/* * 背包 DP:考虑前 i 个物品的最大价值,在仅有 t 容量的情况下。 */ #include using namespace std; struct Item { int weight, value; }; constexpr int MAX_N = 105, MAX_CAPACITY = 1005; int capacity, n; Item items[MAX_N]; int dp[MAX_N][MAX_CAPACITY]; void log_dp() { for (int i = 0; i <= n; i++) { for (int j = 0; j <= capacity; j++) { clog << dp[i][j] << "\t"; } clog << endl; } } void solve_dp() { for (int i = 0; i <= capacity; i++) { dp[0][i] = 0; } for (int i = 0; i <= n; i++) { dp[i][0] = 0; } for (int stop_item = 1; stop_item <= n; stop_item++) { for (int w = 1; w <= capacity; w++) { dp[stop_item][w] = dp[stop_item - 1][w]; if (w >= items[stop_item - 1].weight) { // 负数 dp[stop_item][w] = max(dp[stop_item][w], dp[stop_item - 1][w - items[stop_item - 1].weight] + items[stop_item - 1].value); } } } } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cin >> capacity >> n; for (int i = 0; i < n; i++) { cin >> items[i].weight >> items[i].value; } solve_dp(); log_dp(); cout << dp[n][capacity] << endl; return 0; }