为什么背包问题的解决方案不起作用？

Question

下面的代码是我解决这个问题的尝试。我使用了基于1的索引。我无法找出错误。我试着调试代码，但没有帮助。我已经被困了两天了。请帮忙。

  #include <iostream>
  #include <limits.h>
  using namespace std;

  int main()
  {
    int n,W;

    cin>>n>>W;    // no. of elements and maxm. Weight
    int v[n+1],w[n+1];   // array for value and weight 
    int dp[n+1][100001];  // dp array with size n+1 and 10^5+1 (for v max value 1000, and for n 100)

    // Initializing arrays

    v[0]=INT_MAX; w[0]=INT_MAX;

    for (int i = 0; i < n+1; ++i)
    {
      for (int j = 0; j < 100001; ++j)
      {
        dp[i][j]=INT_MAX;      
      }
    }

    for (int i = 1; i < n+1; ++i){
      cin>>w[i]>>v[i];
    }
    
    dp[1][0]=0; // for 0 value, no value for weight
    dp[1][v[1]]=w[1]; 

    
    for (int i = 2; i < n+1; ++i) 
    {
      dp[i][0]=0;
      
      for (int j = 1; j < 100001; ++j)
      {
        dp[i][j]=dp[i-1][j]; // excluding the element

        if(j-v[i]>=1){ 
          dp[i][j]=min(dp[i][j],w[i]+dp[i-1][j-v[i]]); // min of including and excluding element
        }
      }
    }

    // to find the max value for which weight is <=W
    for(int i=100000; i>=1; i--){
      if(dp[n][i]<=W){
        cout<<i; break;
      }
    }

    return 0;
  }

Answer 1

您的代码存在一些问题：

• 最大值可以为0
• 达到某个值所需的权重可以是>INT_MAX
• dp[1][v[1]]=w[1]；uneeded行
• 对于（int j=1；j<100001；++j)j为0是有效权重，但
• 如果(j-v[i]>=1){同上

以下是一个固定的版本：

 #include <iostream>
  #include <limits.h>
#define ll long long
  using namespace std;

  int main()
  {
    int n,W;

    cin>>n>>W;    // no. of elements and maxm. Weight
    ll v[n+1],w[n+1];   // array for value and weight 
    ll dp[n+1][100001];  // dp array with size n+1 and 10^5+1 (for v max value 1000, and for n 100)

    // Initializing arrays

    v[0]=1e17; w[0]=1e17;

    for (int i = 0; i < n+1; ++i)
    {
      for (int j = 0; j < 100001; ++j)
      {
        dp[i][j]=INT_MAX;      
      }
    }

    for (int i = 1; i < n+1; ++i){
      cin>>w[i]>>v[i];
    }
    
    dp[0][0]=0; // for 0 value, no value for weight

    for (int i = 1; i < n+1; ++i) 
    {
      dp[i][0]=0;
      
      for (int j = 0; j < 100001; ++j)
      {
        dp[i][j]=dp[i-1][j]; // excluding the element

        if(j-v[i]>=0){ 
          dp[i][j]=min(dp[i][j],w[i]+dp[i-1][j-v[i]]); // min of including and excluding element
        }
      }
    }

    // to find the max value for which weight is <=W
    for(int i=100000; i>=0; i--){
      if(dp[n][i]<=W){
        cout<<i; break;
      }
    }

    return 0;
  }