From 4a57f7737f1595024adf810dab4f035a3c9f4e8f Mon Sep 17 00:00:00 2001
From: Amit Suthar <sutharamit707@gmail.com>
Date: Sat, 14 Oct 2023 20:50:38 +0530
Subject: [PATCH] Added a problem (#23)

---
 .../{ => Array}/01-arrays.md                  |  0
 .../Array/02-second-largest.md                | 88 +++++++++++++++++++
 2 files changed, 88 insertions(+)
 rename Data-Structures/Linear-Data-Structures/{ => Array}/01-arrays.md (100%)
 create mode 100644 Data-Structures/Linear-Data-Structures/Array/02-second-largest.md

diff --git a/Data-Structures/Linear-Data-Structures/01-arrays.md b/Data-Structures/Linear-Data-Structures/Array/01-arrays.md
similarity index 100%
rename from Data-Structures/Linear-Data-Structures/01-arrays.md
rename to Data-Structures/Linear-Data-Structures/Array/01-arrays.md
diff --git a/Data-Structures/Linear-Data-Structures/Array/02-second-largest.md b/Data-Structures/Linear-Data-Structures/Array/02-second-largest.md
new file mode 100644
index 0000000..fdb8e3a
--- /dev/null
+++ b/Data-Structures/Linear-Data-Structures/Array/02-second-largest.md
@@ -0,0 +1,88 @@
+## Find Second largest element in the array
+
+Approach :
+
+1. Brute : Sort --> Traverse from n - 2 --> if (a[i] != largest) ==> secondLargest == a[i]
+
+   Time Complexity : O(N Log N) + N ==> [Sort + Traversal]
+
+Code :
+
+```cpp
+int secondLargest(vector<int> &arr, int n){
+    int secondLargest = -1;
+    sort(arr.begin(), arr.end()); // O(N Log N)
+    for (int i = n - 2; i >= 0; i++) { // O(N)
+        if (arr[i] != largest) {
+            secondLargest = arr[i];
+        }
+    }
+    return secondLargest;
+}
+```
+
+2. Better : Traverse for Largest --> set SecondLargest = -1 --> Traverse again --> if (arr[i] > SecondLargest and arr[i] != largest) ==> secondLargest == a[i]
+
+   Time Complexity : O(2N) ==> [Two Traversals]
+
+Code :
+
+```cpp
+int secondLargest(vector<int> &arr, int n){
+    int largest = arr[0];
+    int secondLargest = -1;
+    for (int i = 0; i < n; i++){ // O(N)
+        if (arr[i] > largest){
+            largest = arr[i];
+        }
+    }
+    for (int i = 0; i < n; i++){ // O(N)
+        if (arr[i] > secondLargest && arr[i] != largest){
+            secondLargest = arr[i];
+        }
+    }
+    return secondLargest;
+}
+```
+
+3. Optimal : set FirstElement to Largest, set SecondLargest = -1 --> Traverse from 0 to n --> if found an a[i] > Largest ==> SecondLargest == Largest and Largest == arr[i] --> else if found an a[i] < largest but a[i] > SecondLargest ==> SecondLargest == a[i]
+
+   Time Complexity : O(N) ==> [Single Traversal]
+
+Code :
+
+```cpp
+int secondLargest(vector<int> &arr, int n){
+    int largest = arr[0];
+    int secondLargest = -1;
+    for (int i = 0; i < n; i++){ // O(N)
+        if (arr[i] > largest){
+            secondLargest = largest;
+            largest = arr[i];
+        } else if (arr[i] < largest && arr[i] > secondLargest){
+            secondLargest = arr[i];
+        }
+    }
+    return secondLargest;
+}
+```
+
+---
+
+### Bonus : Find Second Smallest
+
+```cpp
+int secondLargest(vector<int> &arr, int n){
+    int smallest = arr[0];
+    int secondSmallest = INT_MAX;
+    for (int i = 0; i < n; i++){
+        if (arr[i] < smallest){
+            secondSmallest = smallest;
+            smallest = arr[i];
+        } else if (arr[i] != smallest && arr[i] < secondSmallest){
+            secondSmallest = arr[i];
+        }
+    }
+    return secondSmallest;
+}
+```