Given a number N, write a function to express N as sum of two or more consecutive positive numbers. If there is no solution, output -1. If there are multiple solution, then print one of them.
Examples:
Input : N = 10 Output : 4 + 3 + 2 + 1 Input : N = 8 Output : -1 Input : N = 24 Output : 9 + 8 + 7
Sum of first n natural numbers = n * (n + 1)/2 Sum of first (n + k) numbers = (n + k) * (n + k + 1)/2 If N is sum of k consecutive numbers, then following must be true. N = [(n+k)(n+k+1) - n(n+1)] / 2 OR 2 * N = [(n+k)(n+k+1) - n(n+1)]
Below is the implementation based on above idea.
C++
// C++ program to print a consecutive sequence// to express N if possible.#include <bits/stdc++.h>using namespace std;// Print consecutive numbers from// last to firstvoid printConsecutive(int last, int first){ cout << first++; for (int x = first; x<= last; x++) cout << " + " << x;}void findConsecutive(int N){ for (int last=1; last<N; last++) { for (int first=0; first<last; first++) { if (2*N == (last-first)*(last+first+1)) { cout << N << " = "; printConsecutive(last, first+1); return; } } } cout << "-1";}// Driver codeint main(){ int n = 12; findConsecutive(n); return 0;} |
Java
// Java program to print a consecutive sequence// to express N if possible.import java.util.*;class GFG{// Print consecutive numbers from// last to firststatic void printConsecutive(int last, int first){ System.out.print(first++); for (int x = first; x<= last; x++) System.out.print(" + " + x);}static void findConsecutive(int N){ for (int last = 1; last < N; last++) { for (int first = 0; first < last; first++) { if (2*N == (last-first)*(last+first+1)) { System.out.print(N+ " = "); printConsecutive(last, first+1); return; } } } System.out.print("-1");}// Driver codepublic static void main(String[] args){ int n = 12; findConsecutive(n);}}// This code is contributed by umadevi9616 |
Python3
# Python3 program to print a consecutive# sequence to express N if possible.# Print consecutive numbers # from last to firstdef printConsecutive(last, first): print (first, end = "") first += 1 for x in range(first, last + 1): print (" +", x, end = "")def findConsecutive(N): for last in range(1, N): for first in range(0, last): if 2 * N == (last - first) * (last + first + 1): print (N, "= ", end = "") printConsecutive(last, first + 1) return print ("-1")# Driver coden = 12findConsecutive(n)# This code is contributed by Shreyanshi Arun. |
C#
// C# program to print a consecutive sequence// to express N if possible.using System;class GfG{ // Print consecutive numbers from // last to first static void printConsecutive(int last, int first) { Console.Write(first++); for (int x = first; x <= last; x++) Console.Write(" + "+x); } static void findConsecutive(int N) { for (int last = 1; last < N; last++) { for (int first = 0; first < last; first++) { if (2 * N == (last - first) * (last + first + 1)) { Console.Write(N + " = "); printConsecutive(last, first + 1); return; } } } Console.Write("-1"); } // Driver code public static void Main () { int n = 12; findConsecutive(n); }}// This code is contributed by vt_m |
PHP
<?php// PHP program to print a consecutive// sequence to express N if possible.// Print consecutive numbers from// last to firstfunction printConsecutive($last, $first){ echo $first++; for ($x = $first; $x<= $last; $x++) echo " + " , $x;}function findConsecutive($N){ for ($last = 1; $last < $N; $last++) { for ($first = 0; $first < $last; $first++) { if (2 * $N == ($last - $first) * ($last + $first + 1)) { echo $N , " = "; printConsecutive($last, $first + 1); return; } } } echo "-1";} // Driver Code $n = 12; findConsecutive($n); // This code is contributed by nitin mittal?> |
Javascript
<script> // Javascript program to print a consecutive// sequence to express N if possible. // Print consecutive numbers from// last to firstfunction printConsecutive(last, first){ document.write(first++); for (let x = first; x<= last; x++) document.write( " + " + x);} function findConsecutive(N){ for (let last = 1; last < N; last++) { for (let first = 0; first < last; first++) { if (2 * N == (last - first) * (last + first + 1)) { document.write(N + " = "); printConsecutive(last, first + 1); return; } } } document.write("-1");} // Driver Code let n = 12; findConsecutive(n); // This code is contributed by _saurabh_jaiswal</script> |
Output:
12 = 3 + 4 + 5
Reference :
https://math.stackexchange.com/questions/139842/in-how-many-ways-can-a-number-be-expressed-as-a-sum-of-consecutive-numbers
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