# Partition the digits of an integer such that it satisfies a given condition

Given an integer X, the task is to partition its digit into two groups either A or B such that the sequence of digits is non decreasing when all the digits of group A are arranged followed by all the digits of group B from left to right as they appear in X. Print -1 if no such partition is possible or else return a string S of the same length as X where S[i] is either A or B.

Examples:

Input: X = 5164
Output: BABA
The digits in group A are 1 and 4 and in group B are 5 and 6. This partition satisfies the condition as when all the digits of A are written and then all the digits of B are written as they appear in X from left to right, the sequence is non-decreasing, i.e., 1456.

Input: X = 654
Output: -1
No such partition is possible that may result in non-decreasing sequence. For example, if we consider BBA and write the sequence, it turns out 465. Similarly for BAA, it is 546. and for AAA it is 654.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. Let us assume a digit D so that all digits less than D goes to group A and all the digits greater than D goes to group B.
2. For the digits equal to D, it will go to group A only if any digit of group B is present before it otherwise it will go to group B.
3. After such partition, check if it forms a non decreasing sequence. Otherwise try for some different D.
4. The value of D ranges from 0 to 9.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to generate sequence ` `// from the given string ` `vector<``int``> makeSeq(string s, ``int` `a[]) ` `{ ` `    ``// Initialize vector to ` `    ``// store sequence ` `    ``vector<``int``> seq; ` ` `  `    ``// First add all the digits ` `    ``// of group A from left to right ` `    ``for` `(``int` `i = 0; i < s.size(); i++) ` `        ``if` `(s[i] == ``'A'``) ` `            ``seq.push_back(a[i]); ` ` `  `    ``// Then add all the digits ` `    ``// of group B from left to right ` `    ``for` `(``int` `i = 0; i < s.size(); i++) ` `        ``if` `(s[i] == ``'B'``) ` `            ``seq.push_back(a[i]); ` ` `  `    ``// Return the sequence ` `    ``return` `seq; ` `} ` ` `  `// Function that returns true if ` `// the sequence is non-decreasing ` `bool` `checkSeq(vector<``int``> v) ` `{ ` `    ``// Initialize result ` `    ``bool` `check = ``true``; ` ` `  `    ``for` `(``int` `i = 1; i < v.size(); i++) ` `        ``if` `(v[i] < v[i - 1]) ` `            ``check = ``false``; ` ` `  `    ``return` `check; ` `} ` ` `  `// Function to partition the digits ` `// of an integer such that it satisfies ` `// the given conditions ` `string digitPartition(``int` `X) ` `{ ` `    ``// Convert the integer to string ` `    ``string num = to_string(X); ` ` `  `    ``// Length of the string ` `    ``int` `l = num.size(); ` ` `  `    ``// Array to store the digits ` `    ``int` `a[l]; ` ` `  `    ``// Storing the digits of X in array ` `    ``for` `(``int` `i = 0; i < l; i++) ` `        ``a[i] = (num[i] - ``'0'``); ` ` `  `    ``for` `(``int` `D = 0; D < 10; D++) { ` ` `  `        ``// Initialize the result ` `        ``string res = ``""``; ` ` `  `        ``// Loop through the digits ` `        ``for` `(``int` `i = 0; i < l; i++) { ` ` `  `            ``// Put into group A if ` `            ``// digit less than D ` `            ``if` `(a[i] < D) ` `                ``res += ``'A'``; ` ` `  `            ``// Put into group B if ` `            ``// digit greater than D ` `            ``else` `if` `(a[i] > D) ` `                ``res += ``'B'``; ` ` `  `            ``// Put into group C if ` `            ``// digit equal to D ` `            ``else` `                ``res += ``'C'``; ` `        ``} ` ` `  `        ``bool` `flag = ``false``; ` ` `  `        ``// Loop through the digits ` `        ``// to decide for group C digits ` `        ``for` `(``int` `i = 0; i < l; i++) { ` ` `  `            ``// Set flag equal to true ` `            ``// if group B digit present ` `            ``if` `(res[i] == ``'B'``) ` `                ``flag = ``true``; ` ` `  `            ``// If flag is true put in ` `            ``// group A or else put in B ` `            ``if` `(res[i] == ``'C'``) ` `                ``res[i] = flag ? ``'A'` `: ``'B'``; ` `        ``} ` ` `  `        ``// Generate the sequence from partition ` `        ``vector<``int``> seq = makeSeq(res, a); ` ` `  `        ``// Check if the sequence is ` `        ``// non decreasing ` `        ``if` `(checkSeq(seq)) ` `            ``return` `res; ` `    ``} ` ` `  `    ``// Return -1 if no such ` `    ``// partition is possible ` `    ``return` `"-1"``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `X = 777147777; ` ` `  `    ``cout << digitPartition(X); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to generate sequence ` `// from the given String ` `static` `Vector makeSeq(String s, ``int` `a[]) ` `{ ` `    ``// Initialize vector to ` `    ``// store sequence ` `    ``Vector seq = ``new` `Vector(); ` ` `  `    ``// First add all the digits ` `    ``// of group A from left to right ` `    ``for` `(``int` `i = ``0``; i < s.length(); i++) ` `        ``if` `(s.charAt(i) == ``'A'``) ` `            ``seq.add(a[i]); ` ` `  `    ``// Then add all the digits ` `    ``// of group B from left to right ` `    ``for` `(``int` `i = ``0``; i < s.length(); i++) ` `        ``if` `(s.charAt(i) == ``'B'``) ` `            ``seq.add(a[i]); ` ` `  `    ``// Return the sequence ` `    ``return` `seq; ` `} ` ` `  `// Function that returns true if ` `// the sequence is non-decreasing ` `static` `boolean` `checkSeq(Vector v) ` `{ ` `    ``// Initialize result ` `    ``boolean` `check = ``true``; ` ` `  `    ``for` `(``int` `i = ``1``; i < v.size(); i++) ` `        ``if` `(v.get(i) < v.get(i - ``1``)) ` `            ``check = ``false``; ` ` `  `    ``return` `check; ` `} ` ` `  `// Function to partition the digits ` `// of an integer such that it satisfies ` `// the given conditions ` `static` `String digitPartition(``int` `X) ` `{ ` `    ``// Convert the integer to String ` `    ``String num = String.valueOf(X); ` ` `  `    ``// Length of the String ` `    ``int` `l = num.length(); ` ` `  `    ``// Array to store the digits ` `    ``int` `[]a = ``new` `int``[l]; ` ` `  `    ``// Storing the digits of X in array ` `    ``for` `(``int` `i = ``0``; i < l; i++) ` `        ``a[i] = (num.charAt(i) - ``'0'``); ` ` `  `    ``for` `(``int` `D = ``0``; D < ``10``; D++)  ` `    ``{ ` ` `  `        ``// Initialize the result ` `        ``String res = ``""``; ` ` `  `        ``// Loop through the digits ` `        ``for` `(``int` `i = ``0``; i < l; i++)  ` `        ``{ ` ` `  `            ``// Put into group A if ` `            ``// digit less than D ` `            ``if` `(a[i] < D) ` `                ``res += ``'A'``; ` ` `  `            ``// Put into group B if ` `            ``// digit greater than D ` `            ``else` `if` `(a[i] > D) ` `                ``res += ``'B'``; ` ` `  `            ``// Put into group C if ` `            ``// digit equal to D ` `            ``else` `                ``res += ``'C'``; ` `        ``} ` ` `  `        ``boolean` `flag = ``false``; ` ` `  `        ``// Loop through the digits ` `        ``// to decide for group C digits ` `        ``for` `(``int` `i = ``0``; i < l; i++)  ` `        ``{ ` ` `  `            ``// Set flag equal to true ` `            ``// if group B digit present ` `            ``if` `(res.charAt(i) == ``'B'``) ` `                ``flag = ``true``; ` ` `  `            ``// If flag is true put in ` `            ``// group A or else put in B ` `            ``if` `(res.charAt(i) == ``'C'``) ` `                ``res = res.substring(``0``, i) +  ` `                ``(flag ? ``'A'` `: ``'B'``) + res.substring(i + ``1``); ` `        ``} ` ` `  `        ``// Generate the sequence from partition ` `        ``Vector seq = makeSeq(res, a); ` ` `  `        ``// Check if the sequence is ` `        ``// non decreasing ` `        ``if` `(checkSeq(seq)) ` `            ``return` `res; ` `    ``} ` ` `  `    ``// Return -1 if no such ` `    ``// partition is possible ` `    ``return` `"-1"``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `X = ``777147777``; ` ` `  `    ``System.out.print(digitPartition(X)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# Function to generate sequence  ` `# from the given string  ` `def` `makeSeq(s, a) :  ` ` `  `    ``# Initialize vector to  ` `    ``# store sequence  ` `    ``seq ``=` `[];  ` ` `  `    ``# First add all the digits  ` `    ``# of group A from left to right  ` `    ``for` `i ``in` `range``(``len``(s)) : ` `        ``if` `(s[i] ``=``=` `'A'``) : ` `            ``seq.append(a[i]);  ` ` `  `    ``# Then add all the digits  ` `    ``# of group B from left to right  ` `    ``for` `i ``in` `range``(``len``(s)) : ` `        ``if` `(s[i] ``=``=` `'B'``) : ` `            ``seq.append(a[i]);  ` ` `  `    ``# Return the sequence  ` `    ``return` `seq;  ` ` `  `# Function that returns true if  ` `# the sequence is non-decreasing  ` `def` `checkSeq(v) :  ` ` `  `    ``# Initialize result  ` `    ``check ``=` `True``;  ` ` `  `    ``for` `i ``in` `range``(``1``, ``len``(v)) : ` `        ``if` `(v[i] < v[i ``-` `1``]) : ` `            ``check ``=` `False``;  ` ` `  `    ``return` `check;  ` ` `  `# Function to partition the digits  ` `# of an integer such that it satisfies  ` `# the given conditions  ` `def` `digitPartition(X) :  ` `     `  `    ``# Convert the integer to string  ` `    ``num ``=` `str``(X);  ` ` `  `    ``# Length of the string  ` `    ``l ``=` `len``(num);  ` ` `  `    ``# Array to store the digits  ` `    ``a ``=` `[``0``]``*``l;  ` ` `  `    ``# Storing the digits of X in array  ` `    ``for` `i ``in` `range``(l) :  ` `        ``a[i] ``=` `(``ord``(num[i]) ``-` `ord``(``'0'``));  ` ` `  `    ``for` `D ``in` `range``(``10``) : ` ` `  `        ``# Initialize the result  ` `        ``res ``=` `"";  ` ` `  `        ``# Loop through the digits  ` `        ``for` `i ``in` `range``(l) :  ` ` `  `            ``# Put into group A if  ` `            ``# digit less than D  ` `            ``if` `(a[i] < D) : ` `                ``res ``+``=` `'A'``;  ` ` `  `            ``# Put into group B if  ` `            ``# digit greater than D  ` `            ``elif` `(a[i] > D) : ` `                ``res ``+``=` `'B'``;  ` ` `  `            ``# Put into group C if  ` `            ``# digit equal to D  ` `            ``else` `: ` `                ``res ``+``=` `'C'``;  ` ` `  `        ``flag ``=` `False``;  ` ` `  `        ``# Loop through the digits  ` `        ``# to decide for group C digits  ` `        ``for` `i ``in` `range``(l) : ` ` `  `            ``# Set flag equal to true  ` `            ``# if group B digit present  ` `            ``if` `(res[i] ``=``=` `'B'``) : ` `                ``flag ``=` `True``;  ` ` `  `            ``# If flag is true put in  ` `            ``# group A or else put in B  ` `            ``res ``=` `list``(res); ` `             `  `            ``if` `(res[i] ``=``=` `'C'``) : ` `                ``res[i] ``=` `'A'` `if` `flag ``else` `'B'``;  ` ` `  `        ``# Generate the sequence from partition  ` `        ``seq ``=` `makeSeq(res, a);  ` ` `  `        ``# Check if the sequence is  ` `        ``# non decreasing  ` `        ``if` `(checkSeq(seq)) : ` `            ``return` `"".join(res);  ` ` `  `    ``# Return -1 if no such  ` `    ``# partition is possible  ` `    ``return` `"-1"``;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``X ``=` `777147777``;  ` ` `  `    ``print``(digitPartition(X));  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to generate sequence ` `// from the given String ` `static` `List<``int``> makeSeq(String s, ``int` `[]a) ` `{ ` `    ``// Initialize vector to ` `    ``// store sequence ` `    ``List<``int``> seq = ``new` `List<``int``>(); ` ` `  `    ``// First add all the digits ` `    ``// of group A from left to right ` `    ``for` `(``int` `i = 0; i < s.Length; i++) ` `        ``if` `(s[i] == ``'A'``) ` `            ``seq.Add(a[i]); ` ` `  `    ``// Then add all the digits ` `    ``// of group B from left to right ` `    ``for` `(``int` `i = 0; i < s.Length; i++) ` `        ``if` `(s[i] == ``'B'``) ` `            ``seq.Add(a[i]); ` ` `  `    ``// Return the sequence ` `    ``return` `seq; ` `} ` ` `  `// Function that returns true if ` `// the sequence is non-decreasing ` `static` `bool` `checkSeq(List<``int``> v) ` `{ ` `    ``// Initialize result ` `    ``bool` `check = ``true``; ` ` `  `    ``for` `(``int` `i = 1; i < v.Count; i++) ` `        ``if` `(v[i] < v[i - 1]) ` `            ``check = ``false``; ` ` `  `    ``return` `check; ` `} ` ` `  `// Function to partition the digits ` `// of an integer such that it satisfies ` `// the given conditions ` `static` `String digitPartition(``int` `X) ` `{ ` `    ``// Convert the integer to String ` `    ``String num = String.Join(``""``,X); ` ` `  `    ``// Length of the String ` `    ``int` `l = num.Length; ` ` `  `    ``// Array to store the digits ` `    ``int` `[]a = ``new` `int``[l]; ` ` `  `    ``// Storing the digits of X in array ` `    ``for` `(``int` `i = 0; i < l; i++) ` `        ``a[i] = (num[i] - ``'0'``); ` ` `  `    ``for` `(``int` `D = 0; D < 10; D++)  ` `    ``{ ` ` `  `        ``// Initialize the result ` `        ``String res = ``""``; ` ` `  `        ``// Loop through the digits ` `        ``for` `(``int` `i = 0; i < l; i++)  ` `        ``{ ` ` `  `            ``// Put into group A if ` `            ``// digit less than D ` `            ``if` `(a[i] < D) ` `                ``res += ``'A'``; ` ` `  `            ``// Put into group B if ` `            ``// digit greater than D ` `            ``else` `if` `(a[i] > D) ` `                ``res += ``'B'``; ` ` `  `            ``// Put into group C if ` `            ``// digit equal to D ` `            ``else` `                ``res += ``'C'``; ` `        ``} ` ` `  `        ``bool` `flag = ``false``; ` ` `  `        ``// Loop through the digits ` `        ``// to decide for group C digits ` `        ``for` `(``int` `i = 0; i < l; i++)  ` `        ``{ ` ` `  `            ``// Set flag equal to true ` `            ``// if group B digit present ` `            ``if` `(res[i] == ``'B'``) ` `                ``flag = ``true``; ` ` `  `            ``// If flag is true put in ` `            ``// group A or else put in B ` `            ``if` `(res[i] == ``'C'``) ` `                ``res = res.Substring(0, i) +  ` `                ``(flag ? ``'A'` `: ``'B'``) + res.Substring(i + 1); ` `        ``} ` ` `  `        ``// Generate the sequence from partition ` `        ``List<``int``> seq = makeSeq(res, a); ` ` `  `        ``// Check if the sequence is ` `        ``// non decreasing ` `        ``if` `(checkSeq(seq)) ` `            ``return` `res; ` `    ``} ` ` `  `    ``// Return -1 if no such ` `    ``// partition is possible ` `    ``return` `"-1"``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `    ``int` `X = 777147777; ` ` `  `    ``Console.Write(digitPartition(X)); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

Output:

```BBBAABBBB
```

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