#include <bits/stdc++.h>
using namespace std;
using tint = long long;
using ld = long double;
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
using pi = pair<int,int>;
using pl = pair<tint,tint>;
using vi = vector<int>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vvi = vector<vi>;
using vl = vector<tint>;
using vb = vector<bool>;
#define pb push_back
#define pf push_front
#define rsz resize
#define all(x) begin(x), end(x)
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)(x).size()
#define ins insert
#define f first
#define s second
#define mp make_pair
#define DBG(x) cerr << #x << " = " << x << endl;
const int MOD = 1e9+7;
const tint mod = 998244353;
const int MX = 20000005;
const tint INF = 1e18;
const int inf = 2e9;
const ld PI = acos(ld(-1));
const ld eps = 1e-5;
const int dx[4] = {1, -1, 0, 0};
const int dy[4] = {0, 0, 1, -1};
template<class T> void remDup(vector<T> &v){
sort(all(v)); v.erase(unique(all(v)),end(v));
}
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0;
}
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0;
}
bool valid(int x, int y, int n, int m){
return (0<=x && x<n && 0<=y && y<m);
}
int cdiv(int a, int b) { return a/b+((a^b)>0&&a%b); } //redondea p arriba
int fdiv(int a, int b) { return a/b-((a^b)<0&&a%b); } //redondea p abajo
void NACHO(string name = ""){
ios_base::sync_with_stdio(0); cin.tie(0);
if(sz(name)){
freopen((name+".in").c_str(), "r", stdin);
freopen((name+".out").c_str(), "w", stdout);
}
}
// la solucion trivial es para cada objeto meter k individuales, y
// luego correr knpascak normal. Sin embargo, hay 10^5 objetos y j <= 10^9.
// esto no es feasible.
// lo que queremos es basicamente descomponer el k en grupos de ese mismo
// objeto tal que con estos grupos puedo formar todas las sumas
// entre 1 y k y tal que la cantidad de grupos es chica.
// hacemos lo siguiente: vamos haciendo grupos de tamaño 2^0, 2^1, 2^2, hasta que
// no podamos seguir restando. A lo último metemos en un grupo lo que sobro.
// es obvio que podemos crear todas las sumas entre 1 y k con esto, y a su vez,
// hay logk grupos por cada objeto.
// sin embargo, esto no alcanza para llegar a 100.
// lo que tenemos que hacer es ver que para cada peso x,
// solo nos interesa ver los W/x items con mayor valor (ya que no puedo meter mas de W/x en la bolsa de capacidad W).
// Como los pesos van hasta 2000, la cantidad de items es a lo sumo 2000/1+2000/2+2000/3+2000/4...=17000 aprox.
// Esto ya da 100.
struct Item{
tint v, w, k;
};
tint dp[2005];
vector<Item> items;
vpi ge[2005];
int main(){
NACHO();
tint n, w; cin >> w >> n;
F0R(i, n){
tint v, w, k; cin >> v >> w >> k;
ge[w].pb(mp(v, k));
}
FOR(i, 1, 2005){
sort(rall(ge[i]));
int quan = w/i;
F0R(j, sz(ge[i])){
while(ge[i][j].s > 0 && quan > 0){
--ge[i][j].s;
--quan;
items.pb({ge[i][j].f, i, 1});
}
}
}
F0R(i, sz(items)){
R0F(j, w){
if(j+items[i].k*items[i].w <= w) ckmax(dp[j+items[i].k*items[i].w], dp[j]+items[i].k*items[i].v);
}
}
cout << dp[w] << "\n";
}
Compilation message
knapsack.cpp: In function 'void NACHO(std::string)':
knapsack.cpp:69:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
