NYOJ - The Triangle

描述

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.

输入

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.

输出

Your program is to write to standard output. The highest sum is written as an integer.

样例输入

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

样例输出

30

一道经典的动态规划问题【外号：我的第一道动态规划！】

#include <cstdio>

int a[105][105];
int b[105][105];
int maxn(int a, int b)
{
    return a > b ? a : b;
}

int main()
{
    int n;
    while (scanf("%d", &n) != EOF)
    {
        for (int i = 1; i <= n; ++i)
        {
            for (int j = 1; j <= i; ++j)
            {
                scanf("%d", &a[i][j]);
            }
        }
        int ans;
        for (int i = 1; i <= n; ++i)
            b[n][i] = a[n][i];
        for (int i = n-1; i > 0; --i)
        {
            for (int j = 1; j <= i; ++j)
            {
                b[i][j] = maxn(b[i+1][j], b[i+1][j+1]) + a[i][j];
            }
        }
        ans = b[1][1];
        printf("%d\n", ans);
    }
    return 0;
}