1691.py

Author: 224apps

1600-1700/1691.py

@@ -0,0 +1,50 @@
+'''
+Given n cuboids where the dimensions of the ith cuboid is cuboids[i] = [widthi, lengthi, heighti] (0-indexed). Choose a subset of cuboids and place them on each other.
+
+You can place cuboid i on cuboid j if widthi <= widthj and lengthi <= lengthj and heighti <= heightj. You can rearrange any cuboid's dimensions by rotating it to put it on another cuboid.
+
+Return the maximum height of the stacked cuboids.
+
+
+Example 1:
+Input: cuboids = [[50,45,20],[95,37,53],[45,23,12]]
+Output: 190
+Explanation:
+Cuboid 1 is placed on the bottom with the 53x37 side facing down with height 95.
+Cuboid 0 is placed next with the 45x20 side facing down with height 50.
+Cuboid 2 is placed next with the 23x12 side facing down with height 45.
+The total height is 95 + 50 + 45 = 190.
+Example 2:
+
+Input: cuboids = [[38,25,45],[76,35,3]]
+Output: 76
+Explanation:
+You can't place any of the cuboids on the other.
+We choose cuboid 1 and rotate it so that the 35x3 side is facing down and its height is 76.
+Example 3:
+
+Input: cuboids = [[7,11,17],[7,17,11],[11,7,17],[11,17,7],[17,7,11],[17,11,7]]
+Output: 102
+Explanation:
+After rearranging the cuboids, you can see that all cuboids have the same dimension.
+You can place the 11x7 side down on all cuboids so their heights are 17.
+The maximum height of stacked cuboids is 6 * 17 = 102.
+'''
+class Solution:
+    def maxHeight(self, cuboids: List[List[int]]) -> int:
+        N = len(cuboids)
+        
+        for c in cuboids:
+            c.sort()
+        cuboids.sort()
+        dp =[0] * N
+        
+        for i in range(N):
+            dp[i] = cuboids[i][2]
+            for j in range(i):
+                if cuboids[j][1] <= cuboids[i][1] and cuboids[j][2] <= cuboids[i][2]:
+                    dp[i] = max(dp[i], dp[j] + cuboids[i][2])
+        
+        return max(dp)
+                
+