The Triangle
题目描述:
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.
输入描述:
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.
输出描述:
Your program is to write to standard output. The highest sum is written as an integer.
样例输入:
复制
5 7 3 8 8 1 0 2 7 4 4 4 5 2 6 5
样例输出:
30
思路:
d[i][j]=max(d[i+1][j],d[i+1][j+1])+map[i][j];(核心)
d[i][j]
d[i+1][j] d[i+1][j+1]
如上d[i][j]的值就是,将它下面两个数中,大的那一个,再加上本身这一点的值map[i][j]
从第n行把状态一直更新到第一行,那d[1][1]就是我们所要求的值。
代码:
#include<stdio.h> #include<string.h> #include<algorithm> using namespace std; int map[105][105],d[105][105]; int main() { int n; while(~scanf("%d",&n)) { memset(map,0,sizeof(map)); memset(d,0,sizeof(d)); for(int i=1;i<=n;i++) for(int j=1;j<=i;j++) scanf("%d",&map[i][j]); for(int i=n;i>0;i--) for(int j=1;j<=i;j++) d[i][j]=max(d[i+1][j],d[i+1][j+1])+map[i][j]; printf("%d\n",d[1][1]); } return 0; }