Triangle leetcode java

題目：

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.

For example, given the following triangle

[
     [2],
    [3,4],
   [6,5,7],
  [4,1,8,3]
]

The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).

Note:
Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.

 

題解：

一道動態規划的經典題目。需要自底向上求解。

遞推公式是： dp[i][j] = dp[i+1][j] + dp[i+1][j+1] ，當前這個點的最小值，由他下面那一行臨近的2個點的最小值與當前點的值相加得到。

由於是三角形，且歷史數據只在計算最小值時應用一次，所以無需建立二維數組，每次更新1維數組值，最后那個值里存的就是最終結果。

代碼如下：

 

 
           1  
          public  
          int minimumTotal(List<List<Integer>> triangle) { 
          
 
           2      
          if(triangle.size()==1) 
          
 
           3          
          return triangle.get(0).get(0); 
          
 
           4          
          
 
           5      
          int[] dp =  
          new  
          int[triangle.size()]; 
          
 
           6  
          
 
           7      
          // 
          initial by last row  
          
 
           8  
               
          for ( 
          int i = 0; i < triangle.get(triangle.size() - 1).size(); i++) { 
          
 
           9         dp[i] = triangle.get(triangle.size() - 1).get(i); 
          
 
          10     } 
          
 
          11   
          
 
          12      
          // 
           iterate from last second row 
          
 
          13  
               
          for ( 
          int i = triangle.size() - 2; i >= 0; i--) { 
          
 
          14          
          for ( 
          int j = 0; j < triangle.get(i).size(); j++) { 
          
 
          15             dp[j] = Math.min(dp[j], dp[j + 1]) + triangle.get(i).get(j); 
          
 
          16         } 
          
 
          17     } 
          
 
          18   
          
 
          19      
          return dp[0]; 
          
 
          20 } 
         

Reference:  http://www.programcreek.com/2013/01/leetcode-triangle-java/