1.5 numtri

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
/*ID: xdzhbin1LANG: C++TASK:numtri*///数字三角形#include <vector>#include <fstream>#include <iostream>#include <cmath>using namespace std;int main(){ifstream in("numtri.in",ios::in);ofstream out("numtri.out",ios::out);int n;in>>n;//读入行数typedef vector<int> array;//每一行定义为arrayvector<array> v;//共有n行v.resize(n);int i,j;for(i=0; i<n; i++)v[i].resize(i+1);//为每行申请存储空间for(i=0; i<n; i++)for(j=0; j<=i; j++)in>>v[i][j];//读入每行的数据for(i=n-2; i>=0; i--){for(j=0; j<v[i].size(); j++){v[i][j] += max(v[i+1][j],v[i+1][j+1]);}}out<<v[0][0]<<endl;return 0;}