69 | freopen((name+".in").c_str(), "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
knapsack.cpp:70:10: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
70 | freopen((name+".out").c_str(), "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
332 KB |
Output is correct |
2 |
Correct |
1 ms |
332 KB |
Output is correct |
3 |
Correct |
1 ms |
332 KB |
Output is correct |
4 |
Correct |
1 ms |
332 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
332 KB |
Output is correct |
2 |
Correct |
2 ms |
332 KB |
Output is correct |
3 |
Correct |
2 ms |
364 KB |
Output is correct |
4 |
Correct |
1 ms |
332 KB |
Output is correct |
5 |
Correct |
1 ms |
332 KB |
Output is correct |
6 |
Correct |
1 ms |
332 KB |
Output is correct |
7 |
Correct |
1 ms |
336 KB |
Output is correct |
8 |
Correct |
1 ms |
332 KB |
Output is correct |
9 |
Correct |
1 ms |
332 KB |
Output is correct |
10 |
Correct |
1 ms |
332 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
332 KB |
Output is correct |
2 |
Correct |
2 ms |
332 KB |
Output is correct |
3 |
Correct |
2 ms |
364 KB |
Output is correct |
4 |
Correct |
1 ms |
332 KB |
Output is correct |
5 |
Correct |
1 ms |
332 KB |
Output is correct |
6 |
Correct |
1 ms |
332 KB |
Output is correct |
7 |
Correct |
1 ms |
336 KB |
Output is correct |
8 |
Correct |
1 ms |
332 KB |
Output is correct |
9 |
Correct |
1 ms |
332 KB |
Output is correct |
10 |
Correct |
1 ms |
332 KB |
Output is correct |
11 |
Correct |
1 ms |
332 KB |
Output is correct |
12 |
Correct |
8 ms |
332 KB |
Output is correct |
13 |
Correct |
2 ms |
332 KB |
Output is correct |
14 |
Correct |
1 ms |
332 KB |
Output is correct |
15 |
Correct |
1 ms |
332 KB |
Output is correct |
16 |
Correct |
1 ms |
332 KB |
Output is correct |
17 |
Correct |
1 ms |
332 KB |
Output is correct |
18 |
Correct |
1 ms |
332 KB |
Output is correct |
19 |
Correct |
2 ms |
332 KB |
Output is correct |
20 |
Correct |
1 ms |
332 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
332 KB |
Output is correct |
2 |
Correct |
1 ms |
332 KB |
Output is correct |
3 |
Correct |
1 ms |
332 KB |
Output is correct |
4 |
Correct |
1 ms |
332 KB |
Output is correct |
5 |
Correct |
1 ms |
332 KB |
Output is correct |
6 |
Correct |
2 ms |
332 KB |
Output is correct |
7 |
Correct |
2 ms |
364 KB |
Output is correct |
8 |
Correct |
1 ms |
332 KB |
Output is correct |
9 |
Correct |
1 ms |
332 KB |
Output is correct |
10 |
Correct |
1 ms |
332 KB |
Output is correct |
11 |
Correct |
1 ms |
336 KB |
Output is correct |
12 |
Correct |
1 ms |
332 KB |
Output is correct |
13 |
Correct |
1 ms |
332 KB |
Output is correct |
14 |
Correct |
1 ms |
332 KB |
Output is correct |
15 |
Correct |
1 ms |
332 KB |
Output is correct |
16 |
Correct |
8 ms |
332 KB |
Output is correct |
17 |
Correct |
2 ms |
332 KB |
Output is correct |
18 |
Correct |
1 ms |
332 KB |
Output is correct |
19 |
Correct |
1 ms |
332 KB |
Output is correct |
20 |
Correct |
1 ms |
332 KB |
Output is correct |
21 |
Correct |
1 ms |
332 KB |
Output is correct |
22 |
Correct |
1 ms |
332 KB |
Output is correct |
23 |
Correct |
2 ms |
332 KB |
Output is correct |
24 |
Correct |
1 ms |
332 KB |
Output is correct |
