Uvod u dinamicko programiranje

Algoritam E: Pseudo kod problema maksimalnog zbira u matrici
Input: Matrica a celih brojeva dimenzije n × m
Output: path - niz elemenata matrice koji predstavlja traženi put
1 d[1][1] = a[1][1];
2 prior[1][1] = (0, 0);
3 for j ← 2 to m do
4 d[1][j] = d[1][j − 1] + a[1][j];
5 prior[1][j] = (1, j − 1);
6 end
7 for i ← 2 to n do
8 d[i][1] = d[i − 1][1] + a[i][1];
9 prior[i][1] = (i − 1, 1);
10 end
11 for i ← 2 to n do
12 for j ← 2 to m do
13 if d[i − 1][j] > d[i][j − 1] then
14
d[i][j] = d[i − 1][j] + a[i][j];
15
prior[i][j] = (i − 1, j);
16 else
17
d[i][j] = d[i][j − 1] + a[i][j];
18
prior[i][j] = (i, j − 1);
19 end
20 end
21 end
22 path = ∅;
23 currentF ield = (n, m);
24 while (currentF ield ≠ (0, 0)) do
25 add currentF ield in path;
26 currentF ield = prior[currentF ield.i][currentF ield.j];
27 end
28
return path;
Slika 3:
Primer problema maksimanog zbira u matrici
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