poj 1163 The Triangle

提交地址：http://poj.org/problem?id=1163&lang=default&change=true

中文翻译：http://codevs.cn/problem/1220/

                                                             The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 43809		Accepted: 26430

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

#include<cstdio>
#include<iostream>
#define N 100+10

using namespace std;

int a[N][N],n;

int main()
  {
      scanf("%d",&n);
      for(int i=1;i<=n;i++)
        for(int j=1;j<=i;j++)        //数字三角形的读入 
          scanf("%d",&a[i][j]);
      for(int i=n-1;i>=1;i--)
        for(int j=1;j<=i;j++)        //从下向上每一个点都可以加上他两个孩子之中较大的那个，当加到a[1][1]是，就是最大的值
                                   //因为不需要输出路径，所以可以直接在原数组上修改 
          a[i][j]+=max(a[i+1][j],a[i+1][j+1]);
      printf("%d",a[1][1]);
      return 0;
  }