Find Closest Person

Find Closest Person - Problem

Math Easy

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

Input & Output

Example 1 — Person 2 Closer

$ Input: x = 1, y = 4, z = 3

› Output: 2

💡 Note: Distance from Person 1 to Person 3: |1-3| = 2. Distance from Person 2 to Person 3: |4-3| = 1. Person 2 is closer, so return 2.

Example 2 — Equal Distance

$ Input: x = 2, y = 6, z = 4

› Output: 0

💡 Note: Distance from Person 1 to Person 3: |2-4| = 2. Distance from Person 2 to Person 3: |6-4| = 2. Both distances are equal, so return 0.

Example 3 — Person 1 Closer

$ Input: x = 10, y = 2, z = 8

› Output: 1

💡 Note: Distance from Person 1 to Person 3: |10-8| = 2. Distance from Person 2 to Person 3: |2-8| = 6. Person 1 is closer, so return 1.

Constraints

-10⁹ ≤ x, y, z ≤ 10⁹
All positions can be anywhere on the number line

Visualization

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Asked in

G Google 15 M Microsoft 12

The key insight is that since both people move at the same speed, whoever has the shorter distance to Person 3 will arrive first. Best approach is calculating absolute distances: Time: O(1), Space: O(1)

Common Approaches

✓ Distance Calculation

⏱️ Time: O(1) Space: O(1)

Since both people move at the same speed, the person with the shorter distance to Person 3 will arrive first. We calculate the absolute distance from each person to Person 3 and compare them.

Mathematical Optimization

⏱️ Time: O(1) Space: O(1)

We can optimize by directly comparing the absolute differences without storing intermediate distance values, leveraging mathematical comparison properties.

Distance Calculation — Algorithm Steps

Step 1: Calculate distance from Person 1 to Person 3 using absolute value
Step 2: Calculate distance from Person 2 to Person 3 using absolute value
Step 3: Compare distances and return appropriate result

Visualization

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Step-by-Step Walkthrough

Calculate Distances

Find absolute distance from each person to Person 3

Compare

Determine which distance is smaller

Result

Return 1, 2, or 0 based on comparison

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>

int solution(int x, int y, int z) {
    int dist1 = abs(x - z);
    int dist2 = abs(y - z);
    
    if (dist1 < dist2) {
        return 1;
    } else if (dist2 < dist1) {
        return 2;
    } else {
        return 0;
    }
}

int main() {
    int x, y, z;
    scanf("%d", &x);
    scanf("%d", &y);
    scanf("%d", &z);
    
    int result = solution(x, y, z);
    printf("%d\n", result);
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Only performs constant time absolute value calculations and comparisons

✓ Linear Growth

Space Complexity

O(1)

Uses only a few variables to store distances

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Distance Calculation — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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