Count numbers divisible by K in a range with Fibonacci digit sum for Q queries
Given an array arr[][] containing Q queries and an integer K where each query consists of a range [L, R], the task is to find the count of integers in the given range whose digit sum is a Fibonacci number and divisible by K.
Examples:
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.
Approach: The idea is to use hashing to precompute and store the Fibonacci nodes up to the maximum value in the given range, to make the checking easy and efficient (in O(1) time).
- After precomputation, mark all the integers from 1 to maxVal which are divisible by K and are fibonacci.
- Find the prefix sum of the marked array.
- Answer the given queries by prefix[right] – prefix[left – 1].
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
const int maxSize = 1e5 + 5;
bool isFib[maxSize];
int prefix[maxSize];
int digitSum( int num)
{
int s = 0;
while (num != 0) {
s = s + num % 10;
num = num / 10;
}
return s;
}
void generateFibonacci()
{
memset (isFib, false , sizeof (isFib));
int prev = 0, curr = 1;
isFib[prev] = isFib[curr] = true ;
while (curr < maxSize) {
int temp = curr + prev;
isFib[temp] = true ;
prev = curr;
curr = temp;
}
}
void precompute( int k)
{
generateFibonacci();
for ( int i = 1; i < maxSize; i++) {
int sum = digitSum(i);
if (isFib[sum] == true
&& sum % k == 0) {
prefix[i]++;
}
}
for ( int i = 1; i < maxSize; i++) {
prefix[i] = prefix[i]
+ prefix[i - 1];
}
}
void performQueries(
int k, int q,
vector<vector< int > >& query)
{
precompute(k);
vector< int > ans;
for ( int i = 0; i < q; i++) {
int l = query[i][0],
r = query[i][1];
int cnt = prefix[r]
- prefix[l - 1];
cout << cnt << endl;
}
}
int main()
{
vector<vector< int > > query
= { { 1, 11 },
{ 5, 15 },
{ 2, 24 } };
int k = 2, q = query.size();
performQueries(k, q, query);
return 0;
}
|
Java
import java.util.*;
class GFG{
static int maxSize = ( int ) (1e5 + 5 );
static boolean []isFib = new boolean [maxSize];
static int []prefix = new int [maxSize];
static int digitSum( int num)
{
int s = 0 ;
while (num != 0 ) {
s = s + num % 10 ;
num = num / 10 ;
}
return s;
}
static void generateFibonacci()
{
Arrays.fill(isFib, false );
int prev = 0 , curr = 1 ;
isFib[prev] = isFib[curr] = true ;
while (curr < maxSize) {
int temp = curr + prev;
if (temp < maxSize)
isFib[temp] = true ;
prev = curr;
curr = temp;
}
}
static void precompute( int k)
{
generateFibonacci();
for ( int i = 1 ; i < maxSize; i++) {
int sum = digitSum(i);
if (isFib[sum] == true
&& sum % k == 0 ) {
prefix[i]++;
}
}
for ( int i = 1 ; i < maxSize; i++) {
prefix[i] = prefix[i]
+ prefix[i - 1 ];
}
}
static void performQueries(
int k, int q,
int [][] query)
{
precompute(k);
for ( int i = 0 ; i < q; i++) {
int l = query[i][ 0 ],
r = query[i][ 1 ];
int cnt = prefix[r]
- prefix[l - 1 ];
System.out.print(cnt + "\n" );
}
}
public static void main(String[] args)
{
int [][]query
= { { 1 , 11 },
{ 5 , 15 },
{ 2 , 24 } };
int k = 2 , q = query.length;
performQueries(k, q, query);
}
}
|
Python3
maxSize = 100005
isFib = [ False ] * (maxSize)
prefix = [ 0 ] * maxSize
def digitSum(num):
s = 0
while (num ! = 0 ):
s = s + num % 10
num = num / / 10
return s
def generateFibonacci():
global isFib
prev = 0
curr = 1
isFib[prev] = True
isFib[curr] = True
while (curr < maxSize):
temp = curr + prev
if temp < maxSize:
isFib[temp] = True
prev = curr
curr = temp
def precompute(k):
generateFibonacci()
global prefix
for i in range ( 1 , maxSize):
sum = digitSum(i)
if (isFib[ sum ] = = True
and sum % k = = 0 ):
prefix[i] + = 1
for i in range ( 1 , maxSize):
prefix[i] = prefix[i] + prefix[i - 1 ]
def performQueries(k, q,query):
precompute(k)
for i in range (q):
l = query[i][ 0 ]
r = query[i][ 1 ]
cnt = prefix[r] - prefix[l - 1 ]
print (cnt)
if __name__ = = "__main__" :
query = [ [ 1 , 11 ],
[ 5 , 15 ],
[ 2 , 24 ] ]
k = 2
q = len (query)
performQueries(k, q, query)
|
C#
using System;
class GFG{
static int maxSize = ( int ) (1e5 + 5);
static bool []isFib = new bool [maxSize];
static int []prefix = new int [maxSize];
static int digitSum( int num)
{
int s = 0;
while (num != 0) {
s = s + num % 10;
num = num / 10;
}
return s;
}
static void generateFibonacci()
{
int prev = 0, curr = 1;
isFib[prev] = isFib[curr] = true ;
while (curr < maxSize) {
int temp = curr + prev;
if (temp < maxSize)
isFib[temp] = true ;
prev = curr;
curr = temp;
}
}
static void precompute( int k)
{
generateFibonacci();
for ( int i = 1; i < maxSize; i++) {
int sum = digitSum(i);
if (isFib[sum] == true
&& sum % k == 0) {
prefix[i]++;
}
}
for ( int i = 1; i < maxSize; i++) {
prefix[i] = prefix[i]
+ prefix[i - 1];
}
}
static void performQueries(
int k, int q,
int [,] query)
{
precompute(k);
for ( int i = 0; i < q; i++) {
int l = query[i, 0],
r = query[i, 1];
int cnt = prefix[r]
- prefix[l - 1];
Console.Write(cnt + "\n" );
}
}
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);
}
}
|
Javascript
<script>
let maxSize = (1e5 + 5);
let isFib = Array.from({length: maxSize}, (_, i) => 0);
let prefix = Array.from({length: maxSize}, (_, i) => 0);
function digitSum(num)
{
let s = 0;
while (num != 0) {
s = s + num % 10;
num = Math.floor(num / 10);
}
return s;
}
function generateFibonacci()
{
isFib = Array.from({length: maxSize}, (_, i) => false );
let prev = 0, curr = 1;
isFib[prev] = isFib[curr] = true ;
while (curr < maxSize) {
let temp = curr + prev;
if (temp < maxSize)
isFib[temp] = true ;
prev = curr;
curr = temp;
}
}
function precompute(k)
{
generateFibonacci();
for (let i = 1; i < maxSize; i++) {
let sum = digitSum(i);
if (isFib[sum] == true
&& sum % k == 0) {
prefix[i]++;
}
}
for (let i = 1; i < maxSize; i++) {
prefix[i] = prefix[i]
+ prefix[i - 1];
}
}
function performQueries(
k, q, query)
{
precompute(k);
for (let i = 0; i < q; i++) {
let l = query[i][0],
r = query[i][1];
let cnt = prefix[r]
- prefix[l - 1];
document.write(cnt + "<br/>" );
}
}
let query
= [[ 1, 11 ],
[ 5, 15 ],
[ 2, 24 ]];
let k = 2, q = query.length;
performQueries(k, q, query);
</script>
|
Time Complexity: O(maxSize,q)
Auxiliary Space: O(maxSize)
Last Updated :
10 Nov, 2021
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