【hihoCoder】1037 : 数字三角形

题目：http://hihocoder.com/problemset/problem/1037

• 一个迷宫有n层，第 i 层有 i 个房间
• 从第i层的第i个房间(i, i)可以走到第i+1层的第i个房间或第i+1房间(i+1, i)/(i+1, i+1)
• 每个房间走出去后都不能回头

样例输入

5 //迷宫的层数
2
6 4
1 2 8
4 0 9 6
6 5 5 3 6
结果： 28
思路
动态规划
maze[i, j] = max(maze[i-1, j], maze[i-1, j-1])
 
源码

• 迭代方式，从下而上

 #include <iostream>
 using namespace std;
 
 static int maze[][];//存储到达每一个房间收集到的最多券
 static int data[][];//存储每一个房间的券
 
 int main()
 {
     int maxLevel, i = , max = ;
     cin >> maxLevel;
 
     for (i = ; i < maxLevel; i++)
         for (int j = ; j <= i; j++)
             cin >> data[i][j];
     //由低层到高层计算
     maze[][] = data[][];
     for (int i = ; i < maxLevel; i++)
     {
         for (int j = ; j <= i; j++)
         {
             if (j >  && maze[i - ][j] < maze[i - ][j - ])
                 maze[i][j] = maze[i - ][j - ];
             else
                 maze[i][j] = maze[i - ][j];
             maze[i][j] += data[i][j];
         }
     }
     //找出最后一层中券最多的房间
     for (i = ; i < maxLevel; i++)
     {
         int tmp = maxLevel - ;
         if (max < maze[tmp][i])
             max = maze[tmp][i];
     }
     cout << max << endl;
     return ;
 }

• 递归方式，从上而下

 #include <iostream>
 using namespace std;
 
 int maze[][];
 int data[][];
 void dp(int level)
 {
     if (level < )
         return;
     dp(level - );
     for (int room = ; room <= level; room++)
     {
         if (level > )
         {
             if (room > )
                 maze[level][room] = maze[level - ][room] > maze[level - ][room - ] ? maze[level - ][room] : maze[level - ][room - ];
             else
                 maze[level][room] = maze[level - ][room];
         }
         else
             maze[level][room] = ;
         maze[level][room] += data[level][room];
     }
 }
 int main()
 {
     int maxLevel, i = , max = ;
     cin >> maxLevel;
 
     for (i = ; i < maxLevel; i++)
         for (int j = ; j <= i; j++)
             cin >> data[i][j];
     dp(maxLevel - );
     for (i = ; i < maxLevel; i++)
     {
         int tmp = maxLevel - ;
         if (max < maze[tmp][i])
             max = maze[tmp][i];
     }
     cout << max << endl;
     return ;
 }