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# Queries to find the count of integers in a range that contain the given pattern

• Last Updated : 16 Jul, 2021

Given a binary pattern patt and Q queries where each query consists of a range [L, R], for every query the task is to find the count of integers from the given range such that they contain the given pattern in their binary representation.
Examples:

Input: q[][] = {{2, 10}}, patt = “101”
Output:

5(101) and 10(1010) are the only valid integers.
Input: q[][] = {{122, 150}, {18, 1000}}, patt = “1111”
Output:

227

Approach:

• Create an array res[] where res[i] will store the count of valid integers from the range [0, i].
• Starting from 0, find the binary representation of all the integer and check whether the given pattern occurs in it.
• Update the res[] array based on the values found in the previous step.
• Now every query can be answered in O(1) as res[R] – res[L – 1].

Below is the implementation of the above approach:

## C++

 `#include``using` `namespace` `std;` `// Function to return the``// pre-calculate array such``// that arr[i] stores the count of``// valid numbers in the range [0, i]``string DecimalToBinaryString(``int` `a)``{``  ``string binary = ``""``;``  ``int` `mask = 1;``  ``for` `(``int` `i = 0; i < 31; i++)``  ``{``    ``if``(mask&a)``      ``binary = ``"1"` `+ binary;``    ``else``      ``binary = ``"0"` `+ binary;``    ``mask <<= 1;``  ``}` `  ``return` `binary;``}` `vector<``int``> preCalculate(``int` `max,``                         ``string pattern)``{``  ``vector<``int``> arr(max + 1, 0);` `  ``// If 0 is a valid number``  ``if` `(pattern == ``"0"``)``    ``arr[0] = 1;``  ``else``    ``arr[0] = 0;` `  ``// For every element i``  ``for` `(``int` `i = 1; i <= max; i++)``  ``{``    ``// If i is avalid number``    ``if` `(DecimalToBinaryString(i).find(pattern) !=``        ``std::string :: npos)``    ``{``      ``arr[i] = 1 + arr[i - 1];``    ``}``    ``else``    ``{``      ``arr[i] = arr[i - 1];``    ``}``  ``}``  ``return` `arr;``}` `// Function to perform the queries``void` `performQueries(vector > queries,``                    ``int` `q, string pattern)``{``  ``// Maximum value for the``  ``// end of any range``  ``int` `ma = INT_MIN;``  ` `  ``for` `(``int` `i = 0; i < q; i++)``    ``ma = max(ma, queries[i][1]);` `  ``// res[i] stores the count of valid``  ``// integers from the range [0, i]``  ``vector<``int``> res = preCalculate(ma,``                                 ``pattern);` `  ``for` `(``int` `i = 0; i < q; i++)``  ``{``    ``int` `l = queries[i][0];``    ``int` `r = queries[i][1];` `    ``if` `(l == 0)``      ``cout << (res[r]) << endl;``    ``else``      ``cout << (res[r] -``               ``res[l - 1]) << endl;``  ``}``}` `// Driver code``int` `main()``{``  ``vector> queries = {{2, 10},``                                 ``{8, 120}};``  ``int` `q = queries.size();``  ``string pattern = ``"101"``;``  ``performQueries(queries, q, pattern);``}` `// This code is contributed by grand_master`

## Java

 `// Java implementation of the approach``import` `java.util.*;``class` `GFG {` `    ``// Function to return the pre-calculate array``    ``// such that arr[i] stores the count of``    ``// valid numbers in the range [0, i]``    ``static` `int``[] preCalculate(``int` `max, String pattern)``    ``{``        ``int` `arr[] = ``new` `int``[max + ``1``];` `        ``// If 0 is a valid number``        ``if` `(pattern == ``"0"``)``            ``arr[``0``] = ``1``;``        ``else``            ``arr[``0``] = ``0``;` `        ``// For every element i``        ``for` `(``int` `i = ``1``; i <= max; i++) {` `            ``// If i is avalid number``            ``if` `(Integer.toBinaryString(i).contains(pattern)) {``                ``arr[i] = ``1` `+ arr[i - ``1``];``            ``}``            ``else` `{``                ``arr[i] = arr[i - ``1``];``            ``}``        ``}``        ``return` `arr;``    ``}` `    ``// Function to perform the queries``    ``static` `void` `performQueries(``int` `queries[][],``                               ``int` `q, String pattern)``    ``{` `        ``// Maximum value for the end of any range``        ``int` `max = Integer.MIN_VALUE;``        ``for` `(``int` `i = ``0``; i < q; i++)``            ``max = Math.max(max, queries[i][``1``]);` `        ``// res[i] stores the count of valid``        ``// integers from the range [0, i]``        ``int` `res[] = preCalculate(max, pattern);` `        ``for` `(``int` `i = ``0``; i < q; i++) {``            ``int` `l = queries[i][``0``];``            ``int` `r = queries[i][``1``];` `            ``if` `(l == ``0``)``                ``System.out.println(res[r]);``            ``else``                ``System.out.println(res[r] - res[l - ``1``]);``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String args[])``    ``{``        ``int` `queries[][] = { { ``2``, ``10` `}, { ``8``, ``120` `} };``        ``int` `q = queries.length;``        ``String pattern = ``"101"``;` `        ``performQueries(queries, q, pattern);``    ``}``}`

