Overview

We compare the total number of leaves falling in the garden with the maximum number of leaves that can be cleaned in \(D\) days to determine whether all leaves can be cleaned.

Analysis

There are \(A\) trees, and \(B\) leaves fall from each tree, so the total number of fallen leaves is \(A \times B\).

On the other hand, at most \(C\) leaves can be cleaned per day, so at most \(C \times D\) leaves can be cleaned over \(D\) days. Therefore, the condition to clean all the leaves is

\(A \times B \leq C \times D\)

For example, when \(A=3,\ B=4,\ C=5,\ D=3\), there are \(12\) fallen leaves and at most \(15\) leaves can be cleaned, so the answer is Yes.

Simulating the process day by day by decreasing the remaining fallen leaves would also easily run within the time limit under these constraints. However, by comparing the products, no loops are necessary.

Also, if you calculate the required number of days using integer division as \(A \times B \div C\), the fractional part may be truncated, which can lead to an incorrect answer. For instance, if there are \(12\) fallen leaves and \(5\) leaves can be cleaned per day, the required number of days is \(3\), not \(2\). Comparing the products allows you to determine the answer without worrying about such rounding issues.

Algorithm

1. Read \(A, B, C, D\).
2. Calculate the total number of fallen leaves \(A \times B\) and the maximum number of leaves that can be cleaned \(C \times D\).
3. If \(A \times B \leq C \times D\), output Yes; otherwise, output No.

Complexity

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

Implementation Notes

• If the total number of fallen leaves is equal to the maximum number of leaves that can be cleaned, all leaves can still be cleaned. Use <= rather than < for the comparison.

• The output is case-sensitive, so make sure to print Yes or No exactly as specified.

  Source Code

import sys

def main():
    A, B, C, D = map(int, sys.stdin.readline().split())
    print("Yes" if A * B <= C * D else "No")

main()

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This editorial was generated by gpt-6-astra-medium.