StaffDynamic Programming
Number of Ways to Stay in the Same Place After Some Steps
You have a pointer at index 0 in an array of size arrLen. At each step, you can move 1 position to the left, 1 position to the right in the array, or stay in the same place. The pointer should not be placed outside the array at any time.
Given two integers steps and arrLen, return the number of ways such that your pointer is still at index 0 after exactly steps steps. Since the answer may be too large, return it modulo 10^9 + 7.
Example 1
Input
steps = 3, arrLen = 2Output
4There are 4 different ways to stay at index 0 after 3 steps: Right then Left then Stay, Stay then Right then Left, Right then Stay then Left, and Stay then Stay then Stay.
Example 2
Input
steps = 2, arrLen = 4Output
2There are 2 different ways to stay at index 0 after 2 steps: Right then Left, and Stay then Stay.
Constraints
- 1 <= steps <= 500
- 1 <= arrLen <= 10^6