1.5.1 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.

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: makeeca1
PROG: numtri
LANG: PASCAL
}
program numtri;
var n,i,j,ans:longint;
    a,f:array[0..1100,0..1100]of longint;
function max(xx,yy:longint):longint;
begin if xx>yy then exit(xx)else exit(yy);end;
begin
  assign(input,'numtri.in');reset(input);
  assign(output,'numtri.out');rewrite(output);
  readln(n);
  for i:=1 to n do
  begin
    for j:=1 to i do read(a[i,j]);
    readln;
  end;
  ans:=0;
  f[1,1]:=a[1,1];
  for i:=2 to n do
    for j:=1 to n do
    begin
      f[i,j]:=max(f[i-1,j],f[i-1,j-1])+a[i,j];
      ans:=max(ans,f[i,j]);
    end;
  writeln(ans);
  close(input);close(output);
end.