人生中的第一个dp（poj 1163）

The Triangle

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

附上代码：

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
int max(int a,int b)
{
if(a<b)
{
return b;
}
return a;
}
int main()
{
int n,i,j;
int s[105][105];
int dp[105][105];
while(cin>>n)
{
for(i=1;i<=n;i++)
{
for(j=1;j<=i;j++)
{
cin>>s[i][j];
}
}
for(i=0;i<=n;i++)
{
for(j=0;j<=n;j++)
{
dp[i][j]=0;
}
}
int maxx=-1;
for(i=1;i<=n;i++)
{
for(j=1;j<=i;j++)
{
dp[i][j]=max(dp[i-1][j-1]+s[i][j],dp[i-1][j]+s[i][j]);//拿左上方与右上方做比较，看谁大
if(maxx<dp[i][j])
{
maxx=dp[i][j];
}
}
}
cout<<maxx<<endl;
}
return 0;
}