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# Nth character in Concatenated Decimal String

If all decimal numbers are concatenated in a string then we will get a string that looks like string P as shown below. We need to tell the Nth character of this string.
P = “12345678910111213141516171819202122232425262728293031….”

Examples:

```N = 10    10th character is 1
N = 11    11th character is 0
N = 50    50th character is 3
N = 190    190th character is 1```

We can solve this problem by breaking the string length-wise. We know that in decimal 9 numbers are of length 1, 90 numbers are of length 2, 900 numbers are of length 3 and so on, so we can skip these numbers according to the given N and can get the desired character.

```Processing for N = 190 is explained below,
P[184..195] = “979899100101”
First getting length of number at N,
190 – 9 = 181        number length is more than 1
181 – 90*2 = 1       number length is more than 2
1 – 900*3 < 0        number length is 3
Now getting actual character at N,
1 character after maximum 2 length number(99) is,  1

Processing for N = 251 is explained below,
P[250..255] = “120121”
First getting length of number at N,
251 - 9 = 242             number length is more than 1
242 – 90*2 = 62           number length is more than 2
62 – 900*3 < 0            number length is 3
Now getting actual character at N,
62 characters after maximum 2 length number(99) is,
Ceil(62/3) = 21,  99 + 21 = 120
120 is the number at N, now getting actual digit,
62%3 = 2,
2nd digit of 120 is 2, so our answer will be 2 only.```

Implementation:

## C++

 `// C++ program to get Nth character in ` `// concatenated Decimal String ` `#include ` `using` `namespace` `std; `   `// Utility method to get dth digit of number N ` `char` `getDigit(``int` `N, ``int` `d) ` `{ ` `    ``string str; ` `    ``stringstream ss; ` `    ``ss << N; ` `    ``ss >> str; ` `    ``return` `str[d - 1]; ` `} `   `// Method to return Nth character in concatenated ` `// decimal string ` `char` `getNthChar(``int` `N) ` `{ ` `    ``// sum will store character escaped till now ` `    ``int` `sum = 0, nine = 9; `   `    ``// dist will store numbers escaped till now ` `    ``int` `dist = 0, len; `   `    ``// loop for number lengths ` `    ``for` `(len = 1; ; len++) ` `    ``{ ` `        ``// nine*len will be incremented characters ` `        ``// and nine will be incremented numbers ` `        ``sum += nine*len; ` `        ``dist += nine; `   `        ``if` `(sum >= N) ` `        ``{ ` `            ``// restore variables to previous correct state ` `            ``sum -= nine*len; ` `            ``dist -= nine; ` `            ``N -= sum; ` `            ``break``; ` `        ``} ` `        ``nine *= 10; ` `    ``} `   `    ``// get distance from last one digit less maximum ` `    ``// number ` `    ``int` `diff = ``ceil``((``double``)N / len); `   `    ``// d will store dth digit of current number ` `    ``int` `d = N % len; ` `    ``if` `(d == 0) ` `        ``d = len; `   `    ``// method will return dth numbered digit ` `    ``// of (dist + diff) number ` `    ``return` `getDigit(dist + diff, d); ` `} `   `// Driver code to test above methods ` `int` `main() ` `{ ` `    ``int` `N = 251; ` `    ``cout << getNthChar(N) << endl; ` `    ``return` `0; ` `} `

## Java

 `// Java program to get Nth character in ` `// concatenated Decimal String `   `class` `GFG` `{` `    `  `// Utility method to get dth digit of number N ` `static` `char` `getDigit(``int` `N, ``int` `d) ` `{ ` `    ``String str=Integer.toString(N);` `    ``return` `str.charAt(d - ``1``); ` `} `   `// Method to return Nth character in concatenated ` `// decimal string ` `static` `char` `getNthChar(``int` `N) ` `{ ` `    ``// sum will store character escaped till now ` `    ``int` `sum = ``0``, nine = ``9``; `   `    ``// dist will store numbers escaped till now ` `    ``int` `dist = ``0``, len; `   `    ``// loop for number lengths ` `    ``for` `(len = ``1``; ; len++) ` `    ``{ ` `        ``// nine*len will be incremented characters ` `        ``// and nine will be incremented numbers ` `        ``sum += nine * len; ` `        ``dist += nine; `   `        ``if` `(sum >= N) ` `        ``{ ` `            ``// restore variables to previous correct state ` `            ``sum -= nine * len; ` `            ``dist -= nine; ` `            ``N -= sum; ` `            ``break``; ` `        ``} ` `        ``nine *= ``10``; ` `    ``} `   `    ``// get distance from last one digit ` `    ``// less maximum number ` `    ``int` `diff = (``int``)(Math.ceil((``double``)(N) / (``double``)(len))); `   `    ``// d will store dth digit of current number ` `    ``int` `d = N % len; ` `    ``if` `(d == ``0``) ` `        ``d = len; `   `    ``// method will return dth numbered digit ` `    ``// of (dist + diff) number ` `    ``return` `getDigit(dist + diff, d); ` `} `   `// Driver code` `public` `static` `void` `main (String[] args)` `{` `    ``int` `N = ``251``; ` `    ``System.out.println(getNthChar(N)); ` `} ` `}`   `// This code is contributed by mits`

