The Triangle

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 48172 Accepted: 29141

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 题目大意：在上面的数字三角形中寻找一条从顶部到底边的路径，使得路径上所经过的数字之和最大。 0-1背包问题 Scanner scan=new Scanner(System.in); public static void main(String[] args){ Test test =new Test(); test.start(); } public void start(){ int num=scan.nextInt(); int array[][] =new int[num][num]; for(int i=0;i<array.length;i++){ for(int j=0;j<i+1;j++){ array[i][j]=scan.nextInt(); } } for(int i=array.length-2;i>=0;i--){ for(int j=0;j<i+1;j++){ array[i][j]=Math.max(array[i][j]+array[i+1][j], array[i][j]+array[i+1][j+1]); } } System.out.println(array[0][0]); }