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
/*
2
ID: 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
/*
2
ID: mercury23
PROG: numtri4
LANG: C++5
*/6
#include <iostream>7
8
using namespace std;9
10
const int Size = 1000;11
int n;12
int a[Size][Size];13
int f[Size][Size];14
15
void 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
24
void 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
33
void output()34
{35
freopen("numtri.out","w",stdout);36
cout << a[0][0] << endl;37
}38
39
int main()40
{41
input();42
cal();43
output();44
return 0;45
}46
