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 < 2Â
Explanation:
The inequality formed is consistent and valid.Input: Integers: [ 8, 34, 25, 1, -5, 10], Signs: [ >, Â >, <, <, > ]
Output: 34 > 25 > -5 < 1 < 10 > 8
Explanation:
The inequality formed is consistent and valid.
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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;Â
// Function to place the integers// in between the inequality signsstring formAnInequality(int integers[], char inequalities[],                        int n1, int n2){Â
    // Sort the integers array and    // set the index of smallest    // and largest element    sort(integers, integers + n1);Â
    int lowerIndex = 0;    int higherIndex = n1 - 1;Â
    string sb = "";Â
    // Iterate over the inequalities    for (int i = 0; i < n2; i++) {Â
        char ch = inequalities[i];Â
        // 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;        }    }Â
    // Add the final integer    sb += " " + to_string(integers[lowerIndex]);Â
    // Return the answer    return sb;}Â
// Driver Codeint main(){    // Given List of Integers    int integers[] = { 2, 5, 1, 0 };Â
    // Given list of inequalities    char inequalities[] = { '<', '>', '<' };Â
    int n1 = 4;    int n2 = 3;Â
    // Function Call    string output        = formAnInequality(integers, inequalities, n1, n2);Â
    // Print the output    cout << output << endl;}Â
// This code is contributed by phasing17 |
Java
// Java program for the above approachimport java.util.Arrays;Â
public class PlacingNumbers {Â
    // Function to place the integers    // in between the inequality signs    static String    formAnInequality(int[] integers,                     char[] inequalities)    {Â
        // Sort the integers array and        // set the index of smallest        // and largest element        Arrays.sort(integers);Â
        int lowerIndex = 0;        int higherIndex = integers.length - 1;Â
        StringBuilder sb = new StringBuilder();Â
        // Iterate over the inequalities        for (char ch : inequalities) {Â
            // Append the necessary            // integers per symbol            if (ch == '<') {                sb.append(" "                          + integers[lowerIndex++]                          + " "                          + ch);            }            else {                sb.append(" "                          + integers[higherIndex--]                          + " "                          + ch);            }        }Â
        // Add the final integer        sb.append(" " + integers[lowerIndex]);Â
        // Return the answer        return sb.toString();    }Â
    // Driver Code    public static void main(String[] args)    {        // Given List of Integers        int[] integers = { 2, 5, 1, 0 };Â
        // Given list of inequalities        char[] inequalities = { '<', '>', '<' };Â
        // Function Call        String output            = formAnInequality(integers,                               inequalities);Â
        // Print the output        System.out.println(output);    }} |
Python3
# Python3 program for # the above approachÂ
# Function to place the integers# in between the inequality signsdef formAnInequality(integers,                     inequalities):Â
    # Sort the integers array and    # set the index of smallest    # and largest element    integers.sort()Â
    lowerIndex = 0    higherIndex = len(integers) - 1    sb = ""Â
    # Iterate over the inequalities    for ch in inequalities:Â
        # 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]))Â
    # Return the answer    return sbÂ
# Driver Codeif __name__ == "__main__":         # Given List of Integers    integers = [2, 5, 1, 0]Â
    # Given list of inequalities    inequalities = ['<', '>', '<']Â
    # Function Call    output = formAnInequality(integers,                              inequalities)Â
    # Print the output    print(output)Â
# This code is contributed by Chitranayal |
C#
// C# program for the above approach using System;using System.Text;Â
class GFG{ Â
// 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); Â
    int lowerIndex = 0;     int higherIndex = integers.Length - 1; Â
    StringBuilder sb = new StringBuilder(); Â
    // 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);         }     } Â
    // Add the readonly integer     sb.Append(" " + integers[lowerIndex]); Â
    // Return the answer     return sb.ToString(); } Â
// Driver Code public static void Main(String[] args) {          // Given List of ints     int[] integers = { 2, 5, 1, 0 }; Â
    // Given list of inequalities     char[] inequalities = { '<', '>', '<' }; Â
    // Function call     String output = formAnInequality(integers,                                       inequalities); Â
    // Print the output     Console.WriteLine(output); } } Â
// This code is contributed by 29AjayKumar |
Javascript
<script>Â
// Javascript program for the above approachÂ
// Function to place the integers// in between the inequality signsfunction formAnInequality(integers, inequalities){         // Sort the integers array and    // set the index of smallest    // and largest element    (integers).sort(function(a, b){return a - b;});Â
    let lowerIndex = 0;    let higherIndex = integers.length - 1;Â
    let sb = "";Â
    // 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];        }    }Â
    // Add the final integer    sb += " " + (integers[lowerIndex]);Â
    // Return the answer    return sb;}Â
// Driver CodeÂ
// Given List of Integerslet integers = [ 2, 5, 1, 0 ];Â
// Given list of inequalitieslet inequalities = [ '<', '>', '<' ];Â
// Function Calllet output = formAnInequality(Â Â Â Â integers, inequalities);Â Â Â Â Â // Print the outputdocument.write(output);Â
// This code is contributed by avanitrachhadiya2155Â
</script> |
Output:Â
0 < 5 > 1 < 2
Â
Time Complexity: O(N*log N)Â
Auxiliary Space: O(1)Â
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