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Largest Number in an Array

Problem Statement:​

Given an array arr[]. The task is to find the largest element and return it.

  • Example:

    Examples:

    Input: arr[] = [1, 8, 7, 56, 90]
    Output: 90
    Explanation: The largest element of the given array is 90.
    Input: arr[] = [5, 5, 5, 5]
    Output: 5
    Explanation: The largest element of the given array is 5.
    Input: arr[] = [10]
    Output: 10
    Explanation: There is only one element which is the largest.

✅ Solution 1: Brute Force​

int largest(vector<int> &arr) {
    int max_ele = INT_MIN;
    for (int i = 0; i < arr.size(); i++) {
        if (arr[i] > max_ele) {
            max_ele = arr[i];
        }
    }
    return max_ele;
}

✅ Solution 2: Sorting Approach​

int largest(vector<int> &arr) {
    sort(arr.begin(), arr.end());  // Sorts the array in increasing order
    return arr.back();             // Last element is the maximum
}

✅ Solution 3: Recursive Approach​

class Solution {
  public:
    int FindMax(vector<int> &arr, int i){
        if(i == arr.size() - 1) return arr[i];
        int max_ele = FindMax(arr, i + 1);
        return max(arr[i], max_ele);
    }

    int largest(vector<int> &arr) {
        return FindMax(arr, 0);
    }
};

📝 How It Works​

  • Brute Force: Linear scan to compare all elements and track the maximum so far.
  • Sorting: Sort the entire array and return the last element (maximum).
  • Recursion: Divide problem by computing max of rest of array and compare with current.

🧩 Key Formula​

  • Brute Force: max = max(arr[i], max)
  • Recursion: max(i) = max(arr[i], max(i+1))

⏱️ Time & Space Complexity​

ApproachTimeSpace
Brute Force ✅O(N)O(1)
SortingO(N log N)O(1) or O(N) (depending on sort)
RecursionO(N)O(N) — call stack

⚠️ Edge Cases​

  • Empty array → should return error/INT_MIN or handle explicitly.
  • All elements same → returns that element.
  • All negative numbers → works as usual.

💡 Other Approaches​

ApproachNotes
Divide and ConquerUseful for parallel processing
Segment TreeIf you need to do multiple range queries

🔁 Related Problems​

  • GFG: Largest element in array
  • LeetCode 162: Find Peak Element
  • GFG: Second largest element
  • Min/Max in recursive array calls

🛠️ Other Notes (Optional)​

  • ✅ Brute force is most optimal for one-time scan.
  • ⚠️ Avoid recursion for large inputs due to stack overflow risk.
  • ❌ Sorting is overkill just to find a single max value.
💬

Discussion & Doubts