# Third largest element in an array of distinct elements

Given an array of n integers, find the third largest element. All the elements in the array are distinct integers. **Example :**

Input:arr[] = {1, 14, 2, 16, 10, 20}Output:The third Largest element is 14Explanation:Largest element is 20, second largest element is 16 and third largest element is 14Input:arr[] = {19, -10, 20, 14, 2, 16, 10}Output:The third Largest element is 16Explanation:Largest element is 20, second largest element is 19 and third largest element is 16

** Naive Approach:** The task is to first find the largest element, followed by the second-largest element and then excluding them both find the third-largest element. The basic idea is to iterate the array twice and mark the maximum and second maximum element and then excluding them both find the third maximum element, i.e the maximum element excluding the maximum and second maximum.

**Algorithm:**- First, iterate through the array and find maximum.
- Store this as first maximum along with its index.
- Now traverse the whole array finding the second max, excluding the maximum element.
- Finally traverse the array the third time and find the third largest element i.e., excluding the maximum and second maximum.

## C++

`// C++ program to find third Largest` `// element in an array of distinct elements` `#include <bits/stdc++.h>` `void` `thirdLargest(` `int` `arr[], ` `int` `arr_size)` `{` ` ` `/* There should be atleast three elements */` ` ` `if` `(arr_size < 3)` ` ` `{` ` ` `printf` `(` `" Invalid Input "` `);` ` ` `return` `;` ` ` `}` ` ` `// Find first largest element` ` ` `int` `first = arr[0];` ` ` `for` `(` `int` `i = 1; i < arr_size ; i++)` ` ` `if` `(arr[i] > first)` ` ` `first = arr[i];` ` ` `// Find second largest element` ` ` `int` `second = INT_MIN;` ` ` `for` `(` `int` `i = 0; i < arr_size ; i++)` ` ` `if` `(arr[i] > second && arr[i] < first)` ` ` `second = arr[i];` ` ` `// Find third largest element` ` ` `int` `third = INT_MIN;` ` ` `for` `(` `int` `i = 0; i < arr_size ; i++)` ` ` `if` `(arr[i] > third && arr[i] < second)` ` ` `third = arr[i];` ` ` `printf` `(` `"The third Largest element is %d\n"` `, third);` `}` `/* Driver program to test above function */` `int` `main()` `{` ` ` `int` `arr[] = {12, 13, 1, 10, 34, 16};` ` ` `int` `n = ` `sizeof` `(arr)/` `sizeof` `(arr[0]);` ` ` `thirdLargest(arr, n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find third` `// Largest element in an array` `// of distinct elements` `class` `GFG` `{` `static` `void` `thirdLargest(` `int` `arr[],` ` ` `int` `arr_size)` `{` ` ` `/* There should be` ` ` `atleast three elements */` ` ` `if` `(arr_size < ` `3` `)` ` ` `{` ` ` `System.out.printf(` `" Invalid Input "` `);` ` ` `return` `;` ` ` `}` ` ` `// Find first` ` ` `// largest element` ` ` `int` `first = arr[` `0` `];` ` ` `for` `(` `int` `i = ` `1` `;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > first)` ` ` `first = arr[i];` ` ` `// Find second` ` ` `// largest element` ` ` `int` `second = Integer.MIN_VALUE;` ` ` `for` `(` `int` `i = ` `0` `;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > second &&` ` ` `arr[i] < first)` ` ` `second = arr[i];` ` ` `// Find third` ` ` `// largest element` ` ` `int` `third = Integer.MIN_VALUE;` ` ` `for` `(` `int` `i = ` `0` `;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > third &&` ` ` `arr[i] < second)` ` ` `third = arr[i];` ` ` `System.out.printf(` `"The third Largest "` `+` ` ` `"element is %d\n"` `, third);` `}` `// Driver code` `public` `static` `void` `main(String []args)` `{` ` ` `int` `arr[] = {` `12` `, ` `13` `, ` `1` `,` ` ` `10` `, ` `34` `, ` `16` `};` ` ` `int` `n = arr.length;` ` ` `thirdLargest(arr, n);` `}` `}` `// This code is contributed` `// by Smitha` |

