Unverified Commit 05d266cb authored by wolfdan666's avatar wolfdan666 Committed by GitHub
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更新01背包和完全背包的核心代码和AC代码,对01背包和前面的记忆化搜索方法进行了联系 

看到文章有点点小小的笔误,然后还有人评论了,所以我就更新01背包和完全背包的核心代码和AC代码,并且对01背包和前面的记忆化搜索方法进行了联系,我在落谷上测试了几遍,应该都是对的希望小编通过我的pr,谢谢啦,感谢oi-wiki,2333
parent 960c014b

docs/dp/knapsack.md

+37 −7
Original line number Diff line number Diff line
@@ -35,7 +35,7 @@ $$ 


```cpp

for (int i = 1; i <= W; i++)

  for (int l = 0; l <= W - i; l++) f[l + w[i]] = max(f[l] + v[i], f[l + w[i]]);

  for (int l = 0; l <= W - w[i]; l++) f[l + w[i]] = max(f[l] + v[i], f[l + w[i]]);

// 由 f[i][l + w[i]] = max(max(f[i - 1][l + w[i]],f[i - 1][l] + w[i]),f[i][l +

// w[i]]); 简化而来

```
@@ -49,15 +49,15 @@ for (int i = 1; i <= W; i++) 
因此实际核心代码为



```cpp

for (int i = 1; i <= W; i++)

  for (int l = W - i; l >= 0; l--) f[l + i] = max(f[l] + w[i], f[l + i]);

for (int i = 1; i <= n; i++)

  for (int l = W ; l >= w[i]; l--) f[l] = max(f[l], f[l - w[i]] + v[i]);

```



??? 例题代码

    ```cpp

    #include <iostream>

    const int maxn = 13010;

    int n, v, w[maxn], v[maxn], f[maxn];

    int n,W, w[maxn], v[maxn], f[maxn];

    int main() {

      std::cin >> n >> W;

      for (int i = 1; i <= n; i++) std::cin >> w[i] >> v[i];
@@ -68,6 +68,36 @@ for (int i = 1; i <= W; i++) 
      return 0;

    }

    ```

### 为什么不用记忆化搜索

是不是看着这个题目和前面的记忆化搜索很相似,前面是总采药时间,这里是总背包大小,前面是每种药的采集时间,这里是每个物品的体积,所以[wolfdan666](https://github.com/wolfdan666)同学尝试了一发,然后很荣幸得MLE,因为这里可以滚动数组(见上面的例题代码),以及可以看看MLE的记忆化搜索代码

??? 记忆化搜索代码会MLE

    ```cpp

    #include<bits/stdc++.h>

    using namespace std;

    // 魔改解决01背包问题

    const int N = 3403;

    const int M = 12881;



    int n, t;

    int tcost[N], mget[N];

    int mem[N][M];

    int dfs(int pos, int tleft) {

      if (mem[pos][tleft] != -1) return mem[pos][tleft];

      if (pos == n + 1) return mem[pos][tleft] = 0;

      int dfs1, dfs2 = -2;

      dfs1 = dfs(pos + 1, tleft);

      if (tleft >= tcost[pos]) dfs2 = dfs(pos + 1, tleft - tcost[pos]) + mget[pos];

      return mem[pos][tleft] = max(dfs1, dfs2);

    }

    int main() {

      memset(mem, -1, sizeof(mem));

      // cin >> t >> n;

      cin >> n >> t;

      for (int i = 1; i <= n; i++) cin >> tcost[i] >> mget[i];

      cout << dfs(1, t) << endl;

      return 0;

    }

    ```



## 完全背包
@@ -103,10 +133,10 @@ $$ 
??? 例题代码

    ```cpp

    #include <iostream>

    const int maxn = 13010;

    int n, v, w[maxn], v[maxn], f[maxn];

    const int maxn = 1e5+10;

    int n, W, w[maxn], v[maxn], f[maxn];

    int main() {

      std::cin >> n >> W;

      std::cin >> W >> n;

      for (int i = 1; i <= n; i++) std::cin >> w[i] >> v[i];

      for (int i = 1; i <= n; i++)

        for (int l = w[i]; l <= W; l++)