POJ1163-数字迷宫（递归加动态规划练习）

The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 55486		Accepted: 33354

Description

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

(Figure 1)

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

maxsum[i][j]表示第i行第j列到最下端的最大值，用递归的方法很直观进行遍历，但是要注意把每一次算的maxsum[i][j]存下来