The Triangle

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

方法描述：从最底下一行开始，逐步向上相加，每次都选取最大的和数

#include <stdio.h>
#include <stdlib.h>

#define MAX 105

int main()
{
    int n;
    int tri[MAX][MAX];  //存放三角形数据
    int maxNum[MAX];    //存放每个子问题的最大数
    int i,j;
    scanf("%d",&n);
    for (i=1; i<=n; i++)
      for (j=1; j<=i; j++)
        scanf("%d",&tri[i][j]);
    for (i=1; i<=n; i++) //先将最底下一行存放进数组
      maxNum[i] = tri[n][i];
    for (i=n; i>1; i--)　　
      for (j=1; j<i; j++)
      {　　//逐步向上一层相加，并将和最大的数存放进数组
        if (maxNum[j]>maxNum[j+1])
          maxNum[j] += tri[i-1][j];
        else
          maxNum[j] = maxNum[j+1]+tri[i-1][j];
      }
　　　　//最后，maxNum[1]即为结果
    printf("%d",maxNum[1]);
    return 0;
}