# Split the given string into Odds: Digit DP

• Last Updated : 09 Dec, 2021

Prerequisites: Digit-DP
Given string str that represents a large number, the task is to find the minimum number of segments the given string can be divided such that each segment is an odd number in the range of 1 to 109.
Examples:

Input: str = “123456789123456789123”
Output:
Explanation:
The number can be divided as {123456789, 123456789, 123}
Input: str = “123456”
Output: -1
Explanation:
We can’t split the given number such that all segments are odd.

Approach: The idea is to use dynamic programming with the help of digit-dp concept to solve this problem. Therefore, a splitDP[] array is defined where splitDP[i] denotes the minimum number of splits required in the prefix string of length â€˜iâ€™ to break it into the odd subdivision.
The splitDP[] array is filled in the following way:

• A loop is used to iterate through all the indices of the given string.
• For every index â€˜iâ€™ from the above loop, another loop is iterated from 1 to 9 to check if the substring from (i + j)th index is Odd or not.
• If it forms a Odd number, then the value at splitDP[] is updated as:
`splitDP[i + j] = min(splitDP[i + j], 1 + splitDP[i]);`
• After updating all the values of the array, the value at the last index is the minimum number of splits for the entire string.

Below is the implementation of the above approach:

## C++

 `// C++ program to split the given string into odds``#include ``using` `namespace` `std;` `// Function to check whether a string``// is an odd number or not``bool` `checkOdd(string number)``{``    ``int` `n = number.length();` `    ``int` `num = number[n - 1] - ``'0'``;` `    ``return` `(num & 1);``}` `// A function to find the minimum``// number of segments the given string``// can be divided such that every``// segment is a odd number``int` `splitIntoOdds(string number)``{``    ``int` `numLen = number.length();` `    ``// Declare a splitdp[] array``    ``// and initialize to -1``    ``int` `splitDP[numLen + 1];``    ``memset``(splitDP, -1, ``sizeof``(splitDP));` `    ``// Build the DP table in``    ``// a bottom-up manner``    ``for` `(``int` `i = 1; i <= numLen; i++) {` `        ``// Initially Check if the entire prefix is odd``        ``if` `(i <= 9 && checkOdd(number.substr(0, i)))``            ``splitDP[i] = 1;` `        ``// If the Given Prefix can be split into Odds``        ``// then for the remaining string from i to j``        ``// Check if Odd. If yes calculate``        ``// the minimum split till j``        ``if` `(splitDP[i] != -1) {``            ``for` `(``int` `j = 1; j <= 9``                            ``&& i + j <= numLen;``                 ``j++) {` `                ``// To check if the substring from i to j``                ``// is a odd number or not``                ``if` `(checkOdd(number.substr(i, j))) {` `                    ``// If it is an odd number,``                    ``// then update the dp array``                    ``if` `(splitDP[i + j] == -1)``                        ``splitDP[i + j] = 1 + splitDP[i];` `                    ``else``                        ``splitDP[i + j] = min(splitDP[i + j],``                                             ``1 + splitDP[i]);``                ``}``            ``}``        ``}``    ``}` `    ``// Return the minimum number of splits``    ``// for the entire string``    ``return` `splitDP[numLen];``}` `// Driver code``int` `main()``{``    ``cout << splitIntoOdds(``"123456789123456789123"``) << ``"\n"``;``    ``return` `0;``}`

