poj1163

maksyuki 发表于 oj 分类，标签:
15 9月 2015
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The Triangle

Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.

Input

Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99.

Output

Your program is to write to standard output. The highest sum is written as an integer.

Sample Input

5

7

3 8

8 1 0

2 7 4 4

4 5 2 6 5

Sample Output

30

Source

IOI 1994

 

题目类型：线性dp

算法分析：本题采用逆向思维，从三角形的底边开始向上计算，每次先判断加到上一行的最大值，然后将最大值所在的下一行的的值加到该行。以此类推向上计算直到三角形的最高顶点