Dynamic program example

.gitignore

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+.idea
+.venv

Uebung-01/perseverance.py

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+data = [
+    [0, 9, 2, 5, 11, 8],
+    [17, 21, 32, 5, 15, 3],
+    [2, 2, 3, 8, 1, 5],
+    [8, 2, 8, 11, 15, 9],
+    [0, 5, 3, 10, 4, 0]
+]
+
+max_y = len(data)
+max_x = len(data[0])
+start = (max_y-1, max_x-1)
+
+# Cache with size of n points
+cache = [[None for _ in range(max_x)] for _ in range(max_y)]
+
+def find_path(y, x):
+    if not (0 <= y < max_y and 0 <= x < max_x):
+        return (), float('-inf')
+
+    if cache[y][x] is not None:
+        return cache[y][x]
+
+    if y == 0 and x == 0:
+        res = (((y, x),), data[y][x])
+    else:
+        west_path, west_val = find_path(y, x-1)
+        north_path, north_val = find_path(y-1, x)
+
+        if west_val > north_val:
+            res = (west_path + ((y, x),), west_val + data[y][x])
+        else:
+            res = (north_path + ((y, x),), north_val + data[y][x])
+
+    cache[y][x] = res
+    return res
+
+path, val = find_path(*start)
+print(f"Val: {val}")
+print(f"Path: {path}")