From 458df737512d64dbdd313498838e85ed1b16b9bd Mon Sep 17 00:00:00 2001
From: jwarren-aifi <112441624+jwarren-aifi@users.noreply.github.com>
Date: Mon, 16 Jan 2023 02:26:03 -0800
Subject: [PATCH] find min path

---
 graphs/minimum_effort_path.py | 34 +++++++++++++++++++++++++++++++++-
 1 file changed, 33 insertions(+), 1 deletion(-)

diff --git a/graphs/minimum_effort_path.py b/graphs/minimum_effort_path.py
index 74fe13b..a26c0cb 100644
--- a/graphs/minimum_effort_path.py
+++ b/graphs/minimum_effort_path.py
@@ -1,3 +1,5 @@
+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 +17,34 @@ 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
+
+    effort = [[float("inf") for _ in range(len(heights[0]))] for _ in range(len(heights))]
+
+    nrows = len(heights)
+    ncols = len(heights[0])
+
+    pq = []
+
+    effort[0][0] = 0
+    heapq.heappush(pq, (0, 0, 0))
+    directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]
+
+    while pq != []:
+        effort_till_now, row, col = heapq.heappop(pq)
+        for i in range(4):
+            new_row = row + directions[i][0]
+            new_col = col + directions[i][1]
+
+            if new_row >= 0 and new_row < nrows and new_col >= 0 and new_col < ncols:
+
+                diff = max(effort_till_now, abs(
+                    heights[new_row][new_col] - heights[row][col])) 
+
+                if diff < effort[new_row][new_col]:
+                    effort[new_row][new_col] = diff
+                    heapq.heappush(pq, (diff, new_row, new_col))
+
+    return (effort[nrows-1][ncols - 1])