## Python3

`# Python 3 program to find` `# third Largest element in` `# an array of distinct elements` `import` `sys` `def` `thirdLargest(arr, arr_size):` ` ` `# There should be` ` ` `# atleast three elements` ` ` `if` `(arr_size < ` `3` `):` ` ` ` ` `print` `(` `" Invalid Input "` `)` ` ` `return` ` ` ` ` `# Find first` ` ` `# largest element` ` ` `first ` `=` `arr[` `0` `]` ` ` `for` `i ` `in` `range` `(` `1` `, arr_size):` ` ` `if` `(arr[i] > first):` ` ` `first ` `=` `arr[i]` ` ` `# Find second` ` ` `# largest element` ` ` `second ` `=` `-` `sys.maxsize` ` ` `for` `i ` `in` `range` `(` `0` `, arr_size):` ` ` `if` `(arr[i] > second ` `and` ` ` `arr[i] < first):` ` ` `second ` `=` `arr[i]` ` ` `# Find third` ` ` `# largest element` ` ` `third ` `=` `-` `sys.maxsize` ` ` `for` `i ` `in` `range` `(` `0` `, arr_size):` ` ` `if` `(arr[i] > third ` `and` ` ` `arr[i] < second):` ` ` `third ` `=` `arr[i]` ` ` `print` `(` `"The Third Largest"` `,` ` ` `"element is"` `, third)` `# Driver Code` `arr ` `=` `[` `12` `, ` `13` `, ` `1` `,` ` ` `10` `, ` `34` `, ` `16` `]` `n ` `=` `len` `(arr)` `thirdLargest(arr, n)` `# This code is contributed` `# by Smitha` |

## C#

`// C# program to find third` `// Largest element in an array` `// of distinct elements` `using` `System;` `class` `GFG` `{` `static` `void` `thirdLargest(` `int` `[]arr,` ` ` `int` `arr_size)` `{` ` ` `/* There should be` ` ` `atleast three elements */` ` ` `if` `(arr_size < 3)` ` ` `{` ` ` `Console.Write(` `" Invalid Input "` `);` ` ` `return` `;` ` ` `}` ` ` `// Find first` ` ` `// largest element` ` ` `int` `first = arr[0];` ` ` `for` `(` `int` `i = 1;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > first)` ` ` `first = arr[i];` ` ` `// Find second` ` ` `// largest element` ` ` `int` `second = -` `int` `.MaxValue;` ` ` `for` `(` `int` `i = 0;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > second &&` ` ` `arr[i] < first)` ` ` `second = arr[i];` ` ` `// Find third` ` ` `// largest element` ` ` `int` `third = -` `int` `.MaxValue;` ` ` `for` `(` `int` `i = 0;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > third &&` ` ` `arr[i] < second)` ` ` `third = arr[i];` ` ` `Console.Write(` `"The third Largest "` `+` ` ` `"element is "` `+ third);` `}` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `[]arr = {12, 13, 1, ` ` ` `10, 34, 16};` ` ` `int` `n = arr.Length;` ` ` `thirdLargest(arr, n);` `}` `}` `// This code is contributed by Smitha` |

## PHP

`<?php` `// PHP program to find third` `// Largest element in an array` `// of distinct elements` `function` `thirdLargest(` `$arr` `, ` `$arr_size` `)` `{` ` ` `/* There should be atleast` ` ` `three elements */` ` ` `if` `(` `$arr_size` `< 3)` ` ` `{` ` ` `echo` `" Invalid Input "` `;` ` ` `return` `;` ` ` `}` ` ` `// Find first largest element` ` ` `$first` `= ` `$arr` `[0];` ` ` `for` `(` `$i` `= 1; ` `$i` `< ` `$arr_size` `; ` `$i` `++)` ` ` `if` `(` `$arr` `[` `$i` `] > ` `$first` `)` ` ` `$first` `= ` `$arr` `[` `$i` `];` ` ` `// Find second largest element` ` ` `$second` `= PHP_INT_MIN;` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$arr_size` `; ` `$i` `++)` ` ` `if` `(` `$arr` `[` `$i` `] > ` `$second` `&&` ` ` `$arr` `[` `$i` `] < ` `$first` `)` ` ` `$second` `= ` `$arr` `[` `$i` `];` ` ` `// Find third largest element` ` ` `$third` `= PHP_INT_MIN;` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `$arr_size` `; ` `$i` `++)` ` ` `if` `(` `$arr` `[` `$i` `] > ` `$third` `&&` ` ` `$arr` `[` `$i` `] < ` `$second` `)` ` ` `$third` `= ` `$arr` `[` `$i` `];` ` ` `echo` `"The third Largest element is "` `,` ` ` `$third` `,` `"\n"` `;` `}` `// Driver Code` `$arr` `= ` `array` `(12, 13, 1,` ` ` `10, 34, 16);` `$n` `= sizeof(` `$arr` `);` `thirdLargest(` `$arr` `, ` `$n` `);` `// This code is contributed by m_kit` `?>` |

