Given a string s of length N consisting of digits from 0 to 9. Find the lexicographically minimum sequence that can be obtained from given string s by performing the given operations:
- Selecting any position i in the string and delete the digit ‘d‘ at ithposition,
- Insert min(d+1, 9) on any position in the string s.
Examples:
Input: s = ” 5217 “
Output: s = ” 1367 “
Explanation:
Choose 0thposition, d = 5 and insert 6 i.e. min(d+1, 9) between 1 and 7 in string; s = ” 2167 “
Choose 0thposition, d = 2 and insert 3 i.e. min(d+1, 9) between 1 and 6 in string; s = ” 1367 “Input: s = ” 09412 “
Output: s = ” 01259 “
Explanation:
Choose 1stposition, d = 9 and insert 9 i.e. min(d+1, 9) at last of string; s = ” 04129 “
Choose 1st position, d = 4 and insert 5 i.e. min(d+1, 9) between 2 and 9 in string; s = ” 0 1 2 5 9 “
Approach: Implement the idea below to solve the problem:
At each position i, we check if there is any digit sj such that sj < si and j > i. As we need the lexicographically minimum string, we need to bring the jthdigit ahead of ithdigit. So delete the ith digit and insert min(si+1, 9) behind the jthdigit. Otherwise, if no lesser digits are present ahead of ith digit, keep the digit as it is and don’t perform the operation.
Follow the below steps to implement the above idea:
- Create a suffix vector to store the minimum digit in the right part of ith position in the string.
- Run a loop from N-2 to 0 and store the minimal digit found till index i from the end. [This can be done by storing suf[i] = min( suf[i+1], s[i] ) ].
- Create a result vector that will store the digits that will be present in the final lexicographically minimum string.
- Traverse for each position from i = 0 to N-1 in the string and check if there is any digit less than the current digit (d = s[i]-‘0’) on the right side:
- If yes then push min(d+1, 9) in result.
- Else push (d) in the result.
- Sort the vector result and print the values [Because we can easily arrange them in that way as there is no constraint on how many times we can perform the operation].
Below is the implementation of the above approach:
// C++ code to implement the approach #include <bits/stdc++.h> using namespace std;
// Function to print the minimum // string after operation string minimumSequence(string& s) { int n = s.size();
vector< int > suf(n);
string sol = "" ;
// Storing values in suf
suf[n - 1] = s[n - 1] - '0' ;
for ( int i = n - 2; i >= 0; i--)
suf[i] = min(suf[i + 1], s[i] - '0' );
// Storing values of final sequence
// after performing given operation
vector< int > res;
for ( int i = 0; i < n; i++) {
// If smaller element is present
// beyond index i
if (suf[i] < s[i] - '0' )
res.push_back(min(9, s[i] - '0' + 1));
else
res.push_back(s[i] - '0' );
}
// Sort the res in increasing order
sort(res.begin(), res.end());
for ( int x : res)
sol += char (x + '0' );
return sol;
} // Driver code int main()
{ string s = "09412" ;
// Function call
cout << minimumSequence(s);
return 0;
} |
// Java code to implement the approach import java.io.*;
import java.util.*;
class GFG {
static String MinimumSequence(String s)
{
int n = s.length();
int [] suf = new int [n];
String sol = "" ;
// Storing values in suf
suf[n - 1 ] = s.charAt(n - 1 ) - '0' ;
for ( int i = n - 2 ; i >= 0 ; i--)
suf[i]
= Math.min(suf[i + 1 ], s.charAt(i) - '0' );
// Storing values of final sequence
// after performing given operation
int [] res = new int [n];
for ( int i = 0 ; i < n; i++) {
// If smaller element is present
// beyond index i
if (suf[i] < s.charAt(i) - '0' )
res[i] = Math.min( 9 , s.charAt(i) - '0' + 1 );
else
res[i] = s.charAt(i) - '0' ;
}
// Sort the res in increasing order
Arrays.sort(res);
for ( int i = 0 ; i < res.length; i++) {
sol += res[i];
}
return sol;
}
public static void main(String[] args)
{
String s = "09412" ;
// Function call
System.out.println(MinimumSequence(s));
}
} // This code is contributed by lokesh. |
# python3 code to implement the approach # Function to print the minimum # string after operation def minimumSequence(s):
n = len (s)
suf = [ 0 for _ in range (n)]
sol = ""
# Storing values in suf
suf[n - 1 ] = ord (s[n - 1 ]) - ord ( '0' )
for i in range (n - 2 , - 1 , - 1 ):
suf[i] = min (suf[i + 1 ], ord (s[i]) - ord ( '0' ))
# Storing values of final sequence
# after performing given operation
res = []
for i in range ( 0 , n):
# If smaller element is present
# beyond index i
if (suf[i] < ord (s[i]) - ord ( '0' )):
res.append( min ( 9 , ord (s[i]) - ord ( '0' ) + 1 ))
else :
res.append( ord (s[i]) - ord ( '0' ))
# Sort the res in increasing order
res.sort()
for x in res:
sol + = str (x)
return sol
# Driver code if __name__ = = "__main__" :
s = "09412"
# Function call
print (minimumSequence(s))
# This code is contributed by rakeshsahni
|
//c# code implementation using System;
using System.Linq;
public class GFG {
static string MinimumSequence( string s)
{
int n = s.Length;
int [] suf = new int [n];
string sol = "" ;
// Storing values in suf
suf[n - 1] = s[n - 1] - '0' ;
for ( int i = n - 2; i >= 0; i--)
suf[i] = Math.Min(suf[i + 1], s[i] - '0' );
// Storing values of final sequence
// after performing given operation
int [] res = new int [n];
for ( int i = 0; i < n; i++) {
// If smaller element is present
// beyond index i
if (suf[i] < s[i] - '0' )
res[i] = Math.Min(9, s[i] - '0' + 1);
else
res[i] = s[i] - '0' ;
}
// Sort the res in increasing order
Array.Sort(res);
for ( int i=0;i<res.Length;i++){
sol += res[i].ToString();
}
return sol;
}
static void Main( string [] args)
{
string s = "09412" ;
// Function call
Console.WriteLine(MinimumSequence(s));
}
} // code by ksam24000 |
// Javascript code to implement the approach // Function to print the minimum // string after operation function minimumSequence(s)
{ let n = s.length;
let suf = new Array(n);
let sol = "" ;
// Storing values in suf
suf[n - 1] = parseInt(s[n - 1]);
for (let i = n - 2; i >= 0; i--)
suf[i] = Math.min(suf[i + 1], parseInt(s[i]));
// Storing values of final sequence
// after performing given operation
let res= [];
for (let i = 0; i < n; i++) {
// If smaller element is present
// beyond index i
if (suf[i] < parseInt(s[i]))
res.push(Math.min(9, parseInt(s[i]) + 1));
else
res.push(parseInt(s[i]));
}
// Sort the res in increasing order
res.sort();
for (let x=0 ; x<res.length; x++)
sol+=res[x];
return sol;
} // Driver code let s = "09412" ;
// Function call
document.write(minimumSequence(s));
|
01259
Time Complexity: O(N * log N)
Auxiliary Space: O(N)
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