Permutation of a string with maximum number of characters greater than its adjacent characters

Given a string str, the task is to print the maximum count of characters which are greater than both its left and right character in any permutation of the string.

Examples:

Input: str = “abc” 
Output: 1 
Permutations of the string with the count of maximal character in each string are: 
abc – 0 
acb – 1 Here a < c > b 
bac – 0 
bca – 1 Here b < c > a 
cab – 0 
cba – 0 

Input: str = “geeks” 
Output: 2 
The string will be “egesk” 

Observations:

• If the string’ length is less than 3 then the answer will be 0 because no permutation is possible which satisfies the given condition.
• If the length of the given string is greater than or equal to 3 then assume that in the resulting string every other character is maximal character, that is there is exactly one character between any two consecutive maximal characters (otherwise we can remove all but the lowest one and add them to the end of the string).
• Assume for simplicity that this number is odd. Then, ideally, the string can have maximal characters in even positions i.e.at most (n-1)/2, where n is the length of the given string while the rest of the remaining characters in odd positions.
• First arrange all the characters in ascending order, place the first half characters at odd positions, and then fill the remaining even positions with the rest of the characters. 
  In this way, all the characters in even positions will be those characters from which character at the left and the right position are smaller if there is no frequency of smaller character that is too high, start placing a character from an odd position, continue with the same character to even positions, and eventually reach a position next to the odd position from which we started to place the character. Here if the frequency of some smaller character in the string is too high then the count of maximal character will always be less than (n-1)/2.

Approach:

1. Calculate the frequency of each character in the given string.
2. Check the character which has the maximum frequency.
3. If the maximum frequency element is the smallest element in the given string then mark the flag as 0 otherwise mark the value of flag equal to 1.
4. The answer will the minimum of ((n – 1) / 2, n – max_freq – flag).

Below is the implementation of the above approach: 

C++

// C++ program to find maximum count
// of such characters which are greater
// its left and right character in
// any permutation of the string
#include <bits/stdc++.h>
using namespace std;

// function to find maximum maximal character in the string
int solve(int freq[])
{
    // to store sum of all frequency
    int n = 0;

    // to store maximum frequency
    int max_freq = 0;

    // frequency of the smallest element
    int first;

    // to check if the smallest
    // element have maximum frequency or not
    int flag = 0;

    // Iterate in the string and count frequency
    for (int i = 0; i < 26; i++) {
        n += freq[i];

        // to store frequency of smallest element
        if (freq[i] != 0 && flag == 0) {
            first = freq[i];
            flag = 1;
        }

        // to store maximum frequency
        if (max_freq < freq[i])
            max_freq = freq[i];
    }

    // if sum of frequency of all element if 0
    if (n == 0)
        return 0;

    // if frequency of smallest character
    // if largest frequency
    if (first != max_freq)
        flag = 1;
    else
        flag = 0;

    return min((n - 1) / 2, n - max_freq - flag);
}

// Function that counts the frequency of
// each element
void solve(string s)
{
    // array to store the frequency of each character
    int freq[26];

    // initialize frequency of all character with 0
    memset(freq, 0, sizeof(freq));

    // loop to calculate frequency of
    // each character in the given string
    for (int i = 0; i < s.length(); i++) {
        freq[s[i] - 'a']++;
    }

    cout << solve(freq);
}

// Driver Code
int main()
{
    string s = "geeks";

    solve(s);
    return 0;
}

Java

// Java program to find maximum count
// of such characters which are greater
// its left and right character in
// any permutation of the string only three characters

class GFG {

// function to find maximum maximal character in the string
    static int solve(int freq[]) {
        // to store sum of all frequency
        int n = 0;

        // to store maximum frequency
        int max_freq = 0;

        // frequency of the smallest element
        int first = 0;

        // to check if the smallest
        // element have maximum frequency or not
        int flag = 0;

        // Iterate in the string and count frequency
        for (int i = 0; i < 26; i++) {
            n += freq[i];

            // to store frequency of smallest element
            if (freq[i] != 0 && flag == 0) {
                first = freq[i];
                flag = 1;
            }

            // to store maximum frequency
            if (max_freq < freq[i]) {
                max_freq = freq[i];
            }
        }

        // if sum of frequency of all element if 0
        if (n == 0) {
            return 0;
        }

        // if frequency of smallest character
        // if largest frequency
        if (first != max_freq) {
            flag = 1;
        } else {
            flag = 0;
        }

        return Math.min((n - 1) / 2, n - max_freq - flag);
    }

// Function that counts the frequency of
// each element
    static void solve(String s) {
        // array to store the frequency of each character
        int freq[] = new int[26];

        // loop to calculate frequency of
        // each character in the given string
        for (int i = 0; i < s.length(); i++) {
            freq[s.charAt(i) - 'a']++;
        }

        System.out.println(solve(freq));
    }

// Driver Code
    public static void main(String[] args) {
        String s = "geeks";

        solve(s);

    }
}
// This code is contributed by 29AjayKumar

Python3

# Python3 program to find maximum
# count of such characters which
# are greater its left and right
# character in any permutation
# of the string

# function to find maximum maximal
# character in the string
def Solve_1(freq):

    # to store sum of all frequency
    n = 0

    # to store maximum frequency
    max_freq = 0

    # to check if the smallest
    # element have maximum
    # frequency or not
    flag = 0

    # Iterate in the string
    # and count frequency
    for i in range(26) :
        n += freq[i]

        # to store frequency of
        # smallest element
        if (freq[i] != 0 and flag == 0) :
            first = freq[i]
            flag = 1

        # to store maximum frequency
        if (max_freq < freq[i]):
            max_freq = freq[i]

    # if sum of frequency of
    # all element if 0
    if (n == 0):
        return 0

    # if frequency of smallest character
    # if largest frequency
    if (first != max_freq):
        flag = 1
    else:
        flag = 0

    return min((n - 1) // 2, n - max_freq - flag)

