算法基础之数字三角形

阳光男孩012023-12-27 10:22

数字三角形

核心思想：线性dp

集合的定义为 f[i][j] --> 到i j点的最大距离
从下往上传值父节点f[i][j] = max(f[i+1][j] , f[i+1][j+1]) + w[i][j]
初始化最后一层 f = w

cpp 复制代码

  #include <bits/stdc++.h>
  
  using namespace std;
  
  const int N = 510;
  
  int w[N][N],f[N][N];
  int n;
  
  int main()
  {
      cin >> n;
      for (int i = 1; i <= n; i++)
          for (int j = 1; j <= i; j++)
              cin >> w[i][j];
  
      for(int i=1;i<=n;i++) f[n][i] = w[n][i]; 
      for (int i = n - 1; i >= 1; i--)
          for (int j = 1; j <= i; j++)
              f[i][j] = max(f[i + 1][j + 1], f[i + 1][j]) + w[i][j];  //左孩子和右孩子取最大 + 距离
  
      cout << f[1][1] << endl;
  }

优化版:

cpp 复制代码

  #include <bits/stdc++.h>
  
  using namespace std;
  
  const int N = 510;
  
  int f[N][N];
  int n;
  
  int main()
  {
      cin >> n;
      for (int i = 1; i <= n; i++)
          for (int j = 1; j <= i; j++)
              cin >> f[i][j];
  
      for (int i = n - 1; i >= 1; i--)
          for (int j = 1; j <= i; j++)
              f[i][j] = max(f[i + 1][j + 1], f[i + 1][j]) + f[i][j];
      		//用完f[i][j]距上一层距离 就将其更新成距底部距离
  
      cout << f[1][1] << endl;
  }