Update CMakeLists.txt

dp/backpack_dp/NOIP2005J_herbs_dp_knapsack.cpp

@@ -0,0 +1,52 @@
+#include <iostream>
+
+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_CAPACITY];
+bool ping_pong;
+
+void log_dp() {
+    // for (int i = 0; i <= 1; i++) {
+    for (int j = 0; j <= capacity; j++) {
+        clog << dp[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++, ping_pong = !ping_pong) {
+        for (int w = capacity; w >= 1; w--) {
+            if (w >= items[stop_item - 1].weight) { // 负数
+                dp[w] = max(dp[w],
+                            dp[w - items[stop_item - 1].weight] + items[stop_item - 1].value);
+            }
+        }
+        // log_dp();
+    }
+}
+
+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();
+    cout << dp[capacity] << endl;
+
+
+    return 0;
+}

dp/backpack_dp/NOIP2005J_herbs_dp_knapsack_MWASTE.cpp

@@ -0,0 +1,48 @@
+/*
+ * 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。
+ * 建议两个维度调换一下，方便乒乓/滚动。
+ */
+
+#include <iostream>
+
+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_CAPACITY][MAX_N];
+
+void solve_dp() {
+    for (int i = 0; i <= capacity; i++) { dp[i][0] = 0; }
+    for (int i = 0; i <= n; i++) { dp[0][i] = 0; }
+    for (int stop_item = 1; stop_item <= n; stop_item++) {
+        for (int w = 1; w <= capacity; w++) {
+            dp[w][stop_item] = dp[w][stop_item - 1];
+            if (w >= items[stop_item - 1].weight) { // 负数
+                dp[w][stop_item] =
+                    max(dp[w][stop_item],
+                        dp[w - items[stop_item - 1].weight][stop_item - 1] + 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();
+    cout << dp[capacity][n] << endl;
+
+
+    return 0;
+}

dp/backpack_dp/NOIP2005J_herbs_dp_knapsack_MWASTE_BETTER.cpp

@@ -0,0 +1,57 @@
+/*
+* 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 <iostream>
+
+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;
+}

dp/backpack_dp/NOIP2005J_herbs_dp_knapsack_PINGPONG.cpp

@@ -0,0 +1,54 @@
+#include <iostream>
+
+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[2][MAX_CAPACITY];
+bool ping_pong;
+
+void log_dp() {
+    // for (int i = 0; i <= 1; i++) {
+        for (int j = 0; j <= capacity; j++) {
+            clog << dp[ping_pong][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++, ping_pong = !ping_pong) {
+        for (int w = 1; w <= capacity; w++) {
+            dp[ping_pong][w] = dp[!ping_pong][w];
+            if (w >= items[stop_item - 1].weight) { // 负数
+                dp[ping_pong][w] =
+                    max(dp[ping_pong][w],
+                        dp[!ping_pong][w - items[stop_item - 1].weight] + items[stop_item - 1].value);
+            }
+        }
+        // log_dp();
+    }
+}
+
+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();
+    cout << dp[!ping_pong][capacity] << endl;
+
+
+    return 0;
+}

dp/backpack_dp/NOIP2006S_jinming_budget_dp_knapsack.cpp

@@ -0,0 +1,86 @@
+#include <iostream>
+#include <vector>
+
+using namespace std;
+
+struct FlatItem {
+    int weight, value;
+
+    FlatItem operator+(const FlatItem& other) const {
+        return {.weight = weight + other.weight, .value = value + other.value};
+    }
+};
+
+struct OriginalItem {
+    FlatItem item{};
+    vector<FlatItem> sons;
+};
+
+constexpr int MAX_N = 65, MAX_CAPACITY = 32005;
+
+int capacity, n;
+vector<OriginalItem> items;
+vector<FlatItem> flat_items;
+int fathers_temp[MAX_N];
+
+int dp[MAX_CAPACITY];
+
+vector<FlatItem> generate_flat_items(OriginalItem item) {
+    switch (item.sons.size()) {
+        case 0:
+            return vector{item.item};
+        case 1:
+            return vector{
+                item.item,
+                item.sons[0] + item.item,
+            };
+        case 2:
+            return vector{
+                item.item,
+                item.sons[0] + item.item,
+                item.sons[1] + item.item,
+                item.sons[0] + item.sons[1] + item.item,
+            };
+        default:
+            throw logic_error("Invalid item size!");
+    }
+}
+
+
+void solve_dp() {
+    for (int i = 0; i < n; i++) {
+        if (items[i].item.value == -1) { continue; }
+        for (int w=capacity; w>=1; w--) {
+            // dp[w] = dp[w] // 不买
+            for (const auto& [weight, value] : generate_flat_items(items[i])) {
+                if (w >= weight) {
+                    dp[w] = max(dp[w], dp[w - weight] + value);
+                }
+            }
+        }
+    }
+}
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> capacity >> n;
+    items.resize(n);
+
+    for (int i = 0; i < n; i++) {
+        cin >> items[i].item.weight >> items[i].item.value >> fathers_temp[i];
+        items[i].item.value *= items[i].item.weight; // 题意
+    }
+    for (int i = 0; i < n; i++) {
+        if (fathers_temp[i] != 0) {
+            items[fathers_temp[i] - 1].sons.push_back(items[i].item);
+            items[i].item.value = -1; // 删掉这个元素！
+        }
+    }
+
+    solve_dp();
+    cout << dp[capacity] << endl;
+
+    return 0;
+}