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# Arrange numbers to form a valid sequence

• Last Updated : 11 May, 2021

Given an array arr[] with N distinct numbers and another array arr1[] with N-1 operators (either < or >), the task is to organize the numbers to form a valid sequence which obeys relational operator rules with respect to provided operators.

Examples:

Input: arr[] = {3, 12, 7, 8, 5}; arr1= {‘<‘, ‘>’, ‘>’, ‘<‘}
Output: {3, 12, 8, 5, 7}
Explanation:
3 < 12 > 8 > 5 < 7
There can be more such combinations. The task is to return one of the combinations.

Input: arr[] = {8, 2, 7, 1, 5, 9}; arr1[] = {‘>’, ‘>’, ‘<‘, ‘>’, ‘<‘}
Output:{9, 8, 1, 7, 2, 5}
Explanation:
9 > 8 > 1 < 7 > 2 < 5

Naive Approach:
A naive approach is to try all different possible arrangement of numbers and check if the sequence is valid.
Time Complexity: O(2N).

Efficient Approach: The idea is to first sort the given array of numbers in ascending order. Then solve the problem using two pointers technique: one pointing at the front and other pointing at the end.

1. Take one resultant array of size same as given array.
2. If the current operator is ‘<‘ then include the element which the top pointer is pointing to in resultant array and increment it by 1.
3. If the current operator is ‘>’ then include the element which the last pointer is pointing to in resultant array and decrement it by 1.

Below is the implementation of the above approach.

## C++

 `// C++ implemenattion of the above approach``#include ``using` `namespace` `std;` `// Function to organize the given numbers``// to form a valid sequence.``vector<``int``> orgazineInOrder(vector<``int``> vec,``                            ``vector<``int``> op, ``int` `n)``{``    ``vector<``int``> result(n);``    ``// Sorting the array``    ``sort(vec.begin(), vec.end());` `    ``int` `i = 0, j = n - 1, k = 0;``    ``while` `(i <= j && k <= n - 2) {``        ``// Two pointer technique``        ``// to organize the numbers``        ``if` `(op[k] == ``'<'``) {``            ``result[k] = vec[i++];``        ``}``        ``else` `{``            ``result[k] = vec[j--];``        ``}``        ``k++;``    ``}``    ``result[n - 1] = vec[i];` `    ``return` `result;``}` `// Driver code``int` `main()``{``    ``vector<``int``> vec({ 8, 2, 7, 1, 5, 9 });` `    ``vector<``int``> op({ ``'>'``, ``'>'``, ``'<'``,``                     ``'>'``, ``'<'` `});` `    ``vector<``int``> result``        ``= orgazineInOrder(vec,``                          ``op, vec.size());` `    ``for` `(``int` `i = 0; i < result.size(); i++) {``        ``cout << result[i] << ``" "``;``    ``}``    ``return` `0;``}`

## Java

 `// Java implemenattion of the above approach``import` `java.util.*;` `class` `GFG``{` `// Function to organize the given numbers``// to form a valid sequence.``static` `int``[] orgazineInOrder(``int` `[]vec,``int``[] op, ``int` `n)``{``    ``int` `[]result = ``new` `int``[n];``    ` `    ``// Sorting the array``    ``Arrays.sort(vec);` `    ``int` `i = ``0``, j = n - ``1``, k = ``0``;``    ``while` `(i <= j && k <= n - ``2``)``    ``{``        ``// Two pointer technique``        ``// to organize the numbers``        ``if` `(op[k] == ``'<'``)``        ``{``            ``result[k] = vec[i++];``        ``}``        ``else``        ``{``            ``result[k] = vec[j--];``        ``}``        ``k++;``    ``}``    ``result[n - ``1``] = vec[i];` `    ``return` `result;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `[]vec ={ ``8``, ``2``, ``7``, ``1``, ``5``, ``9` `};` `    ``int``[] op ={ ``'>'``, ``'>'``, ``'<'``,``                    ``'>'``, ``'<'` `};` `    ``int` `[]result = orgazineInOrder(vec,``                        ``op, vec.length);` `    ``for` `(``int` `i = ``0``; i < result.length; i++)``    ``{``        ``System.out.print(result[i]+ ``" "``);``    ``}``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 implemenattion of the above approach` `# Function to organize the given numbers``# to form a valid sequence.``def` `orgazineInOrder(vec, op, n) :` `    ``result ``=` `[``0``] ``*` `n;``    ` `    ``# Sorting the array``    ``vec.sort();``    ``i ``=` `0``;``    ``j ``=` `n ``-` `1``;``    ``k ``=` `0``;``    ` `    ``while` `(i <``=` `j ``and` `k <``=` `n ``-` `2``) :``        ` `        ``# Two pointer technique``        ``# to organize the numbers``        ``if` `(op[k] ``=``=` `'<'``) :``            ``result[k] ``=` `vec[i];``            ``i ``+``=` `1``;``        ` `        ``else` `:``            ``result[k] ``=` `vec[j];``            ``j ``-``=` `1``;``        ` `        ``k ``+``=` `1``;` `    ``result[n ``-` `1``] ``=` `vec[i];` `    ``return` `result;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``vec ``=` `[ ``8``, ``2``, ``7``, ``1``, ``5``, ``9` `];``    ``op ``=` `[ ``'>'``, ``'>'``, ``'<'``, ``'>'``, ``'<'` `];` `    ``result ``=` `orgazineInOrder(vec, op, ``len``(vec));` `    ``for` `i ``in` `range``(``len``(result)) :``        ``print``(result[i], end ``=` `" "``);` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{``    ` `    ``// Function to organize the given numbers``    ``// to form a valid sequence.``    ``static` `int``[] orgazineInOrder(``int` `[]vec,``int``[] op, ``int` `n)``    ``{``        ``int` `[]result = ``new` `int``[n];``        ` `        ``// Sorting the array``        ``Array.Sort(vec);``    ` `        ``int` `i = 0, j = n - 1, k = 0;``        ``while` `(i <= j && k <= n - 2)``        ``{``            ``// Two pointer technique``            ``// to organize the numbers``            ``if` `(op[k] == ``'<'``)``            ``{``                ``result[k] = vec[i++];``            ``}``            ``else``            ``{``                ``result[k] = vec[j--];``            ``}``            ``k++;``        ``}``        ``result[n - 1] = vec[i];``    ` `        ``return` `result;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main()``    ``{``        ``int` `[]vec ={ 8, 2, 7, 1, 5, 9 };``    ` `        ``int``[] op ={ ``'>'``, ``'>'``, ``'<'``,``                        ``'>'``, ``'<'` `};``    ` `        ``int` `[]result = orgazineInOrder(vec,``                            ``op, vec.Length);``    ` `        ``for` `(``int` `i = 0; i < result.Length; i++)``        ``{``            ``Console.Write(result[i] + ``" "``);``        ``}``    ``}``}` `// This code is contributed by AnkitRai01`

## Javascript

 ``
Output:
`9 8 1 7 2 5`

Time Complexity: O(NlogN)

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