## Javascript

`<script>` `// JavaScript program to find third` `// Largest element in an array` `// of distinct elements` `function` `thirdLargest(arr, arr_size)` `{` ` ` `/* There should be` ` ` `atleast three elements */` ` ` `if` `(arr_size < 3)` ` ` `{` ` ` `document.write(` `" Invalid Input "` `);` ` ` `return` `;` ` ` `}` ` ` ` ` `// Find first` ` ` `// largest element` ` ` `let first = arr[0];` ` ` `for` `(let i = 1;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > first)` ` ` `first = arr[i];` ` ` ` ` `// Find second` ` ` `// largest element` ` ` `let second = Number.MIN_VALUE;` ` ` `for` `(let i = 0;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > second &&` ` ` `arr[i] < first)` ` ` `second = arr[i];` ` ` ` ` `// Find third` ` ` `// largest element` ` ` `let third = Number.MIN_VALUE;` ` ` `for` `(let i = 0;` ` ` `i < arr_size ; i++)` ` ` `if` `(arr[i] > third &&` ` ` `arr[i] < second)` ` ` `third = arr[i];` ` ` ` ` `document.write(` `"The third Largest "` `+` ` ` `"element is "` `, third);` `}` `// Driver Code` ` ` `let arr = [12, 13, 1,` ` ` `10, 34, 16];` ` ` `let n = arr.length;` ` ` `thirdLargest(arr, n);` ` ` `</script>` |

**Output:**

The third Largest element is 13

**Complexity Analysis:****Time Complexity:**O(n).

As the array is iterated thrice and is done in a constant time**Space complexity:**O(1).

No extra space is needed as the indices can be stored in constant space.

** Efficient Approach:** The problem deals with finding the third largest element in the array in a single traversal. The problem can be cracked by taking help of a similar problem- finding the second maximum element. So the idea is to traverse the array from start to end and to keep track of the three largest elements up to that index

*(stored in variables)*. So after traversing the whole array, the variables would have stored the indices

*(or value)*of the three largest elements of the array.

**Algorithm:**- Create three variables,
*first*,*second*,*third*, to store indices of three largest elements of the array. (Initially all of them are initialized to a minimum value). - Move along the input array from start to the end.
- For every index check if the element is larger than
*first*or not. Update the value of*first*, if the element is larger, and assign the value of*first*to*second*and*second*to*third*. So the largest element gets updated and the elements previously stored as largest becomes second largest, and the second largest element becomes third largest. - Else if the element is larger than the
*second*, then update the value of*second*,and the second largest element becomes third largest. - If the previous two conditions fail, but the element is larger than the
*third*, then update the*third*. - Print the value of
*third*after traversing the array from start to end

- Create three variables,

## C++

`// C++ program to find third` `// Largest element in an array` `#include <bits/stdc++.h>` `void` `thirdLargest(` `int` `arr[], ` `int` `arr_size)` `{` ` ` `/* There should be atleast three elements */` ` ` `if` `(arr_size < 3)` ` ` `{` ` ` `printf` `(` `" Invalid Input "` `);` ` ` `return` `;` ` ` `}` ` ` `// Initialize first, second and third Largest element` ` ` `int` `first = arr[0], second = INT_MIN, third = INT_MIN;` ` ` `// Traverse array elements to find the third Largest` ` ` `for` `(` `int` `i = 1; i < arr_size ; i ++)` ` ` `{` ` ` `/* If current element is greater than first,` ` ` `then update first, second and third */` ` ` `if` `(arr[i] > first)` ` ` `{` ` ` `third = second;` ` ` `second = first;` ` ` `first = arr[i];` ` ` `}` ` ` `/* If arr[i] is in between first and second */` ` ` `else` `if` `(arr[i] > second)` ` ` `{` ` ` `third = second;` ` ` `second = arr[i];` ` ` `}` ` ` `/* If arr[i] is in between second and third */` ` ` `else` `if` `(arr[i] > third)` ` ` `third = arr[i];` ` ` `}` ` ` `printf` `(` `"The third Largest element is %d\n"` `, third);` `}` `/* Driver program to test above function */` `int` `main()` `{` ` ` `int` `arr[] = {12, 13, 1, 10, 34, 16};` ` ` `int` `n = ` `sizeof` `(arr)/` `sizeof` `(arr[0]);` ` ` `thirdLargest(arr, n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find third Largest element in an array` `class` `GFG {` ` ` `static` `void` `thirdLargest(` `int` `arr[], ` `int` `arr_size) {` ` ` `/* There should be atleast three elements */` ` ` `if` `(arr_size < ` `3` `) {` ` ` `System.out.printf(` `" Invalid Input "` `);` ` ` `return` `;` ` ` `}` ` ` `// Initialize first, second and third Largest element` ` ` `int` `first = arr[` `0` `], second = Integer.MIN_VALUE,` ` ` `third = Integer.MIN_VALUE;` ` ` `// Traverse array elements to find the third Largest` ` ` `for` `(` `int` `i = ` `1` `; i < arr_size; i++) {` ` ` `/* If current element is greater than first,` ` ` `then update first, second and third */` ` ` `if` `(arr[i] > first) {` ` ` `third = second;` ` ` `second = first;` ` ` `first = arr[i];` ` ` `} ` `/* If arr[i] is in between first and second */` ` ` `else` `if` `(arr[i] > second) {` ` ` `third = second;` ` ` `second = arr[i];` ` ` `} ` `/* If arr[i] is in between second and third */` ` ` `else` `if` `(arr[i] > third) {` ` ` `third = arr[i];` ` ` `}` ` ` `}` ` ` `System.out.printf(` `"The third Largest element is %d\n"` `, third);` ` ` `}` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `main(String []args) {` ` ` `int` `arr[] = {` `12` `, ` `13` `, ` `1` `, ` `10` `, ` `34` `, ` `16` `};` ` ` `int` `n = arr.length;` ` ` `thirdLargest(arr, n);` ` ` `}` `}` `//This code is contributed by 29AjayKumar` |

