++)
        read(a[i]), Maxs += a[i];
    for (int i = 0; i < ns; i++)
        slove(st[i]);
    printf("%lld\n", ans);
}