Arrange the numbers in the Array as per given inequalities

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Given a list of N distinct integers and a list of N-1 inequality signs, the task is to insert the integers between the inequality signs, such that the final inequality formed always holds true.
Note: The order of the inequality signs should not be changed.

Examples:

Input: Integers: [ 2, 5, 1, 0 ], Signs: [ <, >, < ]Output: 0 < 5 > 1 < 2
Explanation:
The inequality formed is consistent and valid.

Input: Integers: [ 8, 34, 25, 1, -5, 10], Signs: [ >, >, <, <, > ]Output: 34 > 25 > -5 < 1 < 10 > 8
Explanation:
The inequality formed is consistent and valid.

Approach: The list of inequality symbols can contain symbols in any order. So to obtain a consistent inequality, put the smallest integer left in the array before each < symbol and the largest integer left before each > symbol. Based on this idea, below are the steps:

Sort the list of integers in ascending order.
Maintain two variables, say low and high, pointing at the first and last index of the list of integers.
Iterate over the list of inequality symbols. If the current symbol is less, then add the integer pointed by low before <, and increment low to point to the next index. If the current symbol is greater, then add the integer pointed by high before >, and decrement high to point to the previous index.
Finally, add the remaining element to the last position.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to place the integers
// in between the inequality signs
string formAnInequality(int integers[], char inequalities[],
                        int n1, int n2)
{
 
    // Sort the integers array and
    // set the index of smallest
    // and largest element
    sort(integers, integers + n1);
 
    int lowerIndex = 0;
    int higherIndex = n1 - 1;
 
    string sb = "";
 
    // Iterate over the inequalities
    for (int i = 0; i < n2; i++) {
 
        char ch = inequalities[i];
 
        // Append the necessary
        // integers per symbol
        if (ch == '<') {
            sb += " ";
            sb += to_string(integers[lowerIndex++]);
            sb += " ";
            sb += ch;
        }
        else {
            sb += " ";
            sb += to_string(integers[higherIndex--]);
            sb += " ";
            sb += ch;
        }
    }
 
    // Add the final integer
    sb += " " + to_string(integers[lowerIndex]);
 
    // Return the answer
    return sb;
}
 
// Driver Code
int main()
{
    // Given List of Integers
    int integers[] = { 2, 5, 1, 0 };
 
    // Given list of inequalities
    char inequalities[] = { '<', '>', '<' };
 
    int n1 = 4;
    int n2 = 3;
 
    // Function Call
    string output
        = formAnInequality(integers, inequalities, n1, n2);
 
    // Print the output
    cout << output << endl;
}
 
// This code is contributed by phasing17

Java

// Java program for the above approach
import java.util.Arrays;
 
public class PlacingNumbers {
 
    // Function to place the integers
    // in between the inequality signs
    static String
    formAnInequality(int[] integers,
                     char[] inequalities)
    {
 
        // Sort the integers array and
        // set the index of smallest
        // and largest element
        Arrays.sort(integers);
 
        int lowerIndex = 0;
        int higherIndex = integers.length - 1;
 
        StringBuilder sb = new StringBuilder();
 
        // Iterate over the inequalities
        for (char ch : inequalities) {
 
            // Append the necessary
            // integers per symbol
            if (ch == '<') {
                sb.append(" "
                          + integers[lowerIndex++]
                          + " "
                          + ch);
            }
            else {
                sb.append(" "
                          + integers[higherIndex--]
                          + " "
                          + ch);
            }
        }
 
        // Add the final integer
        sb.append(" " + integers[lowerIndex]);
 
        // Return the answer
        return sb.toString();
    }
 
    // Driver Code
    public static void main(String[] args)
    {
        // Given List of Integers
        int[] integers = { 2, 5, 1, 0 };
 
        // Given list of inequalities
        char[] inequalities = { '<', '>', '<' };
 
        // Function Call
        String output
            = formAnInequality(integers,
                               inequalities);
 
        // Print the output
        System.out.println(output);
    }
}

Python3

# Python3 program for 
# the above approach
 
# Function to place the integers
# in between the inequality signs
def formAnInequality(integers,
                     inequalities):
 
