To solve the problem of determining the minimal number of jumps a frog needs to make from position X to reach or exceed position Y with each jump of distance D, we can break down the solution as follows:

Understanding the Problem:

• Inputs:

  • X: Starting position of the frog.
  • Y: Target position the frog wants to reach or exceed.
  • D: Fixed distance that the frog can jump in one move.

• Output:

  • Number of jumps required for the frog to reach or exceed Y starting from X.

If distance is exactly divisible by D (i.e., distance % D == 0), then the number of jumps required is:

If distance is not exactly divisible by D, then the frog needs one additional jump to cover the remaining distance:

Approach:

We determine how far the frog needs to jump to reach Y from X. This can be found using:

Then we calculate the number of jumps required to cover this distance:

Here, (leftlceil x rightrceil) denotes the ceiling function, which rounds up to the nearest integer.

Implementation in JavaScript:

Here’s how you can implement this in JavaScript:

function solution(X, Y, D) {
    const distance = Y - X;
    if (distance % D === 0) {
        return distance / D;
    } else {
        return Math.ceil(distance / D);
    }
}

We compute distance as Y - X.

Use modulo operation (%) to check if distance is exactly divisible by D.

If divisible, return distance / D.

If not divisible, use Math.ceil(distance / D) to round up to the nearest integer.

Example Usage

console.log(solution(10, 85, 30)); // Output: 3

• For X = 10, Y = 85, and D = 30, the frog needs 3 jumps:
  • 1st jump: 10 + 30 = 40
  • 2nd jump: 40 + 30 = 70
  • 3rd jump: 70 + 30 = 100 (exceeds 85, so it’s sufficient).

This solution efficiently computes the minimal number of jumps required using basic arithmetic operations, ensuring optimal performance even for large inputs within the specified constraints.