数字三角形问题

Myth丶恋晨 2022-07-12 02:46 159阅读 0赞

#### Problem Description ####

给定一个由n行数字组成的数字三角形如下图所示。试设计一个算法，计算出从三角形的顶至底的一条路径，使该路径经过的数字总和最大。  
![1730.png][]  
对于给定的由n行数字组成的数字三角形，计算从三角形的顶至底的路径经过的数字和的最大值。

#### Input ####

输入数据的第1行是数字三角形的行数n，1≤n≤100。接下来n行是数字三角形各行中的数字。所有数字在0..99之间。

#### Output ####

输出数据只有一个整数，表示计算出的最大值。

#### Example Input ####

5
    7
    3 8
    8 1 0
    2 7 4 4
    4 5 2 6 5

#### Example Output ####

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  <tr style="margin:0px!important; padding:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; font-size:1em!important; min-height:inherit!important; background:none!important"> 
   <td style="padding:0px!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:top!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:3em!important; line-height:1.1em!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; min-height:inherit!important; color:rgb(175,175,175)!important; background:none!important"> <code style="color:rgb(199,37,78); font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px 0.3em 0px 0px!important; margin:0px!important; border:0px!important; outline:0px!important; text-align:right!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:2.7em!important; line-height:1.1em!important; min-height:inherit!important; display:block!important; background:none!important">24</code></td> 
   <td style="padding:0px 0px 0px 0.5em!important; margin:0px!important; border-width:0px 0px 0px 3px!important; border-left-style:solid!important; border-left-color:rgb(108,226,108)!important; outline:0px!important; float:none!important; vertical-align:top!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; min-height:inherit!important; background:none!important"> <code style="color:rgb(199,37,78); font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; min-height:inherit!important; background:none!important">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</code><code style="font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px!important; color:rgb(0,102,153)!important; font-weight:bold!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; min-height:inherit!important; background:none!important">return</code>&nbsp;<code style="font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; min-height:inherit!important; background:none!important">a;</code></td> 
  </tr> 
 </tbody> 
</table>

<table style="border-spacing:0px; border-collapse:collapse!important; margin:0px!important; padding:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; font-size:1em!important; min-height:inherit!important; background:none!important"> 
 <tbody style="margin:0px!important; padding:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; font-size:1em!important; min-height:inherit!important; background:none!important"> 
  <tr style="margin:0px!important; padding:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; font-size:1em!important; min-height:inherit!important; background:none!important"> 
   <td style="padding:0px!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:top!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:3em!important; line-height:1.1em!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; min-height:inherit!important; color:rgb(175,175,175)!important; background:none!important"> <code style="color:rgb(199,37,78); font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px 0.3em 0px 0px!important; margin:0px!important; border:0px!important; outline:0px!important; text-align:right!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:2.7em!important; line-height:1.1em!important; min-height:inherit!important; display:block!important; background:none!important">26</code></td> 
   <td style="padding:0px 0px 0px 0.5em!important; margin:0px!important; border-width:0px 0px 0px 3px!important; border-left-style:solid!important; border-left-color:rgb(108,226,108)!important; outline:0px!important; float:none!important; vertical-align:top!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; min-height:inherit!important; background:none!important"> <code style="color:rgb(199,37,78); font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; min-height:inherit!important; background:none!important">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</code><code style="font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px!important; color:rgb(0,102,153)!important; font-weight:bold!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; min-height:inherit!important; background:none!important">return</code>&nbsp;<code style="font-family:Consolas,'Bitstream Vera Sans Mono','Courier New',Courier,monospace!important; font-size:1em!important; padding:0px!important; margin:0px!important; border:0px!important; outline:0px!important; float:none!important; vertical-align:baseline!important; position:static!important; left:auto!important; top:auto!important; right:auto!important; bottom:auto!important; height:auto!important; width:auto!important; line-height:1.1em!important; min-height:inherit!important; background:none!important">b;</code></td> 
  </tr> 
 </tbody> 
</table>

[1730.png]: http://acm.sdut.edu.cn/image/1730.png