Given a non-empty string S of uppercase alphabets of length L the task is to find the longest string from the given string with characters arranged in descending order of their ASCII code and in arithmetic progression such that the common difference should be as low as possible and the characters of the string to be of higher ASCII value.
Note: The string contains a minimum of three different characters.
Examples:
Input : S = “ABCPQR”
Output : “RQP”
Two strings of maximum length are possible – “CBA” and “RPQ”. But since the string should be of higher ASCII value hence, the output is “RPQ”.Input : S = “ADGJPRT”
Output : “JGDA”
Approach:
The maximum possible common difference for minimum 3 characters to be in arithmetic progression is 12. Hence, precompute all characters that are present in the string using a hashmap and then iterate from the character having maximum ASCII value i.e. ‘Z’ to the character having minimum ASCII value i.e. ‘A’. If the current character exists in the given string, consider it as the starting character of the arithmetic progression sequence and iterate again over all possible common differences i.e. from 1 to 12.
check for every current common difference that if the character exists in the given string, increment the current length of the longest required string. Now, there exist two cases when maximum length ans minimum common difference needs to be updated.
- When the current length is more than the maximum length.
- When the current length is equal to the maximum length and current common difference is less than the minimum common difference, then common difference needs to be updated.
Also, at every updation of these two parameters, starting character of the string or arithmetic progression sequence must also be updated.
Below is the implementation of above approach:
// C++ Program to find the longest string // with characters arranged in non-decreasing // order of ASCII and in arithmetic progression #include <bits/stdc++.h> using namespace std;
// Function to find the longest String string findLongestString(string S) { // Stores the maximum length of required string
int maxLen = 0;
// Stores the optimal starting character of
// required string or arithmetic progression sequence
int bestStartChar;
// Stores the optimal i.e. minimum common difference
// of required string
int minCommonDifference = INT_MAX;
unordered_map< char , bool > mp;
for ( int i = 0; i < S.size(); i++)
mp[S[i]] = true ;
// Iterate over the loop in non decreasing order
for ( int startChar = 'Z' ; startChar > 'A' ; startChar--) {
// Process further only if current character
// exists in the given string
if (mp[startChar]) {
// Iterate over all possible common differences
// of AP sequence and update maxLen accordingly
for ( int currDiff = 1; currDiff <= 12; currDiff++) {
int currLen = 1;
// Iterate over the characters at any interval
// of current common difference
for ( int ch = startChar - currDiff; ch >= 'A' ;
ch -= currDiff) {
if (mp[ch])
currLen++;
else
break ;
}
// Update maxLen and other parameters if the currLen
// is greater than maxLen or if the current
// difference is smaller than minCommonDifference
if (currLen > maxLen || (currLen == maxLen
&& currDiff < minCommonDifference)) {
minCommonDifference = currDiff;
maxLen = currLen;
bestStartChar = startChar;
}
}
}
}
string longestString = "" ;
// Store the string in decreasing order of
// arithmetic progression
for ( int i = bestStartChar;
i >= (bestStartChar - (maxLen - 1) * minCommonDifference);
i -= minCommonDifference)
longestString += char (i);
return longestString;
} // Driver Code int main()
{ string S = "ADGJPRT" ;
cout << findLongestString(S) << endl;
return 0;
} |
// Java Program to find the longest string // with characters arranged in non-decreasing // order of ASCII and in arithmetic progression import java.util.*;
import java.lang.*;
public class GFG {
// Function to find the longest String
static String findLongestString(String S)
{
// Stores the maximum length of required string
int maxLen = 0 ;
// Stores the optimal starting character of
// required string or arithmetic progression sequence
int bestStartChar = 0 ;
// Stores the optimal i.e. minimum common difference
// of required string
int minCommonDifference = Integer.MAX_VALUE;
HashMap <Character, Boolean> hm = new HashMap
<Character, Boolean>();
for ( int i = 0 ; i < S.length(); i++)
hm.put(S.charAt(i), true );
// Iterate over the loop in non decreasing order
for ( int startChar = 'Z' ; startChar > 'A' ; startChar--) {
// Process further only if current character
// exists in the given string
if (hm.containsKey(( char )startChar)) {
// Iterate over all possible common differences
// of AP sequence and update maxLen accordingly
for ( int currDiff = 1 ; currDiff <= 12 ; currDiff++) {
int currLen = 1 ;
// Iterate over the characters at any interval
// of current common difference
for ( int ch = startChar - currDiff; ch >= 'A' ;
ch -= currDiff) {
if (hm.containsKey(( char )ch))
currLen++;
else
break ;
}
// Update maxLen and other parameters if the currLen
// is greater than maxLen or if the current
// difference is smaller than minCommonDifference
if (currLen > maxLen || (currLen == maxLen
&& currDiff < minCommonDifference)) {
minCommonDifference = currDiff;
maxLen = currLen;
bestStartChar = startChar;
}
}
}
}
String longestString = "" ;
// Store the string in decreasing order of
// arithmetic progression
char ch;
for ( int i = bestStartChar;
i >= (bestStartChar - (maxLen - 1 ) * minCommonDifference);
i -= minCommonDifference)
{
ch = ( char )i;
longestString += ch;
}
return longestString;
}
// Driver Code
public static void main(String args[])
{
String S = "ADGJPRT" ;
System.out.println(findLongestString(S));
}
} // This code is contributed by Nishant Tanwar |
# Python 3 Program to find the longest string # with characters arranged in non-decreasing # order of ASCII and in arithmetic progression import sys
# Function to find the longest String def findLongestString(S):
# Stores the maximum length of required string
maxLen = 0
# Stores the optimal starting character of
# required string or arithmetic progression sequence
bestStartChar = 0
# Stores the optimal i.e. minimum common difference
# of required string
minCommonDifference = sys.maxsize
mp = {}
for i in range ( len (S)):
mp[S[i]] = True
# Iterate over the loop in non decreasing order
for startChar in range ( ord ( 'Z' ), ord ( 'A' ), - 1 ):
# Process further only if current character
# exists in the given string
if chr (startChar) in mp:
# Iterate over all possible common differences
# of AP sequence and update maxLen accordingly
for currDiff in range ( 1 , 13 ):
currLen = 1
# Iterate over the characters at any interval
# of current common difference
for ch in range (startChar - currDiff, ord ( 'A' ) - 1 , - currDiff):
if ( chr (ch) in mp):
currLen + = 1
else :
break
# Update maxLen and other parameters if the currLen
# is greater than maxLen or if the current
# difference is smaller than minCommonDifference
if (currLen > maxLen or (currLen = = maxLen
and currDiff < minCommonDifference)):
minCommonDifference = currDiff
maxLen = currLen
bestStartChar = startChar
longestString = ""
# Store the string in decreasing order of
# arithmetic progression
for i in range (bestStartChar,
(bestStartChar - (maxLen - 1 ) * minCommonDifference) - 1 , - minCommonDifference):
longestString + = chr (i)
return longestString
# Driver Code if __name__ = = "__main__" :
S = "ADGJPRT"
print (findLongestString(S))
