给定两个整数n和m，任务是找到一个满足以下条件的数p：
->数字p应当小于或等于n。
->该数字应与2到p(含)之间的所有整数互质，即将两个数字相除的唯一正整数为1。
例子 ：
Input : n = 16, m = 3
Output : 13
Explanation : We need to find largest number
smaller than n and co-prime with all numbers
in set [2, 3, ... m] which is [2, 3] here.
Note that numbers {2, 4, 6, 8, ..} are not
co-prime with 2 and numbers {3, 6, 9, .. }
are not co-prime with 3.
Input : n = 6, m = 5
Output : -1 (Number doesn't exists)
Explanation : In this example 2 will cancel
out 2, 4, 6 and 3 will cancel out 3, 6
and 5 will cancel out 5. No number is left,
so the answer does not exists.方法1：创建一个从2到n的数字列表。然后运行i = 2到m的循环，并标记所有为i的倍数的数字。如果我已被标记，请不要运行循环，因为其倍数已被标记。当循环终止时，请运行从n到2的循环，直到找到未标记的数字。如果没有未标记的号码而不存在数字，则第一个未标记的号码为答案。该方法占用O(n)个辅助空间，因此，如果n的值太大，则此方法将不起作用。
方法2：从n到p + 1循环，并检查每个数字是否不能被2到m之间的任何数字整除。
C++
#include
using namespace std;
// Returns true if i is co-prime with numbers
// in set [2, 3, ... m]
bool isValid(long long int i, long long int m)
{
// Running the loop till square root of n
// to reduce the time complexity from n
long long int sq_i = sqrt(i);
// Find the minimum of square root of n
// and m to run the loop until the smaller
// one
long long int sq = min(m, sq_i);
// Check from 2 to min(m, sqrt(n))
for (long long int j = 2; j <= sq; j++)
if (i % j == 0)
return false;
return true;
}
// Function to find the largest number less than n
// which is Co-prime with all numbers from 2 to m
void findLargestNum(long long int n, long long int m)
{
// Iterating from n to m+1 to find the number
for (long long int i = n; i > m; i--) {
// checking every number for the given
// conditions
if (isValid(i, m)) {
// The first number which satisfy the
// conditions is the answer
cout << i << '\n';
return;
}
}
// If there is no number which satisfy the
// conditions, then print number does not exist.
cout << "Number Doesn't Exists\n";
}
// Driver Program
int main()
{
long long int n = 16, m = 3;
findLargestNum(n, m);
return 0;
} Java
// Java Largest number in [2, 3, .. n]
// which is co-prime with numbers
// in [2, 3, .. m]
import java.io.*;
class GFG
{
// Returns true if i is co-prime with numbers
// in set [2, 3, ... m]
static boolean isValid(long i, long m)
{
// Running the loop till square root of n
// to reduce the time complexity from n
long sq_i = (long)Math.sqrt(i);
// Find the minimum of square root of n
// and m to run the loop until the smaller
// one
long sq = Math.min(m, sq_i);
// Check from 2 to min(m, sqrt(n))
for (long j = 2; j <= sq; j++)
if (i % j == 0)
return false;
return true;
}
// Function to find the largest number less than n
// which is Co-prime with all numbers from 2 to m
static void findLargestNum(long n, long m)
{
// Iterating from n to m+1 to find the number
for (long i = n; i > m; i--) {
// checking every number for the given
// conditions
if (isValid(i, m)) {
// The first number which satisfy the
// conditions is the answer
System.out.println (i);
return;
}
}
// If there is no number which satisfy the
// conditions, then print number does not exist.
System.out.println("Number Doesn't Exists");
}
// Driver Program
public static void main (String[] args)
{
long n = 16, m = 3;
findLargestNum(n, m);
}
}
// This code is contributed by vt_m.Python3
# Python3 code to find
# Largest number in
# [2, 3, .. n] which is
# co-prime with
# numbers in [2, 3, .. m]
import math
# Returns true if i is
# co-prime with numbers
# in set [2, 3, ... m]
def isValid(i,m) :
# Running the loop
# till square root of n
# to reduce the time
# complexity from n
sq_i = math.sqrt(i)
# Find the minimum of
# square root of n
# and m to run the loop
# until the smaller
# one
sq = min(m, sq_i)
# Check from 2 to
# min(m, sqrt(n))
for j in range(2, sq + 1) :
if (i % j == 0) :
return False
return True
# def to find the
# largest number less
# than n which is Co-prime
# with all numbers from
# 2 to m
def findLargestNum(n, m) :
# Iterating from n to m+1
# to find the number
for i in range(n, m, -1) :
# checking every number for
# the given conditions
if (isValid(i, m)) :
# The first number
# which satisfy the
# conditions is the
# answer
print ("{}\n".format(i));
return
# If there is no number
# which satisfy the
# conditions, then print
# number does not exist.
print ("Number Doesn't Exists\n")
# Driver Code
n = 16
m = 3
findLargestNum(n, m)
# This code is contributed by
# Manish Shaw(manishshaw1)C#
// C# Largest number in [2, 3, .. n]
// which is co-prime with numbers
// in [2, 3, .. m]
using System;
class GFG
{
// Returns true if i is co-prime
// with numbers in set [2, 3, ... m]
static bool isValid(long i, long m)
{
// Running the loop till square root
// of n to reduce the time complexity
// from n
long sq_i = (long)Math.Sqrt(i);
// Find the minimum of square root
// of n and m to run the loop until
// the smaller one
long sq = Math.Min(m, sq_i);
// Check from 2 to min(m, sqrt(n))
for (long j = 2; j <= sq; j++)
if (i % j == 0)
return false;
return true;
}
// Function to find the largest number
// less than n which is Co-prime with
// all numbers from 2 to m
static void findLargestNum(long n, long m)
{
// Iterating from n to m+1 to find the
// number
for (long i = n; i > m; i--) {
// checking every number for the given
// conditions
if (isValid(i, m)) {
// The first number which satisfy the
// conditions is the answer
Console.WriteLine(i);
return;
}
}
// If there is no number which satisfy
// the conditions, then print number does
// not exist.
Console.WriteLine("Number Doesn't Exists");
}
// Driver Program
public static void Main ()
{
long n = 55, m = 25;
findLargestNum(n, m);
}
}
// This code is contributed by vt_m.PHP
$m; $i--)
{
// checking every number for
// the given conditions
if (isValid($i, $m))
{
// The first number
// which satisfy the
// conditions is the
// answer
echo $i , "\n";
return;
}
}
// If there is no number
// which satisfy the
// conditions, then print
// number does not exist.
echo "Number Doesn't Exists\n";
}
// Driver Code
$n = 16; $m = 3;
findLargestNum($n, $m);
// This code is contributed by anuj_67
?>Javascript
输出 ：
13