Number of Increasing Paths in a Grid
The problem can be solved using dynamic programming with memoization. We’ll break down the solution into simple steps:
 Define a recursive function to compute the number of strictly increasing paths from a given cell (x, y).
 In the recursive function, for every adjacent cell (i, j) of the current cell (x, y): a. If the value in the adjacent cell (i, j) is greater than the current cell (x, y), call the recursive function for the adjacent cell. b. Add the result to the current count of paths.
 Use memoization to store the results of subproblems and avoid redundant computations.
 Iterate through all cells and call the recursive function for each cell. Sum the results.
 Return the total number modulo (10^9 + 7).
Here’s the code:


This solution has time complexity (O(m \times n)) and space complexity (O(m \times n)), where (m) and (n) are the dimensions of the grid. It returns the total number of strictly increasing paths in the grid.
10 Prerequisite LeetCode Problems
“2328. Number of Increasing Paths in a Grid” involves dynamic programming and grid traversal. Here are 10 problems to prepare:
“62. Unique Paths”: This is a basic dynamic programming problem to understand grid traversal.
“64. Minimum Path Sum”: An introduction to dynamic programming with grids where you also have to keep track of a sum.
“63. Unique Paths II”: This extends the concept of grid traversal with dynamic programming to include obstacles.
“120. Triangle”: This problem introduces a variant of the grid traversal where the grid is not necessarily rectangular.
“221. Maximal Square”: This problem involves dynamic programming with a grid and understanding local and global optimality.
“931. Minimum Falling Path Sum”: This problem also includes the concept of path sum in a grid traversal.
“174. Dungeon Game”: This problem extends grid traversal to include negative values.
“96. Unique Binary Search Trees”: While not directly relevant, this problem involves dynamic programming and helps with understanding the concept of number of unique paths.
“1143. Longest Common Subsequence”: This problem introduces the concept of dynamic programming with two pointers, which could be useful in more complex grid traversal problems.
“198. House Robber”: This problem introduces the concept of keeping track of two states in dynamic programming, which could also be useful for grid problems.


Problem Classification
You are given an m x n integer matrix grid, where you can move from a cell to any adjacent cell in all 4 directions. Return the number of strictly increasing paths in the grid such that you can start from any cell and end at any cell. Since the answer may be very large, return it modulo 109 + 7. Two paths are considered different if they do not have exactly the same sequence of visited cells.
Example 1:
Input: grid = [[1,1],[3,4]] Output: 8 Explanation: The strictly increasing paths are:
 Paths with length 1: [1], [1], [3], [4].
 Paths with length 2: [1 > 3], [1 > 4], [3 > 4].
 Paths with length 3: [1 > 3 > 4]. The total number of paths is 4 + 3 + 1 = 8.
Example 2:
Input: grid = [[1],[2]] Output: 3 Explanation: The strictly increasing paths are:
 Paths with length 1: [1], [2].
 Paths with length 2: [1 > 2]. The total number of paths is 2 + 1 = 3.
Constraints:
m == grid.length n == grid[i].length 1 <= m, n <= 1000 1 <= m * n <= 105 1 <= grid[i][j] <= 105
Grid Traversal Pathfinder
Language Agnostic Coding Drills
This is a problem of finding all possible paths in a 2D grid using DepthFirst Search (DFS). Here’s a breakdown of the learning concepts involved:
Variable and List Initialization: Understand how to create and initialize variables and lists.
2D Lists (Matrices): Familiarize yourself with 2D lists (Matrices) operations such as creating a 2D list and accessing elements in it.
Iterating Over a List: Learn how to use loops to iterate over a list or 2D list.
Recursive Functions: Understand the concept of recursion and how to implement a recursive function.
DepthFirst Search (DFS) Algorithm: Learn about DFS as a method for traversing or searching tree or graph data structures.
Modulo Operation: Understand the use of the modulo operation to prevent integer overflow in your calculations.
2D Dynamic Programming: Get the grasp of using 2D dynamic programming to optimize the recursive calls and store intermediate results.
Directions Array for Grid Traversal: Understand the use of a directions array for grid traversal.
Conditional Statements: Learn how to use ifelse conditions to control the flow of the program.
Function Arguments: Understand how to pass arguments to a function, especially when passing a data structure like a list or a matrix.
Each of these concepts can be practiced and mastered individually, and once comfortable, they can be combined to understand and solve the overall problem.
Targeted Drills in Python
 Variable and List Initialization:


 2D Lists (Matrices):


 Iterating Over a List:


 Recursive Functions:


 DepthFirst Search (DFS) Algorithm:


 Modulo Operation:


 2D Dynamic Programming:


 Directions Array for Grid Traversal:


 Conditional Statements:


 Function Arguments:


Each of these drills can help you practice a specific concept in isolation. Once you are comfortable with each of them, you can start combining them.