Overview

A problem to determine whether, when planting \(N\) flowers in a flower bed of width \(W\) with one flower at each end and equally spaced, the interval between adjacent flowers is at least \(K\) centimeters.

Analysis

In this problem, we are required to arrange the flowers at equal intervals. Furthermore, it is determined that flowers are planted at both ends (positions \(0\) and \(W\)). This means there are a total of \(N - 1\) gaps between flowers, and all of these gaps have the same length.

Therefore, the interval between adjacent flowers can be calculated as:

\[ \text{interval} = \frac{W}{N - 1} \]

If this value is at least \(K\), the condition for healthy growth is satisfied.

For example, when \(N = 3\), \(W = 10\), \(K = 4\):

• The interval is \(10 / (3 - 1) = 5\) centimeters
• This satisfies the required minimum interval \(K = 4\), so the answer is Yes

On the other hand, when \(N = 3\), \(W = 10\), \(K = 6\):

• The interval is \(5\) centimeters, but it does not satisfy the required minimum of \(6\), so the answer is No

Also, when \(N = 1\), there is only one flower and there is no need to consider intervals, so the condition is always satisfied.

Algorithm

1. Read \(N\), \(W\), \(K\) from input.
2. If \(N = 1\), output Yes and terminate.
3. Otherwise, compute the interval \(\text{interval} = \frac{W}{N - 1}\).
4. If \(\text{interval} \geq K\), output Yes; otherwise, output No.

Complexity

• Time complexity: \(O(1)\)
• Space complexity: \(O(1)\)

Implementation Notes

• Using floating-point numbers does not cause issues with comparisons (since the inputs are integers and the constraints are small).
• Be sure not to forget handling the case where \(N = 1\).

## Source Code

```python
N, W, K = map(int, input().split())

if N == 1:
    print("Yes")
else:
    interval = W / (N - 1)
    if interval >= K:
        print("Yes")
    else:
        print("No")

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