正奇数的升序为1，3，5，7，9，11，13，15，17，19…。分为（1）、（3、5）、（7、9、11）、（13、15、17、19）组…。等等 因此，第一组是（1），第二组是（3，5），第三组是（7，9，11），等等 th 组包含序列中接下来的k个元素。 鉴于 K ，求k的和 th 组 例如：
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Input : k = 3Output : 273rd group is (7, 9, 11) and the sum is 27.Input : k = 1Output : 1
方法1:O（n） 我们的想法是找到kth群的第一个元素。 例如：
- 第一组的第一个元素是1，它是第一个奇数。
- 第二组的第一个元素是3，这是2st奇数。
- 第三组的第一个元素是7，这是第四个奇数。
- 第4组的第一个元素是13，这是第7个奇数。
- 等等
一般来说，第k个群的第一个元素是第n个奇数，其中 n=（1+2+3+…+（k–1））+1。 我们知道，第n个奇数是2n–1。这给了我们kth群的第一个元素。我们也知道群中有k个元素，所以我们可以通过简单地从2n–1向上计数，乘以2，k次，然后将它们全部相加来求和。这给了我们一个线性时间解。
C++
// CPP program to find sum of k-th group of // positive odd integers. #include <bits/stdc++.h> using namespace std; // Return the sum of k-th group of positive // odd integers. int kthgroupsum( int k) { // Finding first element of kth group. int cur = (k * (k - 1)) + 1; int sum = 0; // Finding the sum. while (k--) { sum += cur; cur += 2; } return sum; } // Driver code int main() { int k = 3; cout << kthgroupsum(k) << endl; return 0; } |
JAVA
// Java code to find sum of k-th group // of positive odd integers. import java.util.Arrays; import java.util.Collections; class GFG { // Return the sum of k-th group // of positive odd integers. public static int kthgroupsum( int k) { // Finding first element of kth group. int cur = (k * (k - 1 )) + 1 ; int sum = 0 ; // Finding the sum. while (k-- > 0 ) { sum += cur; cur += 2 ; } return sum; } // Driver program to test above methods public static void main(String[] args) { int k = 3 ; System.out.print(kthgroupsum(k)); } } // This code is contributed by Chhavi |
Python3
# Python3 code to find sum of k-th group # of positive odd integers. # Return the sum of k-th group of # positive odd integers. def kthgroupsum( k ): # Finding first element of kth group. cur = int ((k * (k - 1 )) + 1 ) sum = 0 # Finding the sum. while k: sum + = cur cur + = 2 k = k - 1 return sum # Driver code k = 3 print (kthgroupsum(k)) # This code is contributed by "Sharad_Bhardwaj". |
C#
// C# code to find sum of k-th group // of positive odd integers. using System; class GFG { // Return the sum of k-th group // of positive odd integers. public static int kthgroupsum( int k) { // Finding first element of kth group. int cur = (k * (k - 1)) + 1; int sum = 0; // Finding the sum. while (k-- > 0) { sum += cur; cur += 2; } return sum; } // Driver program to test above methods public static void Main() { int k = 3; Console.WriteLine(kthgroupsum(k)); } } // This code is contributed by vt_m. |
PHP
<?php // PHP program to find // sum of k-th group of // positive odd integers. // Return the sum of // k-th group of positive // odd integers. function kthgroupsum( $k ) { // Finding first element // of kth group. $cur = ( $k * ( $k - 1)) + 1; $sum = 0; // Finding the sum. while ( $k --) { $sum += $cur ; $cur += 2; } return $sum ; } // Driver code $k = 3; echo kthgroupsum( $k ) ; // This code is contributed by anuj_67. ?> |
Javascript
<script> // javascript program to find // sum of k-th group of // positive odd integers. // Return the sum of // k-th group of positive // odd integers. function kthgroupsum(k) { // Finding first element // of kth group. let cur = (k * (k - 1)) + 1; let sum = 0; // Finding the sum. while (k--) { sum += cur; cur += 2; } return sum; } // Driver code let k = 3; document.write(kthgroupsum(k)); // This code is contributed by _saurabh_jaiswal. </script> |
输出：
27
方法2:O（1） 一个棘手的解决办法是找到k 3. 可以很容易地观察到，第k个群的和是k 3. . 以下是该方法的实施情况：
C++
// Efficient CPP program to find sum of k-th // group of positive odd integers. #include <bits/stdc++.h> using namespace std; // Return the sum of kth group of positive // odd integer. int kthgroupsum( int k) { return k * k * k; } // Driven Program int main() { int k = 3; cout << kthgroupsum(k) << endl; return 0; } |
JAVA
// Efficient Java code to find sum of k-th // group of positive odd integers. import java.util.Arrays; import java.util.Collections; class GFG { // Return the sum of kth group of // positive odd integer. public static int kthgroupsum( int k) { return k * k * k; } // Driver program to test above methods public static void main(String[] args) { int k = 3 ; System.out.print( kthgroupsum(k)); } } // This code is contributed by Chhavi |
Python3
# Efficient Python code to find sum of # k-th group of positive odd integers. # Return the sum of kth group of positive # odd integer. def kthgroupsum( k ): return k * k * k # Driver code k = 3 print (kthgroupsum(k)) # This code is contributed by "Sharad_Bhardwaj". |
C#
// Efficient C# code to find sum of k-th // group of positive odd integers. using System; class GFG { // Return the sum of kth group of // positive odd integer. public static int kthgroupsum( int k) { return k * k * k; } // Driver program to test above methods public static void Main() { int k = 3; Console.WriteLine(kthgroupsum(k)); } } // This code is contributed by vt_m. |
PHP
<?php // Efficient PHP program to // find sum of k-th group of // positive odd integers. // Return the sum of kth group // of positive odd integer. function kthgroupsum( $k ) { return $k * $k * $k ; } // Driven Code $k = 3; echo kthgroupsum( $k ); // This code is contributed by anuj_67. ?> |
Javascript
<script> // Efficient Javascript program to // find sum of k-th group of // positive odd integers. // Return the sum of kth group // of positive odd integer. function kthgroupsum(k) { return k * k * k; } // Driven Code let k = 3; document.write(kthgroupsum(k)); // This code is contributed by _saurabh_jaiswal. </script> |
输出：
27
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