25 |
Correct |
1 ms |
332 KB |
Output is correct |
26 |
Correct |
13 ms |
472 KB |
Output is correct |
27 |
Correct |
1 ms |
332 KB |
Output is correct |
28 |
Correct |
1 ms |
332 KB |
Output is correct |
29 |
Correct |
1 ms |
332 KB |
Output is correct |
30 |
Correct |
3 ms |
332 KB |
Output is correct |
31 |
Correct |
1 ms |
332 KB |
Output is correct |
32 |
Correct |
1 ms |
332 KB |
Output is correct |
33 |
Correct |
1 ms |
332 KB |
Output is correct |
34 |
Correct |
2 ms |
332 KB |
Output is correct |
# |
Verdict |
Execution time |
Memory |
Grader output |
1 |
Correct |
1 ms |
332 KB |
Output is correct |
2 |
Correct |
1 ms |
332 KB |
Output is correct |
3 |
Correct |
1 ms |
332 KB |
Output is correct |
4 |
Correct |
1 ms |
332 KB |
Output is correct |
5 |
Correct |
1 ms |
332 KB |
Output is correct |
6 |
Correct |
2 ms |
332 KB |
Output is correct |
7 |
Correct |
2 ms |
364 KB |
Output is correct |
8 |
Correct |
1 ms |
332 KB |
Output is correct |
9 |
Correct |
1 ms |
332 KB |
Output is correct |
10 |
Correct |
1 ms |
332 KB |
Output is correct |
11 |
Correct |
1 ms |
336 KB |
Output is correct |
12 |
Correct |
1 ms |
332 KB |
Output is correct |
13 |
Correct |
1 ms |
332 KB |
Output is correct |
14 |
Correct |
1 ms |
332 KB |
Output is correct |
15 |
Correct |
1 ms |
332 KB |
Output is correct |
16 |
Correct |
8 ms |
332 KB |
Output is correct |
17 |
Correct |
2 ms |
332 KB |
Output is correct |
18 |
Correct |
1 ms |
332 KB |
Output is correct |
19 |
Correct |
1 ms |
332 KB |
Output is correct |
20 |
Correct |
1 ms |
332 KB |
Output is correct |
21 |
Correct |
1 ms |
332 KB |
Output is correct |
22 |
Correct |
1 ms |
332 KB |
Output is correct |
23 |
Correct |
2 ms |
332 KB |
Output is correct |
24 |
Correct |
1 ms |
332 KB |
Output is correct |
25 |
Correct |
1 ms |
332 KB |
Output is correct |
26 |
Correct |
13 ms |
472 KB |
Output is correct |
27 |
Correct |
1 ms |
332 KB |
Output is correct |
28 |
Correct |
1 ms |
332 KB |
Output is correct |
29 |
Correct |
1 ms |
332 KB |
Output is correct |
30 |
Correct |
3 ms |
332 KB |
Output is correct |
31 |
Correct |
1 ms |
332 KB |
Output is correct |
32 |
Correct |
1 ms |
332 KB |
Output is correct |
33 |
Correct |
1 ms |
332 KB |
Output is correct |
34 |
Correct |
2 ms |
332 KB |
Output is correct |
35 |
Correct |
33 ms |
1456 KB |
Output is correct |
36 |
Correct |
51 ms |
1508 KB |
Output is correct |
37 |
Correct |
46 ms |
2380 KB |
Output is correct |
38 |
Correct |
36 ms |
2632 KB |
Output is correct |
39 |
Correct |
43 ms |
3400 KB |
Output is correct |
40 |
Correct |
95 ms |
4116 KB |
Output is correct |
41 |
Correct |
63 ms |
3312 KB |
Output is correct |
42 |
Correct |
67 ms |
3332 KB |
Output is correct |
43 |
Correct |
93 ms |
3364 KB |
Output is correct |
44 |
Correct |
87 ms |
3332 KB |
Output is correct |
45 |
Correct |
45 ms |
3652 KB |
Output is correct |
46 |
Correct |
40 ms |
3136 KB |
Output is correct |
47 |
Correct |
50 ms |
3828 KB |
Output is correct |
48 |
Correct |
66 ms |
3880 KB |
Output is correct |
49 |
Correct |
37 ms |
3416 KB |
Output is correct |
50 |
Correct |
71 ms |
3860 KB |
Output is correct |