## Java

 `// Java program to split the given string into odds``class` `GFG {` `    ``// Function to check whether a string``    ``// is an odd number or not``    ``static` `int` `checkOdd(String number)``    ``{``        ``int` `n = number.length();``    ` `        ``int` `num = number.charAt(n - ``1``) - ``'0'``;``    ` `        ``return` `(num & ``1``);``    ``}` `    ``// A function to find the minimum``    ``// number of segments the given string``    ``// can be divided such that every``    ``// segment is a odd number``    ``static` `int` `splitIntoOdds(String number)``    ``{``        ``int` `numLen = number.length();``    ` `        ``// Declare a splitdp[] array``        ``// and initialize to -1``        ``int` `splitDP[] = ``new` `int``[numLen + ``1``];``        ` `        ``for``(``int` `i= ``0``; i < numLen + ``1``; i++)``            ``splitDP[i] = -``1``;``            ` `        ``// Build the DP table in``        ``// a bottom-up manner``        ``for` `(``int` `i = ``1``; i <= numLen; i++) {``    ` `            ``// Initially Check if the entire prefix is odd``            ``if` `(i <= ``9` `&& (checkOdd(number.substring(``0``, i)) == ``1``))``                ``splitDP[i] = ``1``;``    ` `            ``// If the Given Prefix can be split into Odds``            ``// then for the remaining string from i to j``            ``// Check if Odd. If yes calculate``            ``// the minimum split till j``            ``if` `(splitDP[i] != -``1``) {``                ``for` `(``int` `j = ``1``; j <= ``9``                                ``&& i + j <= numLen;``                    ``j++) {``    ` `                    ``// To check if the substring from i to j``                    ``// is a odd number or not``                    ``if` `(checkOdd(number.substring(i, i + j)) == ``1``) {``    ` `                        ``// If it is an odd number,``                        ``// then update the dp array``                        ``if` `(splitDP[i + j] == -``1``)``                            ``splitDP[i + j] = ``1` `+ splitDP[i];``    ` `                        ``else``                            ``splitDP[i + j] = Math.min(splitDP[i + j],``                                                ``1` `+ splitDP[i]);``                    ``}``                ``}``            ``}``        ``}``    ` `        ``// Return the minimum number of splits``        ``// for the entire string``        ``return` `splitDP[numLen];``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``System.out.println(splitIntoOdds(``"123456789123456789123"``));``    ``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 program to split the given string into odds` `# Function to check whether a string``# is an odd number or not``def` `checkOdd(number):``    ``n ``=` `len``(number)``    ``num ``=` `ord``(number[n ``-` `1``]) ``-` `48``    ``return` `(num & ``1``)` `# A function to find the minimum``# number of segments the given string``# can be divided such that every``# segment is a odd number``def` `splitIntoOdds(number):``    ``numLen ``=` `len``(number)``    ` `    ``# Declare a splitdp[] array``    ``# and initialize to -1``    ``splitDP ``=` `[``-``1` `for` `i ``in` `range``(numLen ``+` `1``)]` `    ``# Build the DP table in``    ``# a bottom-up manner``    ``for` `i ``in` `range``(``1``, numLen ``+` `1``):` `        ``# Initially Check if the entire prefix is odd``        ``if` `(i <``=` `9` `and` `checkOdd(number[``0``:i]) > ``0``):``            ``splitDP[i] ``=` `1` `        ``# If the Given Prefix can be split into Odds``        ``# then for the remaining string from i to j``        ``# Check if Odd. If yes calculate``        ``# the minimum split till j``        ``if` `(splitDP[i] !``=` `-``1``):``            ``for` `j ``in` `range``(``1``, ``10``):``                ``if``(i ``+` `j > numLen):``                    ``break``;` `                ``# To check if the substring from i to j``                ``# is a odd number or not``                ``if` `(checkOdd(number[i:i ``+` `j])):``                    ` `                    ``# If it is an odd number,``                    ``# then update the dp array``                    ``if` `(splitDP[i ``+` `j] ``=``=` `-``1``):``                        ``splitDP[i ``+` `j] ``=` `1` `+` `splitDP[i]``                    ``else``:``                        ``splitDP[i ``+` `j] ``=` `min``(splitDP[i ``+` `j], ``1` `+` `splitDP[i])` `    ``# Return the minimum number of splits``    ``# for the entire string``    ``return` `splitDP[numLen]` `# Driver code``print``(splitIntoOdds(``"123456789123456789123"``))` `# This code is contributed by Sanjit_Prasad`

## C#

 `// C# program to split the given string into odds``using` `System;` `class` `GFG {` `    ``// Function to check whether a string``    ``// is an odd number or not``    ``static` `int` `checkOdd(``string` `number)``    ``{``        ``int` `n = number.Length;``    ` `        ``int` `num = number[n - 1] - ``'0'``;``    ` `        ``return` `(num & 1);``    ``}` `    ``// A function to find the minimum``    ``// number of segments the given string``    ``// can be divided such that every``    ``// segment is a odd number``    ``static` `int` `splitIntoOdds(``string` `number)``    ``{``        ``int` `numLen = number.Length;``    ` `        ``// Declare a splitdp[] array``        ``// and initialize to -1``        ``int` `[]splitDP = ``new` `int``[numLen + 1];``        ` `        ``for``(``int` `i= 0; i < numLen + 1; i++)``            ``splitDP[i] = -1;``            ` `        ``// Build the DP table in``        ``// a bottom-up manner``        ``for` `(``int` `i = 1; i <= numLen; i++) {``    ` `            ``// Initially Check if the entire prefix is odd``            ``if` `(i <= 9 && (checkOdd(number.Substring(0, i)) == 1))``                ``splitDP[i] = 1;``    ` `            ``// If the Given Prefix can be split into Odds``            ``// then for the remaining string from i to j``            ``// Check if Odd. If yes calculate``            ``// the minimum split till j``            ``if` `(splitDP[i] != -1) {``                ``for` `(``int` `j = 1; j <= 9``                                ``&& i + j <= numLen;``                    ``j++) {``    ` `                    ``// To check if the substring from i to j``                    ``// is a odd number or not``                    ``if` `(checkOdd(number.Substring(i, j)) == 1) {``    ` `                        ``// If it is an odd number,``                        ``// then update the dp array``                        ``if` `(splitDP[i + j] == -1)``                            ``splitDP[i + j] = 1 + splitDP[i];``    ` `                        ``else``                            ``splitDP[i + j] = Math.Min(splitDP[i + j],``                                                ``1 + splitDP[i]);``                    ``}``                ``}``            ``}``        ``}``    ` `        ``// Return the minimum number of splits``        ``// for the entire string``        ``return` `splitDP[numLen];``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main (``string``[] args)``    ``{``        ``Console.WriteLine(splitIntoOdds(``"123456789123456789123"``));``    ``}``}` `// This code is contributed by AnkitRai01`

## Javascript

 ``

Output:

`3`

Time Complexity: O(N)

Auxiliary Space: O(numLen)

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