Given two integers L and R, the task is to find the minimum difference between any two prime numbers in the range [L, R].
Examples:
Input: L = 21, R = 50
Output: 2
(29, 31) and (41, 43) are the only valid pairs
that give the minimum difference.Input: L = 1, R = 11
Output: 1
The difference between (2, 3) is minimum.
Approach:
- Find all the prime numbers upto R using Sieve of Eratosthenes.
- Now starting from L, find the difference between any two prime numbers within the range and update minimum difference so far.
- If the number of primes in the range were < 2 then print -1.
- Else print the minimum difference.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std;
const int sz = 1e5;
bool isPrime[sz + 1];
// Function for Sieve of Eratosthenes void sieve()
{ memset(isPrime, true, sizeof(isPrime));
isPrime[0] = isPrime[1] = false;
for (int i = 2; i * i <= sz; i++) {
if (isPrime[i]) {
for (int j = i * i; j < sz; j += i) {
isPrime[j] = false;
}
}
}
} // Function to return the minimum difference // between any two prime numbers // from the given range [L, R] int minDifference(int L, int R)
{ // Find the first prime from the range
int fst = 0;
for (int i = L; i <= R; i++) {
if (isPrime[i]) {
fst = i;
break;
}
}
// Find the second prime from the range
int snd = 0;
for (int i = fst + 1; i <= R; i++) {
if (isPrime[i]) {
snd = i;
break;
}
}
// If the number of primes in
// the given range is < 2
if (snd == 0)
return -1;
// To store the minimum difference between
// two consecutive primes from the range
int diff = snd - fst;
// Range left to check for primes
int left = snd + 1;
int right = R;
// For every integer in the range
for (int i = left; i <= right; i++) {
// If the current integer is prime
if (isPrime[i]) {
// If the difference between i
// and snd is minimum so far
if (i - snd <= diff) {
fst = snd;
snd = i;
diff = snd - fst;
}
}
}
return diff;
} // Driver code int main()
{ // Generate primes
sieve();
int L = 21, R = 50;
cout << minDifference(L, R);
return 0;
} |
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Java
// Java implementation of the approach import java.util.*;
class GFG
{ static int sz = (int) 1e5;
static boolean []isPrime = new boolean [sz + 1];
// Function for Sieve of Eratosthenes static void sieve()
{ Arrays.fill(isPrime, true);
isPrime[0] = isPrime[1] = false;
for (int i = 2; i * i <= sz; i++)
{
if (isPrime[i])
{
for (int j = i * i; j < sz; j += i)
{
isPrime[j] = false;
}
}
}
} // Function to return the minimum difference // between any two prime numbers // from the given range [L, R] static int minDifference(int L, int R)
{ // Find the first prime from the range
int fst = 0;
for (int i = L; i <= R; i++)
{
if (isPrime[i])
{
fst = i;
break;
}
}
// Find the second prime from the range
int snd = 0;
for (int i = fst + 1; i <= R; i++)
{
if (isPrime[i])
{
snd = i;
break;
}
}
// If the number of primes in
// the given range is < 2
if (snd == 0)
return -1;
// To store the minimum difference between
// two consecutive primes from the range
int diff = snd - fst;
// Range left to check for primes
int left = snd + 1;
int right = R;
// For every integer in the range
for (int i = left; i <= right; i++)
{
// If the current integer is prime
if (isPrime[i])
{
// If the difference between i
// and snd is minimum so far
if (i - snd <= diff)
{
fst = snd;
snd = i;
diff = snd - fst;
}
}
}
return diff;
} // Driver code public static void main(String []args)
{ // Generate primes
sieve();
int L = 21, R = 50;
System.out.println(minDifference(L, R));
} } // This code is contributed by 29AjayKumar |
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Python3
# Python3 implementation of the approach from math import sqrt
sz = int(1e5);
isPrime = [True] * (sz + 1);
# Function for Sieve of Eratosthenes def sieve() :
isPrime[0] = isPrime[1] = False;
for i in range(2, int(sqrt(sz)) + 1) :
if (isPrime[i]) :
for j in range(i * i, sz, i) :
isPrime[j] = False;
# Function to return the minimum difference # between any two prime numbers # from the given range [L, R] def minDifference(L, R) :
# Find the first prime from the range
fst = 0;
for i in range(L, R + 1) :
if (isPrime[i]) :
fst = i;
break;
# Find the second prime from the range
snd = 0;
for i in range(fst + 1, R + 1) :
if (isPrime[i]) :
snd = i;
break;
# If the number of primes in
# the given range is < 2
if (snd == 0) :
return -1;
# To store the minimum difference between
# two consecutive primes from the range
diff = snd - fst;
# Range left to check for primes
left = snd + 1;
right = R;
# For every integer in the range
for i in range(left, right + 1) :
# If the current integer is prime
if (isPrime[i]) :
# If the difference between i
# and snd is minimum so far
if (i - snd <= diff) :
fst = snd;
snd = i;
diff = snd - fst;
return diff;
# Driver code if __name__ == "__main__" :
# Generate primes
sieve();
L = 21; R = 50;
print(minDifference(L, R));
# This code is contributed by AnkitRai01 |
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C#
// C# implementation of the approach using System;
class GFG
{ static int sz = (int) 1e5;
static Boolean []isPrime = new Boolean [sz + 1];
// Function for Sieve of Eratosthenes static void sieve()
{ for(int i = 2; i< sz + 1; i++)
isPrime[i] = true;
for (int i = 2; i * i <= sz; i++)
{
if (isPrime[i])
{
for (int j = i * i; j < sz; j += i)
{
isPrime[j] = false;
}
}
}
} // Function to return the minimum difference // between any two prime numbers // from the given range [L, R] static int minDifference(int L, int R)
{ // Find the first prime from the range
int fst = 0;
for (int i = L; i <= R; i++)
{
if (isPrime[i])
{
fst = i;
break;
}
}
// Find the second prime from the range
int snd = 0;
for (int i = fst + 1; i <= R; i++)
{
if (isPrime[i])
{
snd = i;
break;
}
}
// If the number of primes in
// the given range is < 2
if (snd == 0)
return -1;
// To store the minimum difference between
// two consecutive primes from the range
int diff = snd - fst;
// Range left to check for primes
int left = snd + 1;
int right = R;
// For every integer in the range
for (int i = left; i <= right; i++)
{
// If the current integer is prime
if (isPrime[i])
{
// If the difference between i
// and snd is minimum so far
if (i - snd <= diff)
{
fst = snd;
snd = i;
diff = snd - fst;
}
}
}
return diff;
} // Driver code public static void Main(String []args)
{ // Generate primes
sieve();
int L = 21, R = 50;
Console.WriteLine(minDifference(L, R));
} } // This code is contributed by 29AjayKumar |
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Output:
2
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