From a5bc083a6f7f37c3cb8e4b7b4c6a25927cc4d50c Mon Sep 17 00:00:00 2001
From: Jamie H <jamiewhorvath@gmail.com>
Date: Fri, 20 Jan 2023 23:42:35 -0500
Subject: [PATCH] finished

---
 graphs/minimum_effort_path.py | 35 ++++++++++++++++++++++++++++++++++-
 1 file changed, 34 insertions(+), 1 deletion(-)

diff --git a/graphs/minimum_effort_path.py b/graphs/minimum_effort_path.py
index 74fe13b..5e06285 100644
--- a/graphs/minimum_effort_path.py
+++ b/graphs/minimum_effort_path.py
@@ -1,3 +1,7 @@
+from collections import defaultdict
+import heapq
+
+
 def min_effort_path(heights):
     """ Given a 2D array of heights, write a function to return
         the path with minimum effort.
@@ -15,4 +19,33 @@ def min_effort_path(heights):
         int
             minimum effort required to navigate the path from (0, 0) to heights[rows - 1][columns - 1]
     """
-    pass
+    graph = defaultdict(list)
+    if not heights:
+        return 0
+    directions = [(0, 1), (1, 0), (-1, 0), (0, -1)]
+    rows = len(heights)
+    cols = len(heights[0])
+
+    for x in range(cols):
+        for y in range(rows):
+            for direction in directions:
+                newx, newy = x + direction[0], y + direction[1]
+                if newx >= 0 and newx < cols and newy >= 0 and newy < rows:
+                    abs_difference = abs(heights[y][x] - heights[newy][newx])
+                    graph[(y,x)].append(((newy, newx), abs_difference))
+    visited = set()
+    min_heap = []
+    start = (0,0)
+    end = (rows-1, cols-1)
+    min_heap.append((0, start))
+    max_abs = 0
+    while min_heap:
+        cost_till, curr, = heapq.heappop(min_heap)
+        visited.add(curr)
+        max_abs = max(max_abs, cost_till)
+        if curr == end:
+            return max_abs
+        for next, to_reach in graph[curr]:
+            if next not in visited:
+                heapq.heappush(min_heap, (to_reach, next))
+    return max_abs