Implements solution

graphs/minimum_effort_path.py

@@ -1,8 +1,10 @@
+import heapq
+
 def min_effort_path(heights):
     """ Given a 2D array of heights, write a function to return
         the path with minimum effort.
 
-        A route's effort is the maximum absolute difference in heights 
+        A route's effort is the maximum absolute difference in heights
         between two consecutive cells of the route.
 
         Parameters
@@ -15,4 +17,32 @@ def min_effort_path(heights):
         int
             minimum effort required to navigate the path from (0, 0) to heights[rows - 1][columns - 1]
     """
-    pass
+    if not heights:
+        return 0
+
+    rows = len(heights)
+    columns = len(heights[0])
+
+    visited = [[False for _ in range(columns)] for _ in range(rows)]
+    effort = [[float('inf') for _ in range(columns)] for _ in range(rows)]
+
+    effort[0][0] = 0
+    heap = [(0, 0, 0)]
+
+    while heap:
+        curr_effort, row, col = heapq.heappop(heap)
+
+        if visited[row][col]:
+            continue
+
+        visited[row][col] = True
+
+        for r, c in [(row-1, col), (row+1, col), (row, col-1), (row, col+1)]:
+            if 0 <= r < rows and 0 <= c < columns:
+                new_effort = max(curr_effort, abs(heights[row][col] - heights[r][c]))
+
+                if new_effort < effort[r][c]:
+                    effort[r][c] = new_effort
+                    heapq.heappush(heap, (new_effort, r, c))
+
+    return effort[rows-1][columns-1]