    # Sort the integers array and
    # set the index of smallest
    # and largest element
    integers.sort()
 
    lowerIndex = 0
    higherIndex = len(integers) - 1
    sb = ""
 
    # Iterate over the inequalities
    for ch in  inequalities:
 
        # Append the necessary
        # integers per symbol
        if (ch == '<'):
            sb += (" " + chr(integers[lowerIndex]) +
                   " " + ch)
            lowerIndex += 1
        else:
            sb += (" " + chr(integers[higherIndex]) +
                   " " + ch)
            higherIndex -= 1
        
    # Add the final integer
    sb += (" " + chr(integers[lowerIndex]))
 
    # Return the answer
    return sb
 
# Driver Code
if __name__ ==  "__main__":
     
    # Given List of Integers
    integers = [2, 5, 1, 0]
 
    # Given list of inequalities
    inequalities = ['<', '>', '<']
 
    # Function Call
    output = formAnInequality(integers,
                              inequalities)
 
    # Print the output
    print(output)
 
# This code is contributed by Chitranayal

C#

// C# program for the above approach 
using System;
using System.Text;
 
class GFG{ 
 
// Function to place the integers 
// in between the inequality signs 
static String 
formAnInequality(int[] integers, 
                char[] inequalities) 
{ 
     
    // Sort the integers array and 
    // set the index of smallest 
    // and largest element 
    Array.Sort(integers); 
 
    int lowerIndex = 0; 
    int higherIndex = integers.Length - 1; 
 
    StringBuilder sb = new StringBuilder(); 
 
    // Iterate over the inequalities 
    foreach(char ch in inequalities)
    { 
         
        // Append the necessary 
        // integers per symbol 
        if (ch == '<')
        { 
            sb.Append(" " + integers[lowerIndex++] +
                      " " + ch); 
        } 
        else
        { 
            sb.Append(" " + integers[higherIndex--] +
                      " " + ch); 
        } 
    } 
 
    // Add the readonly integer 
    sb.Append(" " + integers[lowerIndex]); 
 
    // Return the answer 
    return sb.ToString(); 
} 
 
// Driver Code 
public static void Main(String[] args) 
{ 
     
    // Given List of ints 
    int[] integers = { 2, 5, 1, 0 }; 
 
    // Given list of inequalities 
    char[] inequalities = { '<', '>', '<' }; 
 
    // Function call 
    String output = formAnInequality(integers, 
                                      inequalities); 
 
    // Print the output 
    Console.WriteLine(output); 
} 
} 
 
// This code is contributed by 29AjayKumar

Javascript

<script>
 
// Javascript program for the above approach
 
// Function to place the integers
// in between the inequality signs
function formAnInequality(integers, inequalities)
{
     
    // Sort the integers array and
    // set the index of smallest
    // and largest element
    (integers).sort(function(a, b){return a - b;});
 
    let lowerIndex = 0;
    let higherIndex = integers.length - 1;
 
    let sb = "";
 
    // Iterate over the inequalities
    for(let ch = 0; ch < inequalities.length; ch++)
    {
         
        // Append the necessary
        // integers per symbol
        if (inequalities[ch] == '<')
        {
            sb += " " + (integers[lowerIndex++]) + 
                  " " + inequalities[ch];
        }
        else
        {
            sb += " " + (integers[higherIndex--]) + 
                  " " + inequalities[ch];
        }
    }
 
    // Add the final integer
    sb += " " + (integers[lowerIndex]);
 
    // Return the answer
    return sb;
}
 
// Driver Code
 
// Given List of Integers
let integers = [ 2, 5, 1, 0 ];
 
// Given list of inequalities
let inequalities = [ '<', '>', '<' ];
 
// Function Call
let output = formAnInequality(
    integers, inequalities);
     
// Print the output
document.write(output);
 
// This code is contributed by avanitrachhadiya2155
 
</script>

Output:

0 < 5 > 1 < 2

Time Complexity: O(N*log N)
Auxiliary Space: O(1)

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