Los números impares positivos en orden ascendente como 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, …. y agrupados como (1), (3, 5), (7, 9, 11), (13, 15, 17, 19),…. y así.
Así, el primer grupo es (1), el segundo grupo es (3, 5) y el tercer grupo es (7, 9, 11), etc. en general, el k-ésimo grupo contiene los siguientes k elementos de la secuencia .
Dado k , encuentra la suma del k- ésimo grupo.
Ejemplos:
Input : k = 3 Output : 27 3rd group is (7, 9, 11) and the sum is 27. Input : k = 1 Output : 1
Método 1: O(n)
La idea es encontrar el primer elemento del k-ésimo grupo.
Por ejemplo:
- El primer elemento del primer grupo es 1, que es el primer número impar.
- El primer elemento del segundo grupo es 3, que es el segundo número impar.
- El primer elemento del tercer grupo es 7, que es el cuarto número impar.
- El primer elemento del cuarto grupo es 13, que es el séptimo número impar.
- y así.
En general, el primer elemento del k-ésimo grupo es el enésimo número impar, donde
n = (1 + 2 + 3 +……+ (k – 1)) + 1.
Ahora, como sabemos, el enésimo número impar es 2n – 1 Esto nos da el primer elemento del k-ésimo grupo. También sabemos que hay k elementos en el grupo, por lo que podemos encontrar su suma simplemente contando hacia arriba desde 2n – 1, por dos, k veces y sumándolos todos. Esto nos da una solución de tiempo lineal.
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>
Producción :
27
Método 2: O(1)
Una solución complicada es encontrar k 3 . Uno puede observar fácilmente que la suma del k-ésimo grupo será k 3 .
A continuación se muestra la implementación de este enfoque:
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>
Producción :
27