Submission #487554

#	Time	Username	Problem	Language	Result	Execution time	Memory
487554		Biaz	Knapsack (NOI18_knapsack)	C++17	12 / 100	7 ms	7544 KiB

knapsack

#include <bits/stdc++.h>
using namespace std;
namespace {
    static const int MAXW = 2005;
    static const int MAXN = 100005;
    static const int MAXC = 1<<12;
    struct BB {
        int w, v, c;
        BB(int w = 0, int v = 0, int c = 0):
            w(w), v(v), c(c) {}
        bool operator<(const BB &x) const {
            return w * c  < x.w * x.c;
        }
    };
    static bool cmpByWeight(BB x, BB y) {
        return x.w < y.w;
    }
    static int run(BB A[], int dp[], int W, int N) {
        static int MQ[MAXC][2];
        
        for (int i = 0, sum = 0; i < N; i++) {
            int w = A[i].w, v = A[i].v, c = A[i].c;
            assert(c < MAXC);
            sum = min(sum + w*c, W);
            if (c != 1) {
                for (int j = 0; j < w; j++) {
                    int l = 0, r = 0;
                    MQ[r][0] = 0, MQ[r][1] = dp[j];
                    int cache_max = MQ[r][1], cache_idx = MQ[r][0];
                    int k_bound;
                    r = (r+1)&(MAXC-1);
                    k_bound = min((sum-j)/w, c);
                    for (int k = 1, tw = w+j, tv = v; k <= k_bound; k++, tw += w, tv += v) {
                        // tw = k*w+j, tv = k*v;
                        int dpv = dp[tw] - tv;
                        while (l != r && MQ[(r-1+MAXC)&(MAXC-1)][1] <= dpv)
                            r = (r-1+MAXC)&(MAXC-1);
                        MQ[r][0] = k, MQ[r][1] = dpv;
                        if (l == r)	cache_max = dpv, cache_idx = k;
                        r = (r+1)&(MAXC-1);
                        dp[tw] = max(dp[tw], cache_max + tv);
                    }
                    k_bound = (sum-j)/w;
                    for (int k = c+1, tw = (c+1)*w+j, tv = (c+1)*v; k <= k_bound; k++, tw += w, tv += v) {
                        int dpv = dp[tw] - tv;
                        while (l != r && MQ[(r-1+MAXC)&(MAXC-1)][1] <= dpv)
                            r--;
                        MQ[r][0] = k, MQ[r][1] = dpv;
                        if (l == r)	cache_max = dpv, cache_idx = k;
                        else if (k - cache_idx > c)	
                            l = (l+1)&(MAXC-1), cache_idx = MQ[l][0], cache_max = MQ[l][1];
                        r = (r+1)&(MAXC-1);
                        dp[tw] = max(dp[tw], cache_max + tv);
                    }
                }
            } else if (c == 1) {
                for (int j = sum; j >= w; j--)
                    dp[j] = max(dp[j], dp[j-w]+v);
            }
        }
    }	
    static int greedy(int C[][3], int N, int W) {
        struct GB {
            int w, v, c;
            GB(int w = 0, int v = 0, int c = 0):
                w(w), v(v), c(c) {}
            bool operator<(const GB &x) const {
                if (v * x.w != x.v * w)
                    return v * x.w > x.v * w;
                return c > x.c;
            }
        };
        vector<GB> A;
        for (int i = 0; i < N; i++) {
            int w = C[i][0], v = C[i][1], c = C[i][2];
            A.push_back(GB(w, v, c));
        }
        sort(A.begin(), A.end());
        int ret = 0;
        for (int i = 0; i < N; i++) {
            int t = min(A[i].c, W/A[i].w);
            if (t == 0)
                return -1;
            W -= t*A[i].w;
            ret += t*A[i].v;
            if (W == 0)
                return ret;
        }
        return ret;
    }
    static int knapsack(int C[][3], int N, int W) {
        // filter
        {
            int filter = greedy(C, N, W);
            if (filter != -1)
                return filter;
        }
        vector<BB> A;
        for (int i = 0; i < N; i++) {
            int w = C[i][0], v = C[i][1], c = C[i][2];
            A.push_back(BB(w, v, c));
        }
        // reduce
        {
            sort(A.begin(), A.end(), cmpByWeight);
            map<pair<int, int>, int> R;
            for (int i = 0; i < N; i++)
                R[make_pair(A[i].w, A[i].v)] = i;
            for (int i = 0; i < N; i++) {
                int c = A[i].c;
                map<pair<int, int>, int>::iterator it;
                for (int k = 1; k <= c; k <<= 1) {
                    int w = A[i].w * k, v = A[i].v * k;
                    it = R.find(make_pair(w, v));
                    if (it != R.end() && i != it->second) {
                        int j = it->second;
                        A[j].c ++;
                        A[i].c -= k;
                    }
                    c -= k;
                }
                if (c > 0) {
                    int w = A[i].w * c, v = A[i].v * c;
                    it = R.find(make_pair(w, v));
                    if (it != R.end() && i != it->second) {
                        int j = it->second;
                        A[j].c ++;
                        A[i].c -= c;
                    }
                }
            }
        }
        static int dp1[MAXW+1], dp2[MAXW+1];
        BB Ar[2][MAXN];
        int ArN[2] = {};
        memset(dp1, 0, sizeof(dp1[0])*(W+1));
        memset(dp2, 0, sizeof(dp2[0])*(W+1));
        sort(A.begin(), A.end());
        int sum[2] = {};
        for (int i = 0; i < N; i++) {
            int ch = sum[1] < sum[0];
            Ar[ch][ArN[ch]] = A[i];
            ArN[ch]++;
            sum[ch] = min(sum[ch] + A[i].w*A[i].c, W);
        }
        run(Ar[0], dp1, W, ArN[0]);
        run(Ar[1], dp2, W, ArN[1]);
        int ret = 0;
        for (int i = 0, j = W, mx = 0; i <= W; i++, j--) {
            mx = max(mx, dp2[i]);
            ret = max(ret, dp1[j] + mx);
        }
        return ret;
    }
}
int main() {
    int W, N;
    assert(scanf("%d %d", &W, &N) == 2);
    int C[MAXN][3];
    for (int i = 0; i < N; i++)
        assert(scanf("%d %d %d", &C[i][1], &C[i][0], &C[i][2]) == 3);
    printf("%d\n", knapsack(C, N, W));
    return 0;
}

Compilation message (stderr)

knapsack.cpp: In function 'int {anonymous}::run({anonymous}::BB*, int*, int, int)':
knapsack.cpp:61:5: warning: control reaches end of non-void function [-Wreturn-type]
   61 |     }
      |     ^

• Subtask 1: 12 / 12
• Subtask 2: 0 / 17
• Subtask 3: 0 / 20
• Subtask 4: 0 / 24
• Subtask 5: 0 / 27