POJ 1163 The Triangle

Description

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

(Figure 1)

Figure 1 shows a number triangle（三角形）. Write a program that calculates the highest sum of numbers passed on a route（路线） that starts at the top and ends somewhere（某处） on the base. Each step can go either diagonally（角） 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

这个是经典的动态规划，也是最最基础、最最简单的动态规划，典型的多段图。
思路就是建立一个数组，由下向上动态规划，保存页子节点到当前节点的最大值。

#include <stdio.h>

int main(int argc, char **argv)
{
        int n, i, j, max;

        scanf("%d", &n);
        getchar();

        int a[n][n];
        for(i = 0; i < n; i++){
                for(j = 0; j <= i; j++){
                        scanf("%d", &a[i][j]);
                }
                getchar();
        }

        for(i = n-1; i >= 1; i--){
                for(j = 0; j < i; j++){
                        max = (a[i][j] > a[i][j+1]) ? a[i][j] : a[i][j+1];
                        a[i-1][j] += max;
                }
        }

        printf("%d\n", a[0][0]);

        return 0;
}