Section 1.5 Number Triangles

 

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.

 1/**//*
 2ID: mercury2
 3PROG: numtri
 4LANG: C++
 5*/
 6#include <iostream>
 7
 8using namespace std;
 9
10const int Size = 1000;
11int n;
12int a[Size][Size];
13int f[Size][Size];
14
15void input()
16{
17     freopen("numtri.in","r",stdin);
18     cin >> n;
19     for( int i = 0; i < n; i++ )
20          for( int j = 0; j < i+1; j++ )
21          cin >> a[i][j];
22}
23
24void cal()
25{
26     for( int i = n - 1; i > 0; i-- )
27     {
28          for( int j = 0; j < i; j++ )
29          a[i-1][j] = max( a[i][j],a[i][j+1] ) + a[i-1][j];
30     }
31}
32
33void output()
34{
35     freopen("numtri.out","w",stdout);
36     cout << a[0][0] << endl;
37}
38
39int main()
40{
41    input();
42    cal();
43    output();
44    return 0;
45}
46