POJ 1163 The Triangle

[align=center]The Triangle[/align]

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 48243		Accepted: 29173

Description

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.

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
IOI 1994

---------------------------------华丽的分割线-------------------------------

解题思路：

题目是求这个数字三角形从上到下（或者相反）的一条路径的最大和。

状态转移方程：

DP[I][J]=MAX(DP[I+1][J],DP[I+1][J+1])+POINT[I][J].

Code:

#include<stdio.h>
#include<cstring>
int tri[102][102];
int dp[102][102];
int i,j,k,n,m,p,t;
int main()
{
memset(tri,0,sizeof(tri));
memset(dp,0,sizeof(dp));

scanf("%d",&n);

for(i=1;i<=n;i++)
for(j=1;j<=i;j++)
scanf("%d",&(tri[i][j]));
for(i=n;i>=1;i--)
for(j=n-(n-i);j>=1;j--)
dp[i][j]=dp[i+1][j]>dp[i+1][j+1]?dp[i+1][j]+tri[i][j]:dp[i+1][j+1]+tri[i][j];
printf("%d\n",dp[1][1]);
return 0;
}