Answer
See the explanation
Work Step by Step
To calculate the number of possible ways a person can run up the stairs, considering they can jump one, two, or three steps at a time, you can use dynamic programming. Here's a Python function to achieve this:
```python
def count_ways(n):
if n <= 0:
return 0
elif n == 1:
return 1
elif n == 2:
return 2
elif n == 3:
return 4
else:
ways = [0] * (n + 1)
ways[1] = 1
ways[2] = 2
ways[3] = 4
for i in range(4, n + 1):
ways[i] = ways[i - 1] + ways[i - 2] + ways[i - 3]
return ways[n]
# Example usage:
num_of_steps = 5
print("Number of ways to climb", num_of_steps, "steps:", count_ways(num_of_steps))
```
Explanation:
- The base cases handle scenarios where the number of steps is less than or equal to 3.
- For any number of steps greater than 3, the function iterates through each step, calculating the number of ways to reach that step by adding the ways to reach the previous three steps.
- Finally, the function returns the total number of ways to climb `n` steps.
