Find Closest Person

EASY

Description

You are given three integers x, y, and z, representing the positions of three people on a number line:

x is the position of Person 1.
y is the position of Person 2.
z is the position of Person 3, who does not move.

Both Person 1 and Person 2 move toward Person 3 at the same speed.

Determine which person reaches Person 3 first:

Return 1 if Person 1 arrives first.
Return 2 if Person 2 arrives first.
Return 0 if both arrive at the same time.

Return the result accordingly.

Example 1:

Input: x = 2, y = 7, z = 4

Output: 1

Explanation:

Person 1 is at position 2 and can reach Person 3 (at position 4) in 2 steps.
Person 2 is at position 7 and can reach Person 3 in 3 steps.

Since Person 1 reaches Person 3 first, the output is 1.

Example 2:

Input: x = 2, y = 5, z = 6

Output: 2

Explanation:

Person 1 is at position 2 and can reach Person 3 (at position 6) in 4 steps.
Person 2 is at position 5 and can reach Person 3 in 1 step.

Since Person 2 reaches Person 3 first, the output is 2.

Example 3:

Input: x = 1, y = 5, z = 3

Output: 0

Explanation:

Person 1 is at position 1 and can reach Person 3 (at position 3) in 2 steps.
Person 2 is at position 5 and can reach Person 3 in 2 steps.

Since both Person 1 and Person 2 reach Person 3 at the same time, the output is 0.

Constraints:

1 <= x, y, z <= 100

Approaches

Checkout 2 different approaches to solve Find Closest Person. Click on different approaches to view the approach and algorithm in detail.

Simulation of Movement

This approach simulates the step-by-step movement of Person 1 and Person 2 towards Person 3. We use a loop that continues until one or both people reach Person 3's position. In each iteration of the loop, we update the positions of Person 1 and Person 2, moving them one unit closer to Person 3, and check if they have arrived.

Algorithm

Initialize a loop that runs indefinitely.
In each iteration, check if Person 1 (x) or Person 2 (y) has reached Person 3 (z).
If both have reached z in the same step, return 0.
If only Person 1 has reached z, return 1.
If only Person 2 has reached z, return 2.
If neither has reached, move both Person 1 and Person 2 one unit closer to z.
- If x < z, increment x. If x > z, decrement x.
- If y < z, increment y. If y > z, decrement y.
Repeat the process.

This method literally simulates the physical movement described in the problem. We treat each iteration of a loop as a single unit of time. In each time unit, both Person 1 and Person 2 move one step closer to Person 3. We continuously check their positions. The first person to have their position equal to z is the winner. If both positions become equal to z in the same time unit, it's a tie.

class Solution {
    public int findClosestPerson(int x, int y, int z) {
        while (true) {
            boolean person1Reached = (x == z);
            boolean person2Reached = (y == z);

            if (person1Reached && person2Reached) {
                return 0; // Both reached at the same time
            }
            if (person1Reached) {
                return 1; // Person 1 reached first
            }
            if (person2Reached) {
                return 2; // Person 2 reached first
            }

            // Move Person 1 one step closer to z
            if (x < z) {
                x++;
            } else if (x > z) {
                x--;
            }

            // Move Person 2 one step closer to z
            if (y < z) {
                y++;
            } else if (y > z) {
                y--;
            }
        }
    }
}

Complexity Analysis

Time Complexity: O(max(|x-z|, |y-z|)) - The loop runs for a number of iterations equal to the distance of the person who is farther away from `z`. For the given constraints, this is at most 99 iterations.Space Complexity: O(1) - We only use a few variables to store the positions, and the space required does not grow with the input values.

Pros and Cons

Pros:

It's a very literal interpretation of the problem statement.
Easy to conceptualize for beginners who think in terms of discrete time steps.

Cons:

Highly inefficient as it performs unnecessary step-by-step calculations.
The code is more complex and longer than necessary.
Scales poorly if the distances are very large.

Code Solutions

Checking out 3 solutions in different languages for Find Closest Person. Click on different languages to view the code.

class Solution {
public
  int findClosest(int x, int y, int z) {
    int a = Math.abs(x - z);
    int b = Math.abs(y - z);
    return a == b ? 0 : (a < b ? 1 : 2);
  }
}

Video Solution

Watch the video walkthrough for Find Closest Person

Patterns:

Math

Find Closest Person

Description

Approaches

Simulation of Movement

Algorithm

Complexity Analysis

Pros and Cons

Code Solutions

Video Solution

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