算法实现题3-7 数字三角形问题

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。<br /> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 7<br /> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;3 &nbsp;8<br /> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;8 &nbsp;1 &nbsp;0<br /> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2 &nbsp;7 &nbsp;4 &nbsp;4<br /> <p> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;4 &nbsp;5 &nbsp;2 &nbsp;6 &nbsp;5 </p> <p> 编程任务：<br /> 对于给定的由n 行数字组成的数字三角形，编程计算从三角形的顶至底的路径经过的数<br /> 字和的最大值。 </p>

由文件input.txt 提供输入数据。文件的第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。<br />

程序运行结束时，将计算结果输出到文件output.txt 中。文件的第1 行中的数是计算出的最大值。<br />