# 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.

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