写一个程序来打印第一个n个非平方数（非完美平方）。
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例如：
Input : 5Output : 2 3 5 6 7Input : 10Output : 2 3 5 6 7 8 10 11 12 13
A. 天真法 是遍历从1到n的所有数字。对于每个数字，检查它是否为完全平方。如果不是一个完美的正方形，打印出来。
C++
// CPP program to print first n // non-square numbers. #include <bits/stdc++.h> using namespace std; // Function to check perfect square bool isPerfectSquare( int n) { if (n < 0) return false ; int root = round( sqrt (n))); return n == root * root; } // function to print all // non square number void printnonsquare( int n) { // variable which stores the // count int count = 0; for ( int i = 1; count < n; ++i) { // not perfect square if (!isPerfectSquare(i)) { cout << i << " " ; count++; } } } int main() { int n = 10; printnonsquare(n); return 0; } |
JAVA
// Java program to print first n // non-square numbers. import java.io.*; import java.math.*; class GFG { // Function to check perfect square static boolean isPerfectSquare( int n) { if (n < 0 ) return false ; int root = Math.round(( int )(Math.sqrt(n))); return n == root * root; } // function to print all // non square number static void printnonsquare( int n) { // variable which stores the // count int count = 0 ; for ( int i = 1 ; count < n; ++i) { // not perfect square if (!isPerfectSquare(i)) { System.out.print(i + " " ); count++; } } } // Driver code public static void main(String args[]) { int n = 10 ; printnonsquare(n); } } /* This code is contributed by Nikita Tiwari.*/ |
Python3
# Python 3 program to print # first n non-square numbers. import math # Function to check perfect # square def isPerfectSquare(n) : if (n < 0 ) : return False root = round (math.sqrt(n)) return (n = = root * root) # function to print all # non square number def printnonsquare(n) : # variable which stores the # count count = 0 i = 1 while (count < n) : # Not perfect square if (isPerfectSquare(i) = = False ) : print (i, end = " " ) count = count + 1 i = i + 1 n = 10 printnonsquare(n) # This code is contributed by Nikita Tiwari. |
C#
// C# program to print first n // non-square numbers. using System; class GFG { // Function to check perfect square static bool isPerfectSquare( int n) { if (n < 0) return false ; double root = Math.Round(( double )(Math.Sqrt(n))); return n == root * root; } // function to print all // non square number static void printnonsquare( int n) { // variable which stores the // count int count = 0; for ( int i = 1; count < n; ++i) { // not perfect square if (!isPerfectSquare(i)) { Console.Write(i + " " ); count++; } } } // Driver code static public void Main () { int n = 10; printnonsquare(n); } } // This code is contributed by jit_t |
PHP
<?php // CPP program to print first // n non-square numbers. // Function to check // perfect square function isPerfectSquare( $n ) { if ( $n < 0) return false; $root = round (sqrt( $n )); return $n == $root * $root ; } // function to print all // non square number function printnonsquare( $n ) { // variable which // stores the count $count = 0; for ( $i = 1; $count < $n ; ++ $i ) { // not perfect square if (!isPerfectSquare( $i )) { echo $i . " " ; $count ++; } } } // Driver Code $n = 10; printnonsquare( $n ); // This code is contributed by mits. ?> |
Javascript
<script> // JavaScript program to print first n // non-square numbers. // Function to check perfect square function isPerfectSquare(n) { if (n < 0) return false ; let root = Math.round((Math.sqrt(n))); return n == root * root; } // function to print all // non square number function printnonsquare(n) { // variable which stores the // count let count = 0; for (let i = 1; count < n; ++i) { // not perfect square if (!isPerfectSquare(i)) { document.write(i + " " ); count++; } } } // Driver code let n = 10; printnonsquare(n); </script> |
输出：
2 3 5 6 7 8 10 11 12 13
我们可以使用下面的公式来改进上述算法 F（n）=n+楼层（1/2+sqrt（n）） 通过应用这个函数，我们得到n个非平方数。 公式的来源和证明： 库拉
下面是上述方法的实现。
C++
// CPP program to print first n // non square number #include <bits/stdc++.h> // Returns n-th non-square number. int nonsquare( int n) { return n + ( int )(0.5 + sqrt (n)); } void printNonSquare( int n) { // loop to print non squares // below n for ( int i = 1; i <= n; i++) printf ( "%d " , nonsquare(i)); } int main() { int n = 10; printNonSquare(n); return 0; } |
JAVA
// Java program to print first n // non-square numbers. import java.io.*; import java.math.*; class GFG { // Returns n-th non-square number. static int nonsquare( int n) { return n + ( int )( 0.5 + (Math.sqrt(n))); } static void printNonSquare( int n) { // loop to print non squares // below n for ( int i = 1 ; i <= n; i++) System.out.print(nonsquare(i)+ " " ); } // Driver code public static void main(String args[]) { int n = 10 ; printNonSquare(n); } } /* This code is contributed by Nikita Tiwari.*/ |
Python3
# Python 3 program to print # first n non-square numbers. import math # Returns n-th non-square # number. def nonsquare(n) : return n + ( int )( 0.5 + math.sqrt(n)) def printNonSquare(n) : # loop to print non # squares below n for i in range ( 1 , n + 1 ) : print (nonsquare(i), end = " " ) n = 10 printNonSquare(n) # This code is contributed by Nikita Tiwari. |
C#