## Python3

 `# Python program to get Nth character in` `# concatenated Decimal String` ` `  `# Method to get dth digit of number N` `def` `getDigit(N, d):` `    ``string ``=` `str``(N)` `    ``return` `string[d``-``1``];` ` `  `# Method to return Nth character in concatenated` `# decimal string` `def` `getNthChar(N):`   `    ``#  sum will store character escaped till now` `    ``sum` `=` `0` `    ``nine ``=` `9` ` `  `    ``#  dist will store numbers escaped till now` `    ``dist ``=` `0` ` `  `    ``#  loop for number lengths` `    ``for` `len` `in` `range``(``1``,N):` `    `  `        ``# nine*len will be incremented characters` `        ``# and nine will be incremented numbers` `        ``sum` `+``=` `nine``*``len` `        ``dist ``+``=` `nine` `        ``if` `(``sum` `>``=` `N):` `        `  `            ``#  restore variables to previous correct state` `            ``sum` `-``=` `nine``*``len` `            ``dist ``-``=` `nine` `            ``N ``-``=` `sum` `            ``break` `            `  `        ``nine ``*``=` `10` ` `  `    ``# get distance from last one digit less maximum` `    ``# number` `    ``diff ``=` `(N ``/``/` `len``) ``+` `1` ` `  `    ``# d will store dth digit of current number` `    ``d ``=` `N ``%` `len` `    ``if` `(d ``=``=` `0``):` `        ``d ``=` `len` ` `  `    ``# method will return dth numbered digit` `    ``# of (dist + diff) number` `    ``return` `getDigit(dist ``+` `diff, d);` ` `  `#  Driver code to test above methods` `N ``=` `251` `print` `(getNthChar(N))`   `# Contributed by Afzal_Saan`

## C#

 `// C# program to get Nth character in ` `// concatenated Decimal String ` `using` `System;`   `class` `GFG` `{` `    `  `// Utility method to get dth digit of number N ` `static` `char` `getDigit(``int` `N, ``int` `d) ` `{ ` `    ``string` `str = Convert.ToString(N);` `    ``return` `str[d - 1]; ` `} `   `// Method to return Nth character in ` `// concatenated decimal string ` `static` `char` `getNthChar(``int` `N) ` `{ ` `    ``// sum will store character` `    ``// escaped till now ` `    ``int` `sum = 0, nine = 9; `   `    ``// dist will store numbers ` `    ``// escaped till now ` `    ``int` `dist = 0, len; `   `    ``// loop for number lengths ` `    ``for` `(len = 1; ; len++) ` `    ``{ ` `        ``// nine*len will be incremented characters ` `        ``// and nine will be incremented numbers ` `        ``sum += nine * len; ` `        ``dist += nine; `   `        ``if` `(sum >= N) ` `        ``{ ` `            ``// restore variables to previous ` `            ``// correct state ` `            ``sum -= nine * len; ` `            ``dist -= nine; ` `            ``N -= sum; ` `            ``break``; ` `        ``} ` `        ``nine *= 10; ` `    ``} `   `    ``// get distance from last one digit ` `    ``// less maximum number ` `    ``int` `diff = (``int``)(Math.Ceiling((``double``)(N) /` `                                  ``(``double``)(len))); `   `    ``// d will store dth digit of ` `    ``// current number ` `    ``int` `d = N % len; ` `    ``if` `(d == 0) ` `        ``d = len; `   `    ``// method will return dth numbered ` `    ``// digit of (dist + diff) number ` `    ``return` `getDigit(dist + diff, d); ` `} `   `// Driver code` `static` `void` `Main() ` `{` `    ``int` `N = 251; ` `    ``Console.WriteLine(getNthChar(N)); ` `} ` `}`   `// This code is contributed by mits`

## PHP

 `= ``\$N``)` `        ``{` `            ``// restore variables to` `            ``// previous correct state` `            ``\$sum` `-= ``\$nine` `* ``\$len``;` `            ``\$dist` `-= ``\$nine``;` `            ``\$N` `-= ``\$sum``;` `            ``break``;` `        ``} ` `        ``\$nine` `*= 10;` `    ``}` `    `  `    ``// get distance from last one ` `    ``// digit less maximum number` `    ``\$diff` `= (``\$N` `/ ``\$len``) + 1;`   `    ``// d will store dth digit ` `    ``// of current number` `    ``\$d` `= ``\$N` `% ``\$len``;` `    ``if` `(``\$d` `== 0)` `        ``\$d` `= ``\$len``;`   `    ``// method will return dth numbered ` `    ``// digit of (dist + diff) number` `    ``return` `getDigit(``\$dist` `+ ``\$diff``, ``\$d``);` `}`   `// Driver code` `\$N` `= 251;` `echo` `getNthChar(``\$N``);`   `// This code is contributed by mits` `?>`

## Javascript

 ``

Output

`2`

Time Complexity: O(Log N), where N is the given integer.
Auxiliary Space: O(1), since no extra Space used.

This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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