The Triangle

最新推荐文章于 2020-05-03 16:51:48 发布

原创最新推荐文章于 2020-05-03 16:51:48 发布 · 371 阅读

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本文探讨了使用动态规划方法解决数列三角形中寻找最高和路径的问题，提供了完整的AC代码实现，适合初学者学习。

H - The Triangle

Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u

Submit Status

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

Sample Output

小结：

动态规划，还真的是我永远的痛....新手表示很头疼！！！

以下是AC代码：

#include<stdio.h>
#include<string.h>
#include<stdlib.h>
int map[200][200];
int dp[200][200];
int ans,n,fans;
int dir[2][2]={1,0,1,1};
int ok(int a,int b)
{
if(a<1||b<1||a>n||b>n||b>a)
return 0;
return 1;
}

int maxlen(int a,int b)
{
if(dp[a][b])
return dp[a][b];
int m=0;
for(int i=0;i<2;i++)
{
int aa=a+dir[i][0];
int bb=b+dir[i][1];
if(!ok(aa,bb))
continue;
m=maxlen(aa,bb)>m?maxlen(aa,bb):m;
}
dp[a][b]=m+map[a][b];
return dp[a][b];
}
int main()
{
while(~scanf("%d",&n))
{
ans=0;
memset(dp,0,sizeof(dp));
for(int i=1;i<=n;i++)
{
for(int j=1;j<=i;j++)
{
scanf("%d",&map[i][j]);
}
}
for(int i=1;i<=n;i++)
{
dp[n][i]=map[n][i];
}
ans=maxlen(1,1);
printf("%d\n",ans);
}
return 0;
}