Algorithm
Problem link- https://www.spoj.com/problems/HARSHAD/
HARSHAD - Devlali Numbers
Devlali numbers were an important coinage by Indian recreational mathemtician D. R. Kaprekar.
For any positive integer n, define d(n) as the sum of n and the digits of n. Eg, d(199) = 199 + 1 + 9 + 9 = 218.
For a positive number m, if there exists no positive number r such that d(r) = m, then m is a Devlali number. First few Devlali numbers are 1, 3, 5, 7, ... so on.
A prime number falling in this family is called a Devlali Prime. First few Devlali Primes are 3, 5, 7, ... so on.
Input
First line contains integer Q
Next Q lines contain two integers A and B
Output
print Q lines, each listing number of Devlali Primes in range [A,B] (both inclusive)
Limits
1 <= Q <= 100000
0 <= A <= B <= 1000000
Example
Input 3 1 3 0 10 5 8 Output 1 3 2
Code Examples
#1 Code Example with C++ Programming
Code -
C++ Programming
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MOD 1000000007LL
#define EPS 1e-9
#define io ios_base::sync_with_stdio(false);cin.tie(NULL);
#define M_PI 3.14159265358979323846
template <typename T> T gcd(T a, T b){return (b==0)?a:gcd(b,a%b);}
template <typename T> T lcm(T a, T b){return a*(b/gcd(a,b));}
template <typename T> T mod_exp(T b, T p, T m){T x = 1;while(p){if(p&1)x=(x*b)%m;b=(b*b)%m;p=p>>1;}return x;}
template <typename T> T invFermat(T a, T p){return mod_exp(a, p-2, p);}
template <typename T> T exp(T b, T p){T x = 1;while(p){if(p&1)x=(x*b);b=(b*b);p=p>>1;}return x;}
const int MAXN = 1e6+5;
bool isPrime[MAXN];
bool Devlali[MAXN] = {false};
void sieve(){
isPrime[0] = isPrime[1] = 1;
for(int i = 2;i*i <= 1000000; i++){
if(isPrime[i] == 0){
if(i*1LL*i <= 1000000){
for(int j = i*i;j <= 1000000; j+=i)
isPrime[j] = 1;
}
}
}
}
int sumDig(int n){
int sum = 0;
while(n > 0){
sum += (n%10);
n /= 10;
}
return sum;
}
bool DP[MAXN];
int DP2[MAXN];
void pre(){
for(int i = 1;i <= 1000000; i++){
int sum = sumDig(i) + i;
if(sum <= 1000000){
Devlali[sum] = true;
}
}
for(int i = 1;i <= 1000000; i++){
if(Devlali[i] == false && isPrime[i] == 0)
DP[i] = true;
}
for(int i = 1;i <= 1000000; i++){
DP2[i] += DP2[i-1];
if(DP[i])
DP2[i]++;
}
}
int main(){
io;
sieve();
pre();
int q;
cin >> q;
while(q--){
int l, r;
cin >> l >> r;
if(l == 0)
cout << DP2[r] << endl;
else
cout << DP2[r] - DP2[l-1] << endl;
}
return 0;
}
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Input
1 3
0 10
5 8
Output
3
2
Demonstration
SPOJ Solution-Devlali Numbers-Solution in C, C++, Java, Python