What is the time complexity of LeetCode 2912. Number of Ways to Reach Destination in the Grid?

The Python solution on this page runs in O(k), where k is the number of moves.

What is the space complexity of LeetCode 2912. Number of Ways to Reach Destination in the Grid?

The Python solution on this page uses O(1) auxiliary space.

Is LeetCode 2912. Number of Ways to Reach Destination in the Grid a premium problem?

Yes. LeetCode 2912. Number of Ways to Reach Destination in the Grid is a LeetCode Premium problem, so the full statement and test cases require a paid LeetCode subscription.

Number of Ways to Reach Destination in the Grid — LeetCode 2912 Python Solution

HardLeetCode PremiumMathDynamic ProgrammingCombinatorics

Problem: #2912
Pattern: Dynamic Programming
Reading time: 3 min
Source: leetcode.com

The problem

You are given two integers n and m which represent the size of a 1-indexed grid. You are also given an integer k, a 1-indexed integer array source and a 1-indexed integer array dest, where source and dest are in the form [x, y] representing a cell on the given grid.

Example

Input: n = 3, m = 2, k = 2, source = [1,1], dest = [2,2]
Output: 2
Explanation: There are 2 possible sequences of reaching [2,2] from [1,1]:

Python solution

Python

class Solution:
    def numberOfWays(
        self, n: int, m: int, k: int, source: List[int], dest: List[int]
    ) -> int:
        mod = 10**9 + 7
        a, b, c, d = 1, 0, 0, 0
        for _ in range(k):
            aa = ((n - 1) * b + (m - 1) * c) % mod
            bb = (a + (n - 2) * b + (m - 1) * d) % mod
            cc = (a + (m - 2) * c + (n - 1) * d) % mod
            dd = (b + c + (n - 2) * d + (m - 2) * d) % mod
            a, b, c, d = aa, bb, cc, dd
        if source[0] == dest[0]:
            return a if source[1] == dest[1] else c
        return b if source[1] == dest[1] else d

Complexity

Measure	Complexity
Time	O(k), where k is the number of moves
Space	O(1) auxiliary

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2912. Number of Ways to Reach Destination in the Grid is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 2912. Number of Ways to Reach Destination in the Grid?: LeetCode 2912. Number of Ways to Reach Destination in the Grid is rated Hard on LeetCode.
What is the time complexity of LeetCode 2912. Number of Ways to Reach Destination in the Grid?: The Python solution on this page runs in O(k), where k is the number of moves.
What is the space complexity of LeetCode 2912. Number of Ways to Reach Destination in the Grid?: The Python solution on this page uses O(1) auxiliary space.
What topics does LeetCode 2912. Number of Ways to Reach Destination in the Grid cover?: LeetCode 2912. Number of Ways to Reach Destination in the Grid is tagged Math, Dynamic Programming and Combinatorics on LeetCode.
Is LeetCode 2912. Number of Ways to Reach Destination in the Grid a premium problem?: Yes. LeetCode 2912. Number of Ways to Reach Destination in the Grid is a LeetCode Premium problem, so the full statement and test cases require a paid LeetCode subscription.