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similarity index 100% rename from TangDou/AcWing/BeiBao/10_SanWei.cpp rename to TangDou/AcWing/Bag/10_SanWei.cpp diff --git a/TangDou/AcWing/BeiBao/11.md b/TangDou/AcWing/Bag/11.md similarity index 100% rename from TangDou/AcWing/BeiBao/11.md rename to TangDou/AcWing/Bag/11.md diff --git a/TangDou/AcWing/BeiBao/11_ErWei_1.cpp b/TangDou/AcWing/Bag/11_ErWei_1.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/11_ErWei_1.cpp rename to TangDou/AcWing/Bag/11_ErWei_1.cpp diff --git a/TangDou/AcWing/BeiBao/11_ErWei_2.cpp b/TangDou/AcWing/Bag/11_ErWei_2.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/11_ErWei_2.cpp rename to TangDou/AcWing/Bag/11_ErWei_2.cpp diff --git a/TangDou/AcWing/BeiBao/11_YiWei_1.cpp b/TangDou/AcWing/Bag/11_YiWei_1.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/11_YiWei_1.cpp rename to TangDou/AcWing/Bag/11_YiWei_1.cpp diff --git a/TangDou/AcWing/BeiBao/11_YiWei_2.cpp b/TangDou/AcWing/Bag/11_YiWei_2.cpp similarity index 100% rename from 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b/TangDou/AcWing/Bag/278_2.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/278_2.cpp rename to TangDou/AcWing/Bag/278_2.cpp diff --git a/TangDou/AcWing/BeiBao/2_ErWei.cpp b/TangDou/AcWing/Bag/2_ErWei.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/2_ErWei.cpp rename to TangDou/AcWing/Bag/2_ErWei.cpp diff --git a/TangDou/AcWing/BeiBao/2_QiaHaoFill.in b/TangDou/AcWing/Bag/2_QiaHaoFill.in similarity index 100% rename from TangDou/AcWing/BeiBao/2_QiaHaoFill.in rename to TangDou/AcWing/Bag/2_QiaHaoFill.in diff --git a/TangDou/AcWing/BeiBao/2_QiaHaoFill_ErWei.cpp b/TangDou/AcWing/Bag/2_QiaHaoFill_ErWei.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/2_QiaHaoFill_ErWei.cpp rename to TangDou/AcWing/Bag/2_QiaHaoFill_ErWei.cpp diff --git a/TangDou/AcWing/BeiBao/2_QiaHaoFill_YiWei.cpp b/TangDou/AcWing/Bag/2_QiaHaoFill_YiWei.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/2_QiaHaoFill_YiWei.cpp rename to TangDou/AcWing/Bag/2_QiaHaoFill_YiWei.cpp diff --git a/TangDou/AcWing/BeiBao/2_YiWei.cpp b/TangDou/AcWing/Bag/2_YiWei.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/2_YiWei.cpp rename to TangDou/AcWing/Bag/2_YiWei.cpp diff --git a/TangDou/AcWing/BeiBao/2_dfs_int.cpp b/TangDou/AcWing/Bag/2_dfs_int.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/2_dfs_int.cpp rename to TangDou/AcWing/Bag/2_dfs_int.cpp diff --git a/TangDou/AcWing/BeiBao/2_dfs_int_jiyihua.cpp b/TangDou/AcWing/Bag/2_dfs_int_jiyihua.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/2_dfs_int_jiyihua.cpp rename to TangDou/AcWing/Bag/2_dfs_int_jiyihua.cpp diff --git a/TangDou/AcWing/BeiBao/2_dfs_void.cpp b/TangDou/AcWing/Bag/2_dfs_void.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/2_dfs_void.cpp rename to TangDou/AcWing/Bag/2_dfs_void.cpp diff --git a/TangDou/AcWing/BeiBao/3.md b/TangDou/AcWing/Bag/3.md similarity index 100% rename from TangDou/AcWing/BeiBao/3.md rename to TangDou/AcWing/Bag/3.md diff --git a/TangDou/AcWing/BeiBao/3_0.cpp b/TangDou/AcWing/Bag/3_0.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/3_0.cpp rename to TangDou/AcWing/Bag/3_0.cpp diff --git a/TangDou/AcWing/BeiBao/3_ErWei.cpp b/TangDou/AcWing/Bag/3_ErWei.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/3_ErWei.cpp rename to TangDou/AcWing/Bag/3_ErWei.cpp diff --git a/TangDou/AcWing/BeiBao/3_YiWei.cpp b/TangDou/AcWing/Bag/3_YiWei.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/3_YiWei.cpp rename to TangDou/AcWing/Bag/3_YiWei.cpp diff --git a/TangDou/AcWing/BeiBao/4.md b/TangDou/AcWing/Bag/4.md similarity index 100% rename from TangDou/AcWing/BeiBao/4.md rename to TangDou/AcWing/Bag/4.md diff --git a/TangDou/AcWing/BeiBao/423.md b/TangDou/AcWing/Bag/423.md similarity index 88% rename from TangDou/AcWing/BeiBao/423.md rename to TangDou/AcWing/Bag/423.md index 4297128..9f70945 100644 --- a/TangDou/AcWing/BeiBao/423.md +++ b/TangDou/AcWing/Bag/423.md @@ -37,13 +37,16 @@ $1≤T≤1000$,$1≤M≤100$ ### 二、题目解析 -注意一下$m$和$n$的录入顺序。 **01背包模型** -**状态表示$f(i,j)$—集合**: 考虑前 $i$ 个物品,且当前已使用体积为$ j$ 的方案 +**状态表示** -**状态表示$f(i,j)$—属性**: 该方案的价值为最大值 $max$ +$f(i,j)$ +- **集合** +考虑前 $i$ 个物品,且当前已使用体积为$ j$ 的方案 +- **属性** +该方案的价值为最大值 $max$ **状态转移$f(i,j)$**: @@ -65,7 +68,6 @@ $$f(i,j)=\begin{equation} ### 三、二维朴素作法 -空间复杂度:$O(n×m)$ 时间复杂度:$O(n×m)$ ```cpp {.line-numbers} diff --git a/TangDou/AcWing/BeiBao/423_1.cpp b/TangDou/AcWing/Bag/423_1.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/423_1.cpp rename to TangDou/AcWing/Bag/423_1.cpp diff --git a/TangDou/AcWing/BeiBao/423_2.cpp b/TangDou/AcWing/Bag/423_2.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/423_2.cpp rename to TangDou/AcWing/Bag/423_2.cpp diff --git a/TangDou/AcWing/BeiBao/426.cpp b/TangDou/AcWing/Bag/426.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/426.cpp rename to TangDou/AcWing/Bag/426.cpp diff --git a/TangDou/AcWing/BeiBao/426.md b/TangDou/AcWing/Bag/426.md similarity index 100% rename from TangDou/AcWing/BeiBao/426.md rename to TangDou/AcWing/Bag/426.md diff --git a/TangDou/AcWing/BeiBao/487.md b/TangDou/AcWing/Bag/487.md similarity index 100% rename from TangDou/AcWing/BeiBao/487.md rename to TangDou/AcWing/Bag/487.md diff --git a/TangDou/AcWing/BeiBao/487_FZ1.cpp b/TangDou/AcWing/Bag/487_FZ1.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/487_FZ1.cpp rename to TangDou/AcWing/Bag/487_FZ1.cpp diff --git a/TangDou/AcWing/BeiBao/487_FZ2.cpp b/TangDou/AcWing/Bag/487_FZ2.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/487_FZ2.cpp rename to TangDou/AcWing/Bag/487_FZ2.cpp diff --git a/TangDou/AcWing/BeiBao/487_Prepare.cpp b/TangDou/AcWing/Bag/487_Prepare.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/487_Prepare.cpp rename to TangDou/AcWing/Bag/487_Prepare.cpp diff --git a/TangDou/AcWing/BeiBao/4_ErWei.cpp b/TangDou/AcWing/Bag/4_ErWei.cpp similarity index 100% rename from TangDou/AcWing/BeiBao/4_ErWei.cpp rename to 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TangDou/AcWing/Bag/【总结】背包问题的至多_恰好_至少-主帖.md diff --git a/TangDou/AcWing/BeiBao/【总结】脑图形式(一维)总结.md b/TangDou/AcWing/Bag/【总结】脑图形式(一维)总结.md similarity index 100% rename from TangDou/AcWing/BeiBao/【总结】脑图形式(一维)总结.md rename to TangDou/AcWing/Bag/【总结】脑图形式(一维)总结.md diff --git a/TangDou/AcWing/BeiBao/【总结】脑图形式(二维)总结.md b/TangDou/AcWing/Bag/【总结】脑图形式(二维)总结.md similarity index 100% rename from TangDou/AcWing/BeiBao/【总结】脑图形式(二维)总结.md rename to TangDou/AcWing/Bag/【总结】脑图形式(二维)总结.md diff --git a/TangDou/AcWing/Bag/背包问题专题,md b/TangDou/AcWing/Bag/背包问题专题,md new file mode 100644 index 0000000..9c22d11 --- /dev/null +++ b/TangDou/AcWing/Bag/背包问题专题,md @@ -0,0 +1,64 @@ +## 背包问题 + +### 一、$01$背包 +**[$AcWing$ $2$. $01$背包问题](https://www.acwing.com/problem/content/2/)** + +**[$AcWing$ $423$. 采药](https://www.acwing.com/problem/content/425/)** + +**[$AcWing$ $1024$. 装箱问题](https://www.acwing.com/problem/content/1026/)** + +二维状态表示 +```cpp {.line-numbers} +#include + +using namespace std; +const int N = 110; +const int M = 1010; + +int n, m; +int w[N], v[N]; +int f[N][M]; + +int main() { + cin >> m >> n; + + for (int i = 1; i <= n; i++) cin >> v[i] >> w[i]; + + for (int i = 1; i <= n; i++) + for (int j = 1; j <= m; j++) { + f[i][j] = f[i - 1][j]; // 不选 + if (j >= v[i]) + f[i][j] = max(f[i][j], f[i - 1][j - v[i]] + w[i]); // 选 + } + printf("%d\n", f[n][m]); + return 0; +} + +``` + +一维状态表示 +```cpp {.line-numbers} +#include + +using namespace std; +const int N = 1010; + +int n, m; +int v[N], w[N]; +int f[N]; + +int main() { + cin >> m >> n; + for (int i = 1; i <= n; i++) cin >> v[i] >> w[i]; + + // 01背包模板 + for (int i = 1; i <= n; i++) + for (int j = m; j >= v[i]; j--) + f[j] = max(f[j], f[j - v[i]] + w[i]); + + printf("%d\n", f[m]); + return 0; +} +``` + + diff --git a/TangDou/AcWing_TiGao/T1/LIS/1010.md b/TangDou/AcWing/LIS/1010.md similarity index 100% rename from TangDou/AcWing_TiGao/T1/LIS/1010.md rename to TangDou/AcWing/LIS/1010.md diff --git a/TangDou/AcWing_TiGao/T1/LIS/1010_Dilworth.cpp 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