Find the maximum height of mud segment between walls

Author: absognety

SymphonyAI/maximumHeightOfMudSegment.py

@@ -0,0 +1,98 @@
+"""
+Problem Statement
+A child likes to build mud walls by placing mud between sticks positioned on 
+a number line. The gap between sticks will be referred to as a cell, and 
+each cell will contain one segment of wall. The height of mud in a segment 
+cannot exceed 1 unit above an adjacent stick or mud segment. Given the 
+placement of a number of sticks and their heights, determine the maximum 
+height segment of mud that can be built. If no mud segment can be built, 
+return 0.
+
+For example, there are n = 3 sticks at stickPositions = [1, 2, 4, 7] with s
+tickHeights = [4, 5, 7, 11]. There is no space between the first two sticks, 
+so there is no cell for mud. Between positions 2 and 4, there is one cell. 
+Heights of the surrounding sticks are 5 and 7, so the maximum height of mud 
+is 5 + 1 = 6. Between positions 4 and 7 there are two cells. The heights of 
+surrounding sticks are 7 and 11. The maximum height mud segment next to the 
+stick of height 7 is 8. The maximum height mud next to a mud segment of 
+height 8 and a stick of height 11 is 9. Mud segment heights are 6, 8 and 9, 
+and the maximum height is 9. In the table below, digits are in the columns 
+of sticks and M is in the mud segments.
+
+      7
+      7
+     M7
+    MM7
+   4MM7
+  M4MM7
+ 2M4MM7
+12M4MM7
+12M4MM7
+12M4MM7
+12M4MM7
+Function Description
+Complete the function maxHeight in the editor below. The function must 
+return an integer, the maximum height mud segment that can be built.
+
+maxHeight has the following parameter(s):
+stickPositions[stickPositions[0],…stickPositions[n-1]]: an array of integers
+stickHeights[stickHeights[0],…stickHeights[n-1]]: an array of integers
+
+Constraints
+1 ≤ n ≤ 105
+1 ≤ stickPositions[i] ≤ 109 (where 0 ≤ i < n)
+1 ≤ stickHeights[i] ≤ 109 (where 0 ≤ i < n)
+
+Sample Input For Custom Testing
+
+3
+1
+3
+7
+3
+4
+3
+3
+Sample Output
+
+5
+Explanation
+
+    M
+1M MMM
+1M3MMM7
+1M3MMM7
+1M3MMM7
+Here stickPositions = [1, 3, 7] and stickHeights = [4, 3, 3]. There can be a 
+segment of height 4 at position 2 supported by sticks of heights 4 and 3. 
+Between positions 3 and 7, there can be a segment of height 4 at positions 4 
+and 6. Between them, a segment can be built of height 5 at position 5.
+
+
+"""
+
+def maxHeight(wallPositions,wallHeights):
+    n = len(wallPositions)
+    maxim = 0
+    for i in range(n-1):
+        if wallPositions[i] < wallPositions[i+1]-1:
+            heightDiff = abs(wallHeights[i+1]-wallHeights[i])
+            gapLen = wallPositions[i+1]-wallPositions[i]-1
+            localMax = 0
+            if gapLen > heightDiff:
+                low = max(wallHeights[i+1],wallHeights[i]) + 1
+                remainingGap = gapLen - heightDiff - 1
+                localMax = low + remainingGap//2
+            else:
+                localMax = min(wallHeights[i+1],wallHeights[i]) + gapLen
+            maxim = max(maxim,localMax)
+    return maxim
+
+
+if __name__ == '__main__':
+    wallPositions = [1,2,4,7]
+    wallHeights = [4,6,8,11]
+    print (maxHeight(wallPositions=wallPositions,wallHeights=wallHeights))
+    wallPositions = [1,3,7]
+    wallHeights = [4,3,3]
+    print (maxHeight(wallPositions,wallHeights))