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++
// C++ implementation for the// above approach#include <bits/stdc++.h>using namespace std;// Function to concatenate// two integers into oneint concat(int a, int b){ // Convert both the integers to string string s1 = to_string(a); string s2 = to_string(b); // Concatenate both strings string s = s1 + s2; // Convert the concatenated string // to integer int c = stoi(s); // return the formed integer return c;}// Function to check if N is a// Astonishing numberbool isAstonishing(int n){ // Loop to find sum of all integers // from i till the sum becomes >= n for (int i = 1; i < n; i++) { // variable to store // sum of all integers // from i to j and // check if sum and // concatenation equals n or not int sum = 0; for (int j = i; j < n; j++) { sum += j; if (sum == n) { // finding concatenation // of i and j int concatenation = concat(i, j); // condition for // Astonishing number if (concatenation == n) { return true; } } } } return false;}// Driver Codeint main(){ // Given Number int n = 429; // Function Call if (isAstonishing(n)) cout << "Yes"; else cout << "No"; return 0;} |
Java
// Java implementation for the// above approachimport java.io.*;class GFG{// Function to concatenate// two integers into onestatic int concat(int a, int b){ // Convert both the integers to String String s1 = Integer.toString(a); String s2 = Integer.toString(b); // Concatenate both Strings String s = s1 + s2; // Convert the concatenated String // to integer int c = Integer.parseInt(s); // return the formed integer return c;}// Function to check if N is a// Astonishing numberstatic boolean isAstonishing(int n){ // Loop to find sum of all integers // from i till the sum becomes >= n for (int i = 1; i < n; i++) { // variable to store // sum of all integers // from i to j and // check if sum and // concatenation equals n or not int sum = 0; for (int j = i; j < n; j++) { sum += j; if (sum == n) { // finding concatenation // of i and j int concatenation = concat(i, j); // condition for // Astonishing number if (concatenation == n) { return true; } } } } return false;}// Driver Codepublic static void main (String[] args){ // Given Number int n = 429; // Function Call if (isAstonishing(n)) System.out.println("Yes"); else System.out.println("No");}}// This code is contributed by shubhamsingh10 |
Python3
# Python3 implementation for the # above approach # Function to concatenate # two integers into one def concat(a, b): # Convert both the integers to string s1 = str(a) s2 = str(b) # Concatenate both strings s = s1 + s2 # Convert the concatenated string # to integer c = int(s) # return the formed integer return c# Function to check if N is a # Astonishing number def isAstonishing(n): # Loop to find sum of all integers # from i till the sum becomes >= n for i in range(n): # variable to store # sum of all integers # from i to j and # check if sum and # concatenation equals n or not sum = 0 for j in range(i, n): sum += j if (sum == n): # finding concatenation # of i and j concatenation = concat(i, j) # condition for # Astonishing number if (concatenation == n): return True return False # Driver Code # Given Number n = 429# Function Call if (isAstonishing(n)): print('Yes')else: print('No')# This code is contributed by Yatin |
C#
// C# implementation for the// above approachusing System;class GFG{// Function to concatenate// two integers into onestatic int concat(int a, int b){ // Convert both the integers to String String s1 = a.ToString(); String s2 = b.ToString(); // Concatenate both Strings String s = s1 + s2; // Convert the concatenated String // to integer int c = Int32.Parse(s); // return the formed integer return c;}// Function to check if N is a// Astonishing numberstatic bool isAstonishing(int n){ // Loop to find sum of all integers // from i till the sum becomes >= n for (int i = 1; i < n; i++) { // variable to store // sum of all integers // from i to j and // check if sum and // concatenation equals n or not int sum = 0; for (int j = i; j < n; j++) { sum += j; if (sum == n) { // finding concatenation // of i and j int concatenation = concat(i, j); // condition for // Astonishing number if (concatenation == n) { return true; } } } } return false;}// Driver Codepublic static void Main(String[] args){ // Given Number int n = 429; // Function Call if (isAstonishing(n)) Console.WriteLine("Yes"); else Console.WriteLine("No");}}// This code is contributed by 29AjayKumar |
Javascript
<script>// Javascript implementation for the// above approach// Function to concatenate// two integers into onefunction concat(a, b){ // Convert both the integers to string var s1 = a.toString(); var s2 = b.toString(); // Concatenate both strings var s = s1 + s2; // Convert the concatenated string // to integer var c = s; // return the formed integer return c;}// Function to check if N is a// Astonishing numberfunction isAstonishing(n){ // Loop to find sum of all integers // from i till the sum becomes >= n for (var i = 1; i < n; i++) { // variable to store // sum of all integers // from i to j and // check if sum and // concatenation equals n or not var sum = 0; for (var j = i; j < n; j++) { sum += j; if (sum == n) { // finding concatenation // of i and j var concatenation = concat(i, j); // condition for // Astonishing number if (concatenation == n) { return true; } } } } return false;}// Driver Code// Given Numbervar n = 429;// Function Callif (isAstonishing(n)) document.write( "Yes");else document.write( "No");</script> |
Output:
Yes
Time Complexity: O(n)
Auxiliary Space: O(1)
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