给定一个二进制模式patt和Q查询，其中每个查询都包含一个范围[L，R] ，对于每个查询，任务是从给定范围中查找整数计数，以使它们在其二进制表示形式中包含给定模式。
例子：
Input: q[][] = {{2, 10}}, patt = “101”
Output:
2
5(101) and 10(1010) are the only valid integers.
Input: q[][] = {{122, 150}, {18, 1000}}, patt = “1111”
Output:
7
227
方法：
- 创建一个数组res [] ，其中res [i]将存储范围为[0，i]的有效整数的数量。
- 从0开始，找到所有整数的二进制表示形式，并检查给定的模式是否出现在其中。
- 根据上一步中找到的值更新res []数组。
- 现在，每个查询都可以在O(1)中以res [R] – res [L – 1]的形式回答。
下面是上述方法的实现：
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 preCalculate(int max,
string pattern)
{
vector 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 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 kanugargngC#
// 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输出：
2
59