给定一个包含Q个查询和一个整数K的数组arr [] [] ，其中每个查询由一个范围[L，R]组成，任务是查找给定范围内的整数计数，该整数的总和是斐波那契数并且可以整除由K。
例子：
Input: arr[][] = { {1, 11}, {5, 15}, {2, 24} }, K = 2
Output: 3 2 5
Explanation:
For query 1: 2, 8 and 11 are the numbers in the given range whose digit sum is Fibonacci and divisible by K.
For query 2: 8 and 11 are the numbers in the given range whose digit sum is Fibonacci and divisible by K.
For query 3: 2, 8, 11, 17 and 20 are the numbers in the given range whose digit sum is Fibonacci and divisible by K.
Input: arr[][] = { {2, 17}, {3, 24} }, K = 3
Output: 4 4
Explanation:
For query 1: 2, 8, 11 and 17 are the numbers in the given range whose digit sum is Fibonacci and divisible by K.
For query 2: 8, 11, 17 and 20 are the numbers in the given range whose digit sum is Fibonacci and divisible by K.
方法：想法是使用散列来预先计算和存储Fibonacci节点，直到给定范围内的最大值，以使检查变得容易和高效(在O(1)时间内)。
- 预计算后，标记所有从1到maxVal的整数，这些整数可以被K整除并且是斐波那契。
- 查找标记数组的前缀和。
- 通过prefix [right] – prefix [left – 1]回答给定的查询。
下面是上述方法的实现：
C/C++
// C++ program to count the integers
// in a range [L, R] such that
// their digit sum is Fibonacci
// and divisible by K
#include
using namespace std;
const int maxSize = 1e5 + 5;
bool isFib[maxSize];
int prefix[maxSize];
// Function to return the
// digit sum of a number
int digitSum(int num)
{
int s = 0;
while (num != 0) {
s = s + num % 10;
num = num / 10;
}
return s;
}
// Function to generate all the Fibonacci
// numbers upto maxSize
void generateFibonacci()
{
memset(isFib, false, sizeof(isFib));
// Adding the first two Fibonacci
// numbers in the set
int prev = 0, curr = 1;
isFib[prev] = isFib[curr] = true;
// Computing the remaining Fibonacci
// numbers based on the previous
// two Fibonacci numbers
while (curr < maxSize) {
int temp = curr + prev;
isFib[temp] = true;
prev = curr;
curr = temp;
}
}
// Pre-Computation till maxSize
// and for a given K
void precompute(int k)
{
generateFibonacci();
for (int i = 1; i < maxSize; i++) {
// Getting the digit sum
int sum = digitSum(i);
// Check if the digit sum
// is Fibonacci and divisible by k
if (isFib[sum] == true
&& sum % k == 0) {
prefix[i]++;
}
}
// Taking Prefix Sum
for (int i = 1; i < maxSize; i++) {
prefix[i] = prefix[i]
+ prefix[i - 1];
}
}
// Function to perform the queries
void performQueries(
int k, int q,
vector >& query)
{
// Precompute the results
precompute(k);
vector ans;
// Iterating through the queries
for (int i = 0; i < q; i++) {
int l = query[i][0],
r = query[i][1];
// Getting count of range
// in range [L, R]
int cnt = prefix[r]
- prefix[l - 1];
cout << cnt << endl;
}
}
// Driver code
int main()
{
vector > query
= { { 1, 11 },
{ 5, 15 },
{ 2, 24 } };
int k = 2, q = query.size();
performQueries(k, q, query);
return 0;
} Java
// Java program to count the integers
// in a range [L, R] such that
// their digit sum is Fibonacci
// and divisible by K
import java.util.*;
class GFG{
static int maxSize = (int) (1e5 + 5);
static boolean []isFib = new boolean[maxSize];
static int []prefix = new int[maxSize];
// Function to return the
// digit sum of a number
static int digitSum(int num)
{
int s = 0;
while (num != 0) {
s = s + num % 10;
num = num / 10;
}
return s;
}
// Function to generate all the Fibonacci
// numbers upto maxSize
static void generateFibonacci()
{
Arrays.fill(isFib, false);
// Adding the first two Fibonacci
// numbers in the set
int prev = 0, curr = 1;
isFib[prev] = isFib[curr] = true;
// Computing the remaining Fibonacci
// numbers based on the previous
// two Fibonacci numbers
while (curr < maxSize) {
int temp = curr + prev;
if(temp < maxSize)
isFib[temp] = true;
prev = curr;
curr = temp;
}
}
// Pre-Computation till maxSize
// and for a given K
static void precompute(int k)
{
generateFibonacci();
for (int i = 1; i < maxSize; i++) {
// Getting the digit sum
int sum = digitSum(i);
// Check if the digit sum
// is Fibonacci and divisible by k
if (isFib[sum] == true
&& sum % k == 0) {
prefix[i]++;
}
}
// Taking Prefix Sum
for (int i = 1; i < maxSize; i++) {
prefix[i] = prefix[i]
+ prefix[i - 1];
}
}
