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Data-Structures/Linear-Data-Structures/Array/02-second-largest.md
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## Find Second largest element in the array | ||
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Approach : | ||
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1. Brute : Sort --> Traverse from n - 2 --> if (a[i] != largest) ==> secondLargest == a[i] | ||
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Time Complexity : O(N Log N) + N ==> [Sort + Traversal] | ||
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Code : | ||
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```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; | ||
} | ||
``` | ||
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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] | ||
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Time Complexity : O(N) ==> [Single Traversal] | ||
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Code : | ||
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```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; | ||
} | ||
``` |