Description
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
(Figure 1)
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
大意
数字三角形问题，给出一个数字三角形，求从顶点开始，到达最下面一行的最大路径（每次只能向下方或向右下方走）。
题解
DP中最简单的一道问题，每次因为只有两种决策（往下方走或者往右下方走），所以状态转移方程很容易可以得出：f[i][j]=max(f[i-1][j]+a[i][j]（下方）,f[i-1][j-1]+a[i][j]（右下方）)，时间复杂度为O(n^2)。
1 #include <cstdio> 2 #include <algorithm> 3 #include <cstring> 4 #include <iostream> 5 using namespace std; 6 int n,a[205][205],f[205][205],maxn; 7 int main() 8 { 9 scanf("%d",&n); 10 for(int i=1;i<=n;i++) 11 for(int j=1;j<=i;j++) 12 scanf("%d",&a[i][j]); 13 for(int i=1;i<=n;i++) 14 for(int j=1;j<=i;j++) 15 f[i][j]=max(f[i-1][j]+a[i][j],f[i-1][j-1]+a[i][j]); 16 for(int i=1;i<=n;i++) 17 maxn=max(f[n][i],maxn); 18 printf("%d",maxn); 19 }
