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What is an astonishing number?

Astonishing Number is a number N whose representation can be decomposed into two parts, a and b, such that N is equal to the sum of the integers from a to b and a + b = N where '+' denotes concatenation. Few Astonishing Numbers are: 15, 27, 429, 1353, 1863, 3388, 3591, 7119..

geeksforgeeks.org - Astonishing Numbers - GeeksforGeeks

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Astonishing Number is a number N whose representation can be decomposed into two parts, a and b, such that N is equal to the sum of the integers from a to b and a + b = N where ‘+’ denotes concatenation.

Few Astonishing Numbers are:

15, 27, 429, 1353, 1863, 3388, 3591, 7119..

Check if N is an Astonishing number

Given a number N, the task is to check if N is an Astonishing Number or not. If N is an Astonishing Number then print “Yes” else print “No”.

Examples:

Input: N = 429

Output: Yes

Explanation:

429 = 4 + 5 + 6 …….. + 29, where a = 4, b = 29

and a + b = 429 where + denotes concatenation

Input: N = 28

Output: No

Approach: The idea is to run two loops of i and j, to find the sum of all integers from i till the sum becomes >= N. If at any point of time the sum becomes equals to N then we will also check if the concatenation of i and j equal to N or not. If equals then the number is an Astonishing number

Below is the implementation of the above approach:

C++

#include using namespace std; int concat( int a, int b) { string s1 = to_string(a); string s2 = to_string(b); string s = s1 + s2; int c = stoi(s); return c; } bool isAstonishing( int n) { for ( int i = 1; i < n; i++) { int sum = 0; for ( int j = i; j < n; j++) { sum += j; if (sum == n) { int concatenation = concat(i, j); if (concatenation == n) { return true ; } } } } return false ; } int main() { int n = 429; if (isAstonishing(n)) cout << "Yes" ; else cout << "No" ; return 0; } Java import java.io.*; class GFG{ static int concat( int a, int b) { String s1 = Integer.toString(a); String s2 = Integer.toString(b); String s = s1 + s2; int c = Integer.parseInt(s); return c; } static boolean isAstonishing( int n) { for ( int i = 1 ; i < n; i++) { int sum = 0 ; for ( int j = i; j < n; j++) { sum += j; if (sum == n) { int concatenation = concat(i, j); if (concatenation == n) { return true ; } } } } return false ; } public static void main (String[] args) { int n = 429 ; if (isAstonishing(n)) System.out.println( "Yes" ); else System.out.println( "No" ); } } Python3 def concat(a, b): s1 = str (a) s2 = str (b) s = s1 + s2 c = int (s) return c def isAstonishing(n): for i in range (n): sum = 0 for j in range (i, n): sum + = j if ( sum = = n): concatenation = concat(i, j) if (concatenation = = n): return True return False n = 429 if (isAstonishing(n)): print ( 'Yes' ) else : print ( 'No' ) C#

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using System; class GFG{ static int concat( int a, int b) { String s1 = a.ToString(); String s2 = b.ToString(); String s = s1 + s2; int c = Int32.Parse(s); return c; } static bool isAstonishing( int n) { for ( int i = 1; i < n; i++) { int sum = 0; for ( int j = i; j < n; j++) { sum += j; if (sum == n) { int concatenation = concat(i, j); if (concatenation == n) { return true ; } } } } return false ; } public static void Main(String[] args) { int n = 429; if (isAstonishing(n)) Console.WriteLine( "Yes" ); else Console.WriteLine( "No" ); } } Javascript

Output: Yes

Time Complexity: O(n)

Auxiliary Space: O(1)

geeksforgeeks.org - Astonishing Numbers - GeeksforGeeks

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