// C# program to print first n // non-square numbers. using System; class GFG { // Returns n-th non-square number. static int nonsquare( int n) { return n + ( int )(0.5 + (Math.Sqrt(n))); } static void printNonSquare( int n) { // loop to print non squares // below n for ( int i = 1; i <= n; i++) Console.Write(nonsquare(i)+ " " ); } // Driver code public static void Main() { int n = 10; printNonSquare(n); } } // This code is contributed // by Akanksha Rai(Abby_akku) |
PHP
<?php // PHP program to print first n // non square number // Returns n-th non-square number. function nonsquare( $n ) { return $n + (int)(0.5 + sqrt( $n )); } function printNonSquare( $n ) { // loop to print non squares // below n for ( $i = 1; $i <= $n ; $i ++) printf(nonsquare( $i ) . " " ); } // Driver Code $n = 10; printNonSquare( $n ); // This code is contributed by mits ?> |
Javascript
<script> // Javascript program to print first n // non square number // Returns n-th non-square number. function nonsquare(n) { return n + parseInt(0.5 + Math.sqrt(n)); } function printNonSquare(n) { // loop to print non squares // below n for (let i = 1; i <= n; i++) document.write(nonsquare(i) + " " ); } // Driver Code let n = 10; printNonSquare(n); // This code is contributed by gfgking. </script> |
输出：
2 3 5 6 7 8 10 11 12 13
一 替代方案 基于两个正方形之间的非正方形数始终是偶数这一事实。 两个连续数字k和k+1之间的非平方数的计数为 =（k+1） 2. –k 2. + 1 =2k 1-4、4-9、9-16……之间的非平方数分别为2、4、6。这些是偶数。
以下是上述方法的实施情况。
C++
// CPP program to print first n // non square number #include <assert.h> #include <math.h> #include <stdio.h> void printNonSquare( int n) { int curr_count = 2, num = 2, count = 0; while (count < n) { // Print curr_count numbers. curr_count // is current gap between two square numbers. for ( int i = 0; i < curr_count && count < n; i++) { printf ( "%d " , num); count++; num++; } // skip a square number. num++; // Count of next non-square numbers // is next even number. curr_count += 2; } } int main() { int n = 10; printNonSquare(n); return 0; } |
JAVA
// Java program to print first n // non-square numbers. import java.io.*; import java.math.*; class GFG { static void printNonSquare( int n) { int curr_count = 2 , num = 2 , count = 0 ; while (count < n) { // Print curr_count numbers. curr_count is // current gap between two square numbers. for ( int i = 0 ; i < curr_count && count < n; i++) { System.out.print( num+ " " ); count++; num++; } // skip a square number. num++; // Count of next non-square // numbers is next even number. curr_count += 2 ; } } // Driver code public static void main(String args[]) { int n = 10 ; printNonSquare(n); } } /* This code is contributed by Nikita Tiwari.*/ |
Python3
# Python 3 program to print # first n non-square numbers. import math # Returns n-th non-square # number. def printNonSquare(n) : curr_count = 2 num = 2 count = 0 while (count < n) : # Print curr_count numbers. # curr_count is current gap # between two square numbers. i = 0 while (i < curr_count and count < n) : print (num, end = " " ) count = count + 1 num = num + 1 i = i + 1 # skip a square number. num = num + 1 # Count of next non-square # numbers is next even number. curr_count = curr_count + 2 n = 10 printNonSquare(n) # This code is contributed by Nikita Tiwari. |
C#
// C# program to print // first n non-square // numbers. using System; class GFG { static void printNonSquare( int n) { int curr_count = 2, num = 2, count = 0; while (count < n) { // Print curr_count // numbers. curr_count // is current gap between // two square numbers. for ( int i = 0; i < curr_count && count < n; i++) { Console.Write(num + " " ); count++; num++; } // skip a square number. num++; // Count of next // non-square numbers // is next even number. curr_count += 2; } } // Driver code static public void Main () { int n = 10; printNonSquare(n); } } // This code is contributed // by akt_mit |
PHP
<?php // PHP program to print first n // non-square numbers. function printNonSquare( $n ) { $curr_count = 2; $num = 2; $count = 0; while ( $count < $n ) { // Print curr_count numbers. curr_count is // current gap between two square numbers. for ( $i = 0; $i < $curr_count && $count < $n ; $i ++) { echo ( $num . " " ); $count ++; $num ++; } // skip a square number. $num ++; // Count of next non-square // numbers is next even number. $curr_count += 2; } } // Driver code $n = 10; printNonSquare( $n ); // This code is contributed by Mukul Singh. ?> |
Javascript
<script> // Javascript program to print first // n non-square numbers. function printNonSquare(n) { let curr_count = 2, num = 2, count = 0; while (count < n) { // Print curr_count // numbers. curr_count // is current gap between // two square numbers. for (let i = 0; i < curr_count && count < n; i++) { document.write(num + " " ); count++; num++; } // Skip a square number. num++; // Count of next // non-square numbers // is next even number. curr_count += 2; } } // Driver code let n = 10; printNonSquare(n); // This code is contributed by decode2207 </script> |
输出：
2 3 5 6 7 8 10 11 12 13
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