## Python3

`# Python3 program to find` `# third Largest element in` `# an array` `import` `sys` `def` `thirdLargest(arr, arr_size):` ` ` `# There should be` ` ` `# atleast three elements` ` ` `if` `(arr_size < ` `3` `):` ` ` ` ` `print` `(` `" Invalid Input "` `)` ` ` `return` ` ` ` ` `# Initialize first, second` ` ` `# and third Largest element` ` ` `first ` `=` `arr[` `0` `]` ` ` `second ` `=` `-` `sys.maxsize` ` ` `third ` `=` `-` `sys.maxsize` ` ` `# Traverse array elements` ` ` `# to find the third Largest` ` ` `for` `i ` `in` `range` `(` `1` `, arr_size):` ` ` ` ` `# If current element is` ` ` `# greater than first,` ` ` `# then update first,` ` ` `# second and third` ` ` `if` `(arr[i] > first):` ` ` ` ` `third ` `=` `second` ` ` `second ` `=` `first` ` ` `first ` `=` `arr[i]` ` ` ` ` `# If arr[i] is in between` ` ` `# first and second` ` ` `elif` `(arr[i] > second):` ` ` ` ` `third ` `=` `second` ` ` `second ` `=` `arr[i]` ` ` ` ` `# If arr[i] is in between` ` ` `# second and third` ` ` `elif` `(arr[i] > third):` ` ` `third ` `=` `arr[i]` ` ` ` ` `print` `(` `"The third Largest"` `,` ` ` `"element is"` `, third)` `# Driver Code` `arr ` `=` `[` `12` `, ` `13` `, ` `1` `,` ` ` `10` `, ` `34` `, ` `16` `]` `n ` `=` `len` `(arr)` `thirdLargest(arr, n)` `# This code is contributed` `# by Smitha` |

## C#

`// C# program to find third Largest element in an array` `using` `System;` `class` `GFG {` `static` `void` `thirdLargest(` `int` `[] arr, ` `int` `arr_size)` `{` ` ` `/* There should be atleast three elements */` ` ` `if` `(arr_size < 3)` ` ` `{` ` ` `Console.Write(` `" Invalid Input "` `);` ` ` `return` `;` ` ` ` ` `}` ` ` `// Initialize first, second and third Largest element` ` ` `int` `first = arr[0], second = ` `int` `.MinValue,` ` ` `third = ` `int` `.MinValue;` ` ` `// Traverse array elements to find the third Largest` ` ` `for` `(` `int` `i = 1; i < arr_size; i++)` ` ` `{` ` ` `/* If current element is greater than first,` ` ` `then update first, second and third */` ` ` `if` `(arr[i] > first) {` ` ` `third = second;` ` ` `second = first;` ` ` `first = arr[i];` ` ` `}` ` ` ` ` `/* If arr[i] is in between first and second */` ` ` `else` `if` `(arr[i] > second) {` ` ` `third = second;` ` ` `second = arr[i];` ` ` `}` ` ` `/* If arr[i] is in between second and third */` ` ` `else` `if` `(arr[i] > third) {` ` ` `third = arr[i];` ` ` `}` ` ` `}` ` ` `Console.Write(` `"The third Largest element is "` `+ third);` `}` `/* Driver program to test above function */` `public` `static` `void` `Main() {` ` ` `int` `[] arr = {12, 13, 1, 10, 34, 16};` ` ` `int` `n = arr.Length;` ` ` `thirdLargest(arr, n);` ` ` `}` `}` `// This code is contributed` `// by Ita_c` |

