From 38b1d86514d05868562900cde9547590c046839e Mon Sep 17 00:00:00 2001
From: Mikael CAPELLE <capelle.mikael@gmail.com>
Date: Mon, 12 Dec 2022 17:50:48 +0100
Subject: [PATCH] One to many Dijkstra.

---
 2022/day12.py | 74 ++++++++++++++++++---------------------------------
 1 file changed, 26 insertions(+), 48 deletions(-)

diff --git a/2022/day12.py b/2022/day12.py
index 814505b..28c54e4 100644
--- a/2022/day12.py
+++ b/2022/day12.py
@@ -9,36 +9,20 @@ Node = TypeVar("Node")
 
 def dijkstra(
     start: Node,
-    end: Node,
     neighbors: Callable[[Node], Iterator[Node]],
     cost: Callable[[Node, Node], float],
-    heuristic: Callable[[Node, Node], float] | None = None,
-) -> list[Node] | None:
+) -> tuple[dict[Node, float], dict[Node, Node]]:
 
-    queue: list[tuple[tuple[float, float, float], Node]] = []
+    queue: list[tuple[float, Node]] = []
 
     visited: set[Node] = set()
     lengths: dict[Node, float] = {start: 0}
     parents: dict[Node, Node] = {}
 
-    if heuristic is None:
+    heapq.heappush(queue, (0, start))
 
-        def priority(node: Node):
-            c = lengths[node]
-            return (c, c, c)
-
-    else:
-
-        def priority(node: Node):
-            assert heuristic is not None
-            h = heuristic(node, end)
-            c = lengths[node]
-            return (h + c, h, c)
-
-    heapq.heappush(queue, (priority(start), start))
-
-    while queue and (end not in visited):
-        (_, _, length), current = heapq.heappop(queue)
+    while queue:
+        length, current = heapq.heappop(queue)
 
         if current in visited:
             continue
@@ -53,12 +37,17 @@ def dijkstra(
             neighbor_cost = length + cost(current, neighbor)
 
             if neighbor_cost < lengths.get(neighbor, float("inf")):
-                lengths[neighbor] = length + 1
+                lengths[neighbor] = neighbor_cost
                 parents[neighbor] = current
 
-                heapq.heappush(queue, (priority(neighbor), neighbor))
+                heapq.heappush(queue, (neighbor_cost, neighbor))
 
-    if end not in visited:
+    return lengths, parents
+
+
+def make_path(parents: dict[Node, Node], start: Node, end: Node) -> list[Node] | None:
+
+    if end not in parents:
         return None
 
     path: list[Node] = [end]
@@ -125,7 +114,7 @@ def heuristic(lhs: tuple[int, int], rhs: tuple[int, int]) -> float:
     return abs(lhs[0] - rhs[0]) + abs(lhs[1] - rhs[1])
 
 
-def neighbors(node: tuple[int, int]) -> Iterator[tuple[int, int]]:
+def neighbors(node: tuple[int, int], up: bool) -> Iterator[tuple[int, int]]:
     c_row, c_col = node
     for n_row, n_col in (
         (c_row - 1, c_col),
@@ -137,38 +126,27 @@ def neighbors(node: tuple[int, int]) -> Iterator[tuple[int, int]]:
         if not (n_row >= 0 and n_row < n_rows and n_col >= 0 and n_col < n_cols):
             continue
 
-        if grid[n_row][n_col] > grid[c_row][c_col] + 1:
+        if up and grid[n_row][n_col] > grid[c_row][c_col] + 1:
+            continue
+        elif not up and grid[n_row][n_col] < grid[c_row][c_col] - 1:
             continue
 
         yield n_row, n_col
 
 
-path = dijkstra(
-    start=start,
-    end=end,
-    neighbors=neighbors,
-    cost=lambda lhs, rhs: 1,
-    heuristic=heuristic,
+lengths_1, parents_1 = dijkstra(
+    start=start, neighbors=lambda n: neighbors(n, True), cost=lambda lhs, rhs: 1
 )
-assert path is not None
+path_1 = make_path(parents_1, start, end)
+assert path_1 is not None
 
-print_path(path, n_rows=len(grid), n_cols=len(grid[0]))
+print_path(path_1, n_rows=len(grid), n_cols=len(grid[0]))
 
-answer_1 = len(path) - 1
+answer_1 = lengths_1[end] - 1
 print(f"answer 1 is {answer_1}")
 
-answer_2 = min(
-    len(path) - 1
-    for start in start_s
-    if (
-        path := dijkstra(
-            start=start,
-            end=end,
-            neighbors=neighbors,
-            cost=lambda lhs, rhs: 1,
-            heuristic=heuristic,
-        )
-    )
-    is not None
+lengths_2, parents_2 = dijkstra(
+    start=end, neighbors=lambda n: neighbors(n, False), cost=lambda lhs, rhs: 1
 )
+answer_2 = min(lengths_2.get(start, float("inf")) for start in start_s)
 print(f"answer 2 is {answer_2}")