linear_knapsack.cpp

/* #pragma GCC optimize("O3,unroll-loops") */
/* #pragma GCC optimize("Ofast,unroll-loops") */
/* #pragma GCC target("avx2,popcnt") */
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define pb push_back
#define mp make_pair
#define all(a) begin(a),end(a)
#define FOR(x,val,to) for(int x=(val);x<int((to));++x)
#define FORE(x,val,to) for(auto x=(val);x<=(to);++x)
#define FORR(x,arr) for(auto &x: arr)
#define FORS(x,plus,arr) for(auto x = begin(arr)+(plus); x != end(arr); ++x)
#define FORREV(x,plus,arr) for(auto x = (arr).rbegin()+(plus); x !=(arr).rend(); ++x)
#define REE(s_) {cout<<s_<<'\n';exit(0);}
#define GET(arr) for(auto &i: (arr)) sc(i)
#define whatis(x) cerr << #x << " is " << (x) << endl;
#define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'
#define e1 first
#define e2 second
#define INF 0x7f7f7f7f
typedef std::pair<int,int> pi;
typedef std::vector<int> vi;
typedef std::vector<std::string> vs;
typedef int64_t ll;
typedef uint64_t ull;
#define umap unordered_map
#define uset unordered_set
using namespace std;
using namespace __gnu_pbds;
 
#ifdef ONLINE_JUDGE
#define whatis(x) ;
#define debug(x...) ;
#endif
#ifdef _WIN32
#define getchar_unlocked() _getchar_nolock()
#define _CRT_DISABLE_PERFCRIT_LOCKS
#endif
template<class A, class B> auto& operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; }
template<class T, enable_if_t<!is_same<T, string>::value, bool> = true> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for(auto e : x) o << (", ")+2*!i++ << e; return o << '}'; }
inline void getch(char &x){while(x = getchar_unlocked(), x < 33){;}}
inline void getstr(string &str){str.clear(); char cur;while(cur=getchar_unlocked(),cur<33){;}while(cur>32){str+=cur;cur=getchar_unlocked();}}
template<typename T> inline bool sc(T &num){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){if(c == EOF) return false;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; return true;}template<typename T, typename ...Args> inline void sc(T &num, Args &...args){ bool neg=0; int c; num=0; while(c=getchar_unlocked(),c<33){;} if(c=='-'){ neg=1; c=getchar_unlocked(); } for(;c>47;c=getchar_unlocked()) num=num*10+c-48; if(neg) num*=-1; sc(args...); }
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>; //s.find_by_order(), s.order_of_key() <- works like lower_bound
template<typename T> using ordered_map = tree<T, int, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
#define N 1000001

// Tomasz Nowak
/*
 * Opis: Plecak zwracający największą otrzymywalną sumę ciężarów <= bound. 
 * Czas: O(n * max(wi)) (zamiast typowego O(n * sum(wi)))
 * Pamięć : O(n + max(wi))
 */

#define LL ll
LL knapsack(vector<int> w, LL bound) {
	{
		vector<int> filtered;
		for(int o : w)
			if(LL(o) <= bound)
				filtered.emplace_back(o);
		w = filtered;
	}
	{
		LL sum = accumulate(w.begin(), w.end(), 0LL);
		if(sum <= bound)
			return sum;
	}
	LL w_init = 0;
	int b;
	for(b = 0; w_init + w[b] <= bound; ++b)
		w_init += w[b];

	int W = *max_element(w.begin(), w.end());
	vector<int> prev_s(2 * W, -1);
	auto get = [&](vector<int> &v, LL i) -> int& {
		return v[i - (bound  - W + 1)];
	};
	for(LL mu = bound + 1; mu <= bound + W; ++mu)
		get(prev_s, mu) = 0;
	get(prev_s, w_init) = b;
	FOR(t, b, w.size()) {
		vector<int> curr_s = prev_s;
		for(LL mu = bound - W + 1; mu <= bound; ++mu)
			get(curr_s, mu + w[t]) = max(get(curr_s, mu + w[t]), get(prev_s, mu));
		for(LL mu = bound + w[t]; mu >= bound + 1; --mu)
			for(int j = get(curr_s, mu) - 1; j >= get(prev_s, mu); --j)
				get(curr_s, mu - w[j]) = max(get(curr_s, mu - w[j]), j);
		swap(prev_s, curr_s);
	}
	for(LL mu = bound; mu >= 0; --mu)
		if(get(prev_s, mu) != -1)
			return mu;
	assert(false);
}
 
int main(){
    ios_base::sync_with_stdio(0);cin.tie(0);
}