USACO Section 1.5 Number Triangles (dp)
Number Triangles
Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be 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.
7 3 8 8 1 0 2 7 4 4 4 5 2 6 5
In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.
PROGRAM NAME: numtri
INPUT FORMAT
The first line contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. All the supplied integers are non-negative and no larger than 100.
SAMPLE INPUT (file numtri.in)
5 7 3 8 8 1 0 2 7 4 4 4 5 2 6 5
OUTPUT FORMAT
A single line containing the largest sum using the traversal specified.
SAMPLE OUTPUT (file numtri.out)
30
分析:经典dp ,唯一要注意是单个案例输入会超时,可能原因是每次打开文件也要时间。
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
1 /* 2 ID: dizzy_l1 3 LANG: C++ 4 TASK: numtri 5 */ 6 #include<iostream> 7 #include<cstring> 8 #include<cstdio> 9 #define MAXN 1010 10 11 using namespace std; 12 13 int map[MAXN][MAXN],d[MAXN][MAXN]; 14 15 int main() 16 { 17 freopen("numtri.in","r",stdin); 18 freopen("numtri.out","w",stdout); 19 int n,i,j; 20 while(scanf("%d",&n)==1) 21 { 22 for(i=1; i<=n; i++) 23 for(j=1; j<=i; j++) 24 scanf("%d",&map[i][j]); 25 memset(d,0,sizeof(d)); 26 for(i=n; i>=1; i--) 27 for(j=1; j<=i; j++) 28 d[i][j]=map[i][j]+max(d[i+1][j],d[i+1][j+1]); 29 printf("%d\n",d[1][1]); 30 } 31 return 0; 32 }