Divide array into increasing and decreasing subsequence without changing the order

Given a merged sequence which consists of two sequences which got merged, one of them was strictly increasing and the other was strictly decreasing. Elements of increasing sequence were inserted between elements of the decreasing one without changing the order.

Sequences [1, 3, 4] and [10, 4, 2] can produce the following resulting sequences:
[10, 1, 3, 4, 2, 4], [1, 3, 4, 10, 4, 2].

The following sequence cannot be the result of these insertions:
[1, 10, 4, 4, 3, 2] because the order of elements in the increasing sequence was changed.

Given a merged sequence, the task is to find any two suitable initial sequences, one of them should be strictly increasing, and another should be strictly decreasing.

Note: An empty sequence and the sequence consisting of one element can be considered as increasing or decreasing.

Examples:

Input: arr[] = {5, 1, 3, 6, 8, 2, 9, 0, 10}
Output: [1, 3, 6, 8, 9, 10] [5, 2, 0]

Input: arr[] = {1, 2, 4, 0, 2}
Output: -1
No such sequences possible.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Method 1: We can modify Longest Increasing Sequence) and solve the required problem. It will take O(nlogn) time.

Method 2: We can also solve this problem only in a single traversal. The Idea used here is that maintain two sorted arrays.
For a new element x,

• If it can be appended to only one of the arrays then append it.
• If it can be appended to neither, then the answer is -1.
• If it can be appended to both then check the next element y, if y > x then append x to the increasing one otherwise append x to the decreasing one.

Below is the implementation of the above approach:

C++

 // C++ implementation of the approach #include using namespace std;    // Function to print strictly increasing and // strictly decreasing sequence if possible void Find_Sequence(int arr[], int n) {     // Arrays to store strictly increasing and     // decreasing sequence     vector inc_arr, dec_arr;        // Initializing last element of both sequence     int flag = 0;     long inc = -1, dec = 1e7;        // Iterating through the array     for (int i = 0; i < n; i++)     {         // If current element can be appended         // to both the sequences         if (inc < arr[i] && arr[i] < dec)         {             // If next element is greater than             // the current element             // Then append it to the strictly             // increasing array             if (arr[i] < arr[i + 1])             {                 inc = arr[i];                 inc_arr.emplace_back(arr[i]);             }                // Otherwise append it to the             // strictly decreasing array             else             {                 dec = arr[i];                 dec_arr.emplace_back(arr[i]);             }         }                    // If current element can be appended         // to the increasing sequence only         else if (inc < arr[i])         {             inc = arr[i];             inc_arr.emplace_back(arr[i]);         }                    // If current element can be appended         // to the decreasing sequence only         else if (dec > arr[i])         {             dec = arr[i];             dec_arr.emplace_back(arr[i]);         }                    // Else we can not make such sequences         // from the given array         else         {             cout << -1 << endl;             flag = 1;             break;         }     }            // Print the required sequences     if (!flag)     {         for (auto i = inc_arr.begin();                    i != inc_arr.end(); i++)             cout << *i << " ";         cout << endl;            for (auto i = dec_arr.begin();                    i != dec_arr.end(); i++)             cout << *i << " ";         cout << endl;     } }    // Driver code int main() {     int arr[] = { 5, 1, 3, 6, 8, 2, 9, 0, 10 };     int n = sizeof(arr) / sizeof(arr);     Find_Sequence(arr, n); }    // This code is contributed by sanjeev2552

Python

 # Python3 implementation of the approach     # Function to print strictly increasing and # strictly decreasing sequence if possible def Find_Sequence(array, n):        # Arrays to store strictly increasing and     # decreasing sequence      inc_arr, dec_arr =[], []        # Initializing last element of both sequence     inc, dec = -1, 1e7        # Iterating through the array     for i in range(n):            # If current element can be appended          # to both the sequences         if inc < array[i] < dec:                # If next element is greater than              # the current element              # Then append it to the strictly              # increasing array              if array[i] < array[i + 1]:                 inc = array[i]                 inc_arr.append(array[i])                # Otherwise append it to the              # strictly decreasing array             else:                 dec = array[i]                 dec_arr.append(array[i])            # If current element can be appended          # to the increasing sequence only         elif inc < array[i]:             inc = array[i]             inc_arr.append(array[i])            # If current element can be appended          # to the decreasing sequence only         elif dec > array[i]:             dec = array[i]             dec_arr.append(array[i])            # Else we can not make such sequences          # from the given array         else:             print('-1')             break        # Print the required sequences     else:         print(inc_arr, dec_arr)    # Driver code arr = [5, 1, 3, 6, 8, 2, 9, 0, 10] n = len(arr) Find_Sequence(arr, n)

PHP

 \$arr[\$i])         {             \$dec = \$arr[\$i];             array_push(\$dec_arr, \$arr[\$i]);          }            // Else we can not make such sequences          // from the given array         else         {             echo '-1';              break;         }     }            // Print the required sequences      print_r(\$inc_arr);     print_r(\$dec_arr); }    // Driver code  \$arr = array(5, 1, 3, 6, 8, 2, 9, 0, 10); \$n = count(\$arr); Find_Sequence(\$arr, \$n);    // This code is contributed by Ryuga ?>

Output:

[1, 3, 6, 8, 9, 10] [5, 2, 0]

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Improved By : AnkitRai01, sanjeev2552

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