## Python3

 `# Python3 implementation of the approach``import` `sys` `# Function to return the pre-calculate array``# such that arr[i] stores the count of``# valid numbers in the range [0, i]``def` `preCalculate(``maX``, pattern) :``    ``arr ``=` `[``0``] ``*` `(``maX` `+` `1``);``    ` `    ``# If 0 is a valid number``    ``if` `(pattern ``=``=` `"0"``) :``        ``arr[``0``] ``=` `1``;``        ` `    ``else` `:``        ``arr[``0``] ``=` `0``;``        ` `    ``# For every element i``    ``for` `i ``in` `range``(``1``, ``maX` `+` `1``) :``        ` `        ``# If i is avalid number``        ``if` `(pattern ``in` `bin``(i)) :``            ``arr[i] ``=` `1` `+` `arr[i ``-` `1``];``            ` `        ``else` `:``            ``arr[i] ``=` `arr[i ``-` `1``];``            ` `    ``return` `arr;` `# Function to perform the queries``def` `performQueries(queries,q, pattern) :``    ` `    ``# Maximum value for the end of any range``    ``maX` `=` `-``(sys.maxsize ``+` `1``);``    ` `    ``for` `i ``in` `range``(q) :``        ` `        ``maX` `=` `max``(``maX``, queries[i][``1``]);``        ` `    ``# res[i] stores the count of valid``    ``# integers from the range [0, i]``    ``res ``=` `preCalculate(``maX``, pattern);` `    ``for` `i ``in` `range``(q) :``        ``l ``=` `queries[i][``0``];``        ``r ``=` `queries[i][``1``];``        ` `        ``if` `(l ``=``=` `0``) :``            ``print``(res[r]);``        ``else` `:``            ``print``(res[r] ``-` `res[l ``-` `1``]);` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:``    ` `    ``queries ``=` `[ [ ``2``, ``10` `], [ ``8``, ``120` `] ];``    ``q ``=` `len``(queries);``    ``pattern ``=` `"101"``;``    ``performQueries(queries, q, pattern);` `# This code is contributed by kanugargng`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Numerics;` `class` `GFG``{` `    ``//integer to binary string``    ``public` `static` `string` `toBinaryString(``int` `x)``    ``{``        ``char``[] bits = ``new` `char``[32];``        ``int` `i = 0;``    ` `        ``while` `(x != 0)``        ``{``            ``bits[i++] = (x & 1) == 1 ? ``'1'` `: ``'0'``;``            ``x >>= 1;``        ``}``    ` `        ``Array.Reverse(bits, 0, i);``        ``return` `new` `string``(bits);``    ``}``    ` `    ``// Function to return the pre-calculate array``    ``// such that arr[i] stores the count of``    ``// valid numbers in the range [0, i]``    ``static` `int``[] preCalculate(``int` `max, ``string` `pattern)``    ``{``        ``int` `[]arr = ``new` `int``[max + 1];` `        ``// If 0 is a valid number``        ``if` `(pattern == ``"0"``)``            ``arr[0] = 1;``        ``else``            ``arr[0] = 0;` `        ``// For every element i``        ``for` `(``int` `i = 1; i <= max; i++)``        ``{``            ``// If i is avalid number``            ``if` `(toBinaryString(i).Contains(pattern))``            ``{``                ``arr[i] = 1 + arr[i - 1];``            ``}``            ``else``            ``{``                ``arr[i] = arr[i - 1];``            ``}``        ``}``        ``return` `arr;``    ``}` `    ``// Function to perform the queries``    ``static` `void` `performQueries(``int` `[,]queries,``                               ``int` `q, ``string` `pattern)``    ``{` `        ``// Maximum value for the end of any range``        ``int` `max = ``int``.MinValue;``        ``for` `(``int` `i = 0; i < q; i++)``            ``max = Math.Max(max, queries[i, 1]);` `        ``// res[i] stores the count of valid``        ``// integers from the range [0, i]``        ``int` `[]res = preCalculate(max, pattern);` `        ``for` `(``int` `i = 0; i < q; i++)``        ``{``            ``int` `l = queries[i, 0];``            ``int` `r = queries[i, 1];` `            ``if` `(l == 0)``                ``Console.WriteLine(res[r]);``            ``else``                ``Console.WriteLine(res[r] - res[l - 1]);``        ``}``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(``string` `[]args)``    ``{``        ``int` `[,]queries = { { 2, 10 }, { 8, 120 } };``        ``int` `q = queries.GetLength(0) ;``        ``string` `pattern = ``"101"``;` `        ``performQueries(queries, q, pattern);``    ``}``}` `// This code is contributed by Arnab Kundu`

## Javascript

 ``
Output:
```2
59```

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