Find Minimum and Maximum in an Array

My Thought Process (Java DSA)

When I saw this problem on GeeksforGeeks, it looked very straightforward. But instead of rushing into coding, I tried to think about the most efficient way to solve it.

---

Problem Statement

We are given an array of integers arr[].
The task is to find the minimum and maximum elements in the array.

---

Initial Thinking

Let’s take an example:

arr = [1, 4, 3, 5, 8, 6]

From this:

• Minimum = 1
• Maximum = 8

At first, one idea was to sort the array and pick the first and last elements.
But sorting takes extra time, which is unnecessary for this problem.

---

Key Observation

We don’t need to rearrange the array.
We just need to scan through it once and keep track of:

• The smallest value seen so far
• The largest value seen so far

---

my Way Approach

1. Assume the first element is both min and max
2. Traverse the array from index 1
3. For every element:

• If it is smaller than min, update min
• If it is larger than max, update max

---

how it Runs

arr = [12, 3, 15, 7, 9]

Start:
min = 12, max = 12

i = 1 → 3 → min = 3  
i = 2 → 15 → max = 15  
i = 3 → 7 → no change  
i = 4 → 9 → no change  

Final Output → [3, 15]

---

Code in (Java)

import java.util.*;

class Solution {
    public ArrayList<Integer> getMinMax(int[] arr) {

        int min = arr[0];
        int max = arr[0];

        for (int i = 1; i < arr.length; i++) {

            if (arr[i] < min) {
                min = arr[i];
            }

            if (arr[i] > max) {
                max = arr[i];
            }
        }

        ArrayList<Integer> result = new ArrayList<>();
        result.add(min);
        result.add(max);

        return result;
    }
}

---

why This Works

• We are checking each element exactly once
• We continuously update min and max
• No unnecessary operations like sorting

---

Complexity Analysis

• Time Complexity: O(n)
• Space Complexity: O(1)

This is optimal because:

• Only one traversal is used
• No extra memory is required

---

Final Thought

This problem is a basic example of array traversal with tracking variables.
It teaches an important lesson:

Instead of doing extra work like sorting, always think if a single pass solution is possible.

---