Submission #1086123

#	Time	Username	Problem	Language	Result	Execution time	Memory
1086123		lukasuliashvili	Knapsack (NOI18_knapsack)	C++17	73 / 100	5 ms	1104 KiB

knapsack

#include <bits/stdc++.h>
using namespace std;

const int N = 10005;
long long v[N], w[N];
long long dp[N];
int k[N];

void binary_decompose(int idx, int n, int s) {
    long long value = v[idx];
    long long weight = w[idx];
    long long count = k[idx];

    // Decompose count into powers of two
    for (long long i = 1; i <= count; i *= 2) {
        long long num = min(i, count); // Take min to avoid exceeding k[i]
        count -= num;

        // Process this number of items
        for (int j = s; j >= num * weight; j--) {
            dp[j] = max(dp[j], dp[j - num * weight] + num * value);
        }
    }

    // If count is still left, process the remaining items
    if (count > 0) {
        for (int j = s; j >= count * weight; j--) {
            dp[j] = max(dp[j], dp[j - count * weight] + count * value);
        }
    }
}

int main() {
    int s, n;
    cin >> s >> n;

    for (int i = 1; i <= n; i++) {
        cin >> v[i] >> w[i] >> k[i]; // v[i] = value, w[i] = weight, k[i] = max times we can take item i
    }

    // Initialize dp array
    fill(dp, dp + s + 1, 0);

    // Process each item using binary decomposition
    for (int i = 1; i <= n; i++) {
        binary_decompose(i, n, s);
    }

    cout << dp[s] << endl;
    return 0;
}

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