// Function to perform the queries
static void performQueries(
int k, int q,
int[][] query)
{
// Precompute the results
precompute(k);
// Iterating through the queries
for (int i = 0; i < q; i++) {
int l = query[i][0],
r = query[i][1];
// Getting count of range
// in range [L, R]
int cnt = prefix[r]
- prefix[l - 1];
System.out.print(cnt +"\n");
}
}
// Driver code
public static void main(String[] args)
{
int [][]query
= { { 1, 11 },
{ 5, 15 },
{ 2, 24 } };
int k = 2, q = query.length;
performQueries(k, q, query);
}
}
// This code is contributed by Princi SinghPython3
# Python 3 program to count the integers
# in a range [L, R] such that
# their digit sum is Fibonacci
# and divisible by K
maxSize = 100005
isFib = [False]*(maxSize)
prefix = [0]*maxSize
# Function to return the
# digit sum of a number
def digitSum(num):
s = 0
while (num != 0):
s = s + num % 10
num = num // 10
return s
# Function to generate all the Fibonacci
# numbers upto maxSize
def generateFibonacci():
global isFib
# Adding the first two Fibonacci
# numbers in the set
prev = 0
curr = 1
isFib[prev] = True
isFib[curr] = True
# Computing the remaining Fibonacci
# numbers based on the previous
# two Fibonacci numbers
while (curr < maxSize):
temp = curr + prev
if temp < maxSize:
isFib[temp] = True
prev = curr
curr = temp
# Pre-Computation till maxSize
# and for a given K
def precompute(k):
generateFibonacci()
global prefix
for i in range(1, maxSize):
# Getting the digit sum
sum = digitSum(i)
# Check if the digit sum
# is Fibonacci and divisible by k
if (isFib[sum] == True
and sum % k == 0):
prefix[i] += 1
# Taking Prefix Sum
for i in range(1, maxSize):
prefix[i] = prefix[i]+ prefix[i - 1]
# Function to perform the queries
def performQueries(k, q,query):
# Precompute the results
precompute(k)
# Iterating through the queries
for i in range(q):
l = query[i][0]
r = query[i][1]
# Getting count of range
# in range [L, R]
cnt = prefix[r]- prefix[l - 1]
print(cnt)
# Driver code
if __name__ == "__main__":
query = [ [ 1, 11 ],
[ 5, 15 ],
[ 2, 24 ] ]
k = 2
q = len(query)
performQueries(k, q, query)
# This code is contributed by chitranayalC#
// C# program to count the integers
// in a range [L, R] such that
// their digit sum is Fibonacci
// and divisible by K
using System;
class GFG{
static int maxSize = (int) (1e5 + 5);
static bool []isFib = new bool[maxSize];
static int []prefix = new int[maxSize];
// Function to return the
// digit sum of a number
static int digitSum(int num)
{
int s = 0;
while (num != 0) {
s = s + num % 10;
num = num / 10;
}
return s;
}
// Function to generate all the Fibonacci
// numbers upto maxSize
static void generateFibonacci()
{
// Adding the first two Fibonacci
// numbers in the set
int prev = 0, curr = 1;
isFib[prev] = isFib[curr] = true;
// Computing the remaining Fibonacci
// numbers based on the previous
// two Fibonacci numbers
while (curr < maxSize) {
int temp = curr + prev;
if(temp < maxSize)
isFib[temp] = true;
prev = curr;
curr = temp;
}
}
// Pre-Computation till maxSize
// and for a given K
static void precompute(int k)
{
generateFibonacci();
for (int i = 1; i < maxSize; i++) {
// Getting the digit sum
int sum = digitSum(i);
// Check if the digit sum
// is Fibonacci and divisible by k
if (isFib[sum] == true
&& sum % k == 0) {
prefix[i]++;
}
}
// Taking Prefix Sum
for (int i = 1; i < maxSize; i++) {
prefix[i] = prefix[i]
+ prefix[i - 1];
}
}
// Function to perform the queries
static void performQueries(
int k, int q,
int[,] query)
{
// Precompute the results
precompute(k);
// Iterating through the queries
for (int i = 0; i < q; i++) {
int l = query[i, 0],
r = query[i, 1];
// Getting count of range
// in range [L, R]
int cnt = prefix[r]
- prefix[l - 1];
Console.Write(cnt +"\n");
}
}
// Driver code
public static void Main(String[] args)
{
int [,]query
= { { 1, 11 },
{ 5, 15 },
{ 2, 24 } };
int k = 2, q = query.GetLength(0);
performQueries(k, q, query);
}
}
// This code is contributed by PrinciRaj1992输出：
3
2
5
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