## PHP

`<?php` `// PHP program to find third` `// Largest element in an array` `function` `thirdLargest(` `$arr` `, ` `$arr_size` `)` `{` ` ` `/* There should be atleast` ` ` `three elements */` ` ` `if` `(` `$arr_size` `< 3)` ` ` `{` ` ` `echo` `" Invalid Input "` `;` ` ` `return` `;` ` ` `}` ` ` `// Initialize first, second and` ` ` `// third Largest element` ` ` `$first` `= ` `$arr` `[0];` ` ` `$second` `= PHP_INT_MIN;` ` ` `$third` `= PHP_INT_MIN;` ` ` `// Traverse array elements to` ` ` `// find the third Largest` ` ` `for` `(` `$i` `= 1; ` `$i` `< ` `$arr_size` `; ` `$i` `++)` ` ` `{` ` ` `/* If current element is greater` ` ` `than first, then update first,` ` ` `second and third */` ` ` `if` `(` `$arr` `[` `$i` `] > ` `$first` `)` ` ` `{` ` ` `$third` `= ` `$second` `;` ` ` `$second` `= ` `$first` `;` ` ` `$first` `= ` `$arr` `[` `$i` `];` ` ` `}` ` ` `/* If arr[i] is in between` ` ` `first and second */` ` ` `else` `if` `(` `$arr` `[` `$i` `] > ` `$second` `)` ` ` `{` ` ` `$third` `= ` `$second` `;` ` ` `$second` `= ` `$arr` `[` `$i` `];` ` ` `}` ` ` `/* If arr[i] is in between` ` ` `second and third */` ` ` `else` `if` `(` `$arr` `[` `$i` `] > ` `$third` `)` ` ` `$third` `= ` `$arr` `[` `$i` `];` ` ` `}` ` ` `echo` `"The third Largest element is "` `,` ` ` `$third` `;` `}` `// Driver Code` `$arr` `= ` `array` `(12, 13, 1,` ` ` `10, 34, 16);` `$n` `= sizeof(` `$arr` `);` `thirdLargest(` `$arr` `, ` `$n` `);` `// This code is contributed by jit_t` `?>` |

## Javascript

`<script>` `// JavaScript program to find third` `// Largest element in an array` `function` `thirdLargest(arr, arr_size)` `{` ` ` `/* There should be atleast three elements */` ` ` `if` `(arr_size < 3)` ` ` `{` ` ` `document.write(` `" Invalid Input "` `);` ` ` `return` `;` ` ` `}` ` ` `// Initialize first, second and third Largest element` ` ` `var` `first = arr[0], second = -1000000000, third = -1000000000;` ` ` `// Traverse array elements to find the third Largest` ` ` `for` `(` `var` `i = 1; i < arr_size ; i ++)` ` ` `{` ` ` `/* If current element is greater than first,` ` ` `then update first, second and third */` ` ` `if` `(arr[i] > first)` ` ` `{` ` ` `third = second;` ` ` `second = first;` ` ` `first = arr[i];` ` ` `}` ` ` `/* If arr[i] is in between first and second */` ` ` `else` `if` `(arr[i] > second)` ` ` `{` ` ` `third = second;` ` ` `second = arr[i];` ` ` `}` ` ` `/* If arr[i] is in between second and third */` ` ` `else` `if` `(arr[i] > third)` ` ` `third = arr[i];` ` ` `}` ` ` `document.write(` `"The third Largest element is "` `+ third);` `}` `/* Driver program to test above function */` `var` `arr = [12, 13, 1, 10, 34, 16];` `var` `n = arr.length;` `thirdLargest(arr, n);` `</script>` |

**Output:**

The third Largest element is 13

**Complexity Analysis:****Time Complexity:**O(n).

As the array is iterated once and is done in a constant time**Space complexity:**O(1).

No extra space is needed as the indices can be stored in constant space.

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**Exercise Problem:** Extend the above solution to find the third largest when array may have duplicates. For example, if the input array is {10, 5, 15, 5, 15, 10, 1, 1}, then output should be 5. The extended solution should also work in one traversal.

**Related Articles:**

- Find the smallest and second smallest element in an array
- k largest(or smallest) elements in an array
- K’th Smallest/Largest Element in Unsorted Array | Set 3 (Worst Case Linear Time)

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