# This code is contributed by ukasp.
|
// C# Program to find the longest string // with characters arranged in non-decreasing // order of ASCII and in arithmetic progression using System;
using System.Collections ;
public class GFG {
// Function to find the longest String
static String findLongestString(String S)
{
// Stores the maximum length of required string
int maxLen = 0;
// Stores the optimal starting character of
// required string or arithmetic progression sequence
int bestStartChar = 0;
// Stores the optimal i.e. minimum common difference
// of required string
int minCommonDifference = Int32.MaxValue ;
Hashtable hm = new Hashtable ();
for ( int i = 0; i < S.Length; i++)
hm.Add(S[i], true );
// Iterate over the loop in non decreasing order
for ( int startChar = 'Z' ; startChar > 'A' ; startChar--) {
// Process further only if current character
// exists in the given string
if (hm.ContainsKey(( char )startChar)) {
// Iterate over all possible common differences
// of AP sequence and update maxLen accordingly
for ( int currDiff = 1; currDiff <= 12; currDiff++) {
int currLen = 1;
// Iterate over the characters at any interval
// of current common difference
for ( int ch = startChar - currDiff; ch >= 'A' ;
ch -= currDiff) {
if (hm.ContainsKey(( char )ch))
currLen++;
else
break ;
}
// Update maxLen and other parameters if the currLen
// is greater than maxLen or if the current
// difference is smaller than minCommonDifference
if (currLen > maxLen || (currLen == maxLen
&& currDiff < minCommonDifference)) {
minCommonDifference = currDiff;
maxLen = currLen;
bestStartChar = startChar;
}
}
}
}
String longestString = "" ;
// Store the string in decreasing order of
// arithmetic progression
char ch1;
for ( int i = bestStartChar;
i >= (bestStartChar - (maxLen - 1) * minCommonDifference);
i -= minCommonDifference)
{
ch1 = ( char )i;
longestString += ch1;
}
return longestString;
}
// Driver Code
public static void Main()
{
String S = "ADGJPRT" ;
Console.WriteLine(findLongestString(S));
}
// This code is contributed by Ryuga
} |
// JavaScript Program to find the longest string // with characters arranged in non-decreasing // order of ASCII and in arithmetic progression // Function to find the longest String function findLongestString(S) {
// Stores the maximum length of required string
let maxLen = 0;
// Stores the optimal starting character of
// required string or arithmetic progression sequence
let bestStartChar;
// Stores the optimal i.e. minimum common difference
// of required string
let minCommonDifference = Number.MAX_SAFE_INTEGER;
let mp = {};
for (let i = 0; i < S.length; i++) {
mp[S[i]] = true ;
}
// Iterate over the loop in non decreasing order
for (let startChar = 'Z' .charCodeAt(0); startChar > 'A' .charCodeAt(0);
startChar--) {
// Process further only if current character
// exists in the given string
if (mp[String.fromCharCode(startChar)]) {
// Iterate over all possible common differences
// of AP sequence and update maxLen accordingly
for (let currDiff = 1; currDiff <= 12; currDiff++) {
let currLen = 1;
// Iterate over the characters at any interval
// of current common difference
for (let ch = startChar - currDiff;
ch >= 'A' .charCodeAt(0); ch -= currDiff) {
if (mp[String.fromCharCode(ch)]) {
currLen++;
} else {
break ;
}
}
// Update maxLen and other parameters if the currLen
// is greater than maxLen or if the current
// difference is smaller than minCommonDifference
if (currLen > maxLen || (currLen === maxLen &&
currDiff < minCommonDifference)) {
minCommonDifference = currDiff;
maxLen = currLen;
bestStartChar = startChar;
}
}
}
}
let longestString = "" ;
// Store the string in decreasing order of
// arithmetic progression
for (let i = bestStartChar; i >= (bestStartChar -
(maxLen - 1) * minCommonDifference); i -= minCommonDifference) {
longestString += String.fromCharCode(i);
}
return longestString;
} // Driver Code console.log(findLongestString( "ADGJPRT" ));
|
JGDA
Time Complexity : O(|S| + 26*12*26), where |S| is the size of the string.
Space complexity : O(1) as the maximum size of unordered_map “mp” is 26 (for 26 characters in the English alphabet), and the size of the variables “maxLen”, “bestStartChar”, and “minCommonDifference” are constant.