dp

Author: Prakash-sa

Dynamic Programming/DP_ENHANCED.md

@@ -169,6 +169,10 @@ def tsp_held_karp(dist):
 
 ### 4. Profile/Broken Profile DP
 
+**Grid Direction Heuristic:**
+- If movement is effectively one-way along dependencies, such as only right/down or only left/up, it is usually a DP problem.
+- If movement is allowed in both directions across those dependencies, such as both right/down and left/up, prefer BFS/graph traversal.
+
 ```python
 def tile_grid_broken_profile(width, height):
     """

Prefix Sum & Partial Sum/Prefix Sum/1622. Fancy Sequence.py

@@ -0,0 +1,45 @@
+# https://leetcode.com/problems/fancy-sequence/description/
+
+'''
+Write an API that generates fancy sequences using the append, addAll, and multAll operations.
+
+Implement the Fancy class:
+
+Fancy() Initializes the object with an empty sequence.
+void append(val) Appends an integer val to the end of the sequence.
+void addAll(inc) Increments all existing values in the sequence by an integer inc.
+void multAll(m) Multiplies all existing values in the sequence by an integer m.
+int getIndex(idx) Gets the current value at index idx (0-indexed) of the sequence modulo 109 + 7. If the index is greater or equal than the length of the sequence, return -1.
+ 
+
+Example 1:
+
+Input
+["Fancy", "append", "addAll", "append", "multAll", "getIndex", "addAll", "append", "multAll", "getIndex", "getIndex", "getIndex"]
+[[], [2], [3], [7], [2], [0], [3], [10], [2], [0], [1], [2]]
+Output
+[null, null, null, null, null, 10, null, null, null, 26, 34, 20]
+
+Explanation
+Fancy fancy = new Fancy();
+fancy.append(2);   // fancy sequence: [2]
+fancy.addAll(3);   // fancy sequence: [2+3] -> [5]
+fancy.append(7);   // fancy sequence: [5, 7]
+fancy.multAll(2);  // fancy sequence: [5*2, 7*2] -> [10, 14]
+fancy.getIndex(0); // return 10
+fancy.addAll(3);   // fancy sequence: [10+3, 14+3] -> [13, 17]
+fancy.append(10);  // fancy sequence: [13, 17, 10]
+fancy.multAll(2);  // fancy sequence: [13*2, 17*2, 10*2] -> [26, 34, 20]
+fancy.getIndex(0); // return 26
+fancy.getIndex(1); // return 34
+fancy.getIndex(2); // return 20
+ 
+
+Constraints:
+
+1 <= val, inc, m <= 100
+0 <= idx <= 105
+At most 105 calls total will be made to append, addAll, multAll, and getIndex.
+'''
+
+

docs/content/Dynamic Programming/DP_ENHANCED.md

@@ -169,6 +169,10 @@ def tsp_held_karp(dist):
 
 ### 4. Profile/Broken Profile DP
 
+**Grid Direction Heuristic:**
+- If movement is effectively one-way along dependencies, such as only right/down or only left/up, it is usually a DP problem.
+- If movement is allowed in both directions across those dependencies, such as both right/down and left/up, prefer BFS/graph traversal.
+
 ```python
 def tile_grid_broken_profile(width, height):
     """