1.5.1 Number Triangles(dp)

最新推荐文章于 2018-09-15 13:55:31 发布

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最新推荐文章于 2018-09-15 13:55:31 发布

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原文链接：http://www.cnblogs.com/shenyw/p/5160322.html

本文介绍了一个通过编程解决寻找从顶点到底边的最大路径和的问题。该路径只能沿着三角形的斜边向下移动。文章提供了完整的C++代码实现，并通过样例说明了如何计算给定三角形的最大路径和。

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.

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)

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)

代码：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 using namespace std;
 5 int m[1005][1005];
 6 int main()
 7 {
 8     freopen("numtri.in","r",stdin);
 9     freopen("numtri.out","w",stdout);
10     int r;
11     cin>>r;
12     for(int i=1;i<=r;i++){
13         for(int j=1;j<=i;j++){
14             cin>>m[i][j];
15         }
16     }
17     for(int i=1;i<=r;i++){
18         for(int j=1;j<=i;j++){
19             if(j==1) m[i][j]+=m[i-1][j];
20             else if(j==i) m[i][j]+=m[i-1][j-1];
21             else m[i][j]+=max(m[i-1][j-1],m[i-1][j]);
22         }
23     }
24     int maxn=0;
25     for(int i=1;i<=r;i++){
26         if(maxn<m[r][i]) maxn=m[r][i]; 
27     }
28     cout<<maxn<<endl;
29     return 0;
30 }