# Function that counts the
# frequency of each element
def solve(s):

    # array to store the frequency
    # of each character initialize
    # frequency of all character with 0
    freq = [0] * 26

    # loop to calculate frequency of
    # each character in the given string
    for i in range(len(s)):

        freq[ord(s[i]) - ord('a')] += 1

    print(Solve_1(freq))

# Driver Code
if __name__ == "__main__":
    s = "geeks"
    solve(s)

# This code is contributed
# by ChitraNayal

C#

// C# program to find maximum count
// of such characters which are greater
// its left and right character in
// any permutation of the string only three characters
using System;
public class GFG{
//JAVA program to find maximum count
// of such characters which are greater
// its left and right character in
// any permutation of the string only three characters


// function to find maximum maximal character in the string
    static int solve(int []freq) {
        // to store sum of all frequency
        int n = 0;

        // to store maximum frequency
        int max_freq = 0;

        // frequency of the smallest element
        int first = 0;

        // to check if the smallest
        // element have maximum frequency or not
        int flag = 0;

        // Iterate in the string and count frequency
        for (int i = 0; i < 26; i++) {
            n += freq[i];

            // to store frequency of smallest element
            if (freq[i] != 0 && flag == 0) {
                first = freq[i];
                flag = 1;
            }

            // to store maximum frequency
            if (max_freq < freq[i]) {
                max_freq = freq[i];
            }
        }

        // if sum of frequency of all element if 0
        if (n == 0) {
            return 0;
        }

        // if frequency of smallest character
        // if largest frequency
        if (first != max_freq) {
            flag = 1;
        } else {
            flag = 0;
        }

        return Math.Min((n - 1) / 2, n - max_freq - flag);
    }

// Function that counts the frequency of
// each element
    static void solve(String s) {
        // array to store the frequency of each character
        int []freq = new int[26];

        // loop to calculate frequency of
        // each character in the given string
        for (int i = 0; i < s.Length; i++) {
            freq[s[i] - 'a']++;
        }

        Console.Write(solve(freq));
    }

// Driver Code
    public static void Main() {
        String s = "geeks";

        solve(s);

    }
}
// This code is contributed by Rajput-JI

PHP

<?php
// PHP program to find maximum count of such
// characters which are greater its left and
// right character in any permutation
// of the string

// function to find maximum maximal
// character in the string
function Solve_1($freq)
{
    // to store sum of all frequency
    $n = 0;

    // to store maximum frequency
    $max_freq = 0;

    // to check if the smallest element
    // have maximum frequency or not
    $flag = 0;

    // Iterate in the string
    // and count frequency
    for($i = 0; $i < 26; $i++)
    {
        $n += $freq[$i];

        // to store frequency of
        // smallest element
        if ($freq[$i] != 0 and $flag == 0)
        {
            $first = $freq[$i];
            $flag = 1;
        }

        // to store maximum frequency
        if ($max_freq < $freq[$i])
            $max_freq = $freq[$i];
    }

    // if sum of frequency of
    // all element if 0
    if ($n == 0)
        return 0;

    // if frequency of smallest character
    // if largest frequency
    if ($first != $max_freq)
        $flag = 1;
    else
        $flag = 0;

    return min(($n - 1) / 2,
                $n - $max_freq - $flag);
}

// Function that counts the
// frequency of each element
function solve($s)
{
    // array to store the frequency
    // of each character initialize
    // frequency of all character with 0
    $freq = array_fill(0, 26, 0);

    // loop to calculate frequency of
    // each character in the given string
    for($i = 0; $i < strlen($s); $i++)

        $freq[ord($s[$i]) - ord('a')] += 1;

    print(Solve_1($freq));
}

// Driver Code
$s = "geeks";
solve($s);

// This code is contributed
// by mits
?>

Javascript

<script>
// Javascript program to find maximum count
// of such characters which are greater
// its left and right character in
// any permutation of the string only three characters

    // function to find maximum maximal character in the string
    function solve1(freq)
    {
        // to store sum of all frequency
        let n = 0;

        // to store maximum frequency
        let max_freq = 0;

        // frequency of the smallest element
        let first = 0;

        // to check if the smallest
        // element have maximum frequency or not
        let flag = 0;

        // Iterate in the string and count frequency
        for (let i = 0; i < 26; i++) {
            n += freq[i];

            // to store frequency of smallest element
            if (freq[i] != 0 && flag == 0) {
                first = freq[i];
                flag = 1;
            }

            // to store maximum frequency
            if (max_freq < freq[i]) {
                max_freq = freq[i];
            }
        }

        // if sum of frequency of all element if 0
        if (n == 0) {
            return 0;
        }

        // if frequency of smallest character
        // if largest frequency
        if (first != max_freq) {
            flag = 1;
        } else {
            flag = 0;
        }

        return Math.min(Math.floor((n - 1) / 2), n - max_freq - flag);
    }

    // Function that counts the frequency of
    // each element
    function solve(s)
    {
        // array to store the frequency of each character
        let freq = new Array(26);
        for(let i=0;i<26;i++)
        {
            freq[i]=0;
        }

        // loop to calculate frequency of
        // each character in the given string
        for (let i = 0; i < s.length; i++) {

            freq[s[i].charCodeAt(0) - 'a'.charCodeAt(0)]++;
        }

        document.write(solve1(freq));
    }

    // Driver Code
    let s = "geeks";

    solve(s);


// This code is contributed by avanitrachhadiya2155
</script>

Output

2

Complexity Analysis:

• Time Complexity: O(n), where n is the size of the given string
• Auxiliary Space: O(26)