Given an array arr[] consisting of 4 integers each between [1-9], the task is to check whether it is possible to get the number 24 by placing the operators +, –, /, and * between the numbers or grouping them using parenthesis. If it is possible then print “Possible“, Otherwise print “Not Possible”.
Examples:
Input: arr[] = {3, 6, 8, 2}
Output: Possible
Explanation:
One possible way to get 24 is 3 × 6 + 8 – 2 = 24.Input: arr[] = {7, 2, 10, 6}
Output: Possible
Explanation:
One possible way to get 24 is (7 × 2–10) x 6 = 24.
Approach: The simplest idea to solve this problem is based on backtracking. Follow the steps below to solve the problem:
- Create a function say isNumber24Possible(arr[]) and apply all the four operations in between each consecutive element and recursively call the function say isNumber24PossibleUtil(op1, op2, op3) which performs all possible operations on 3 numbers.
- The function isNumber24PossibleUtil(op1, op2, op3) applies all the four operation in between each consecutive elements and call the overloaded function isNumber24PossibleUtil(op1, op2) which applies operation on 2 numbers.
- The function isNumber24PossibleUtil(op1, op2) is used to check whether the given two numbers can reduce to 24 using any of the 4 operations i.e +, –, /, and *. Try every operation between the numbers, if any of them result in 24 then return true otherwise return false.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Division operation might loose some// precision consider 0.001 as tolerance.#define TOLERANCE 0.001// This function is used to check whether// given two number can reduce to 24 using// any of the 4 operationsbool isNumber24PossibleUtil(double op1, double op2){ // Check if any of the operation result to 24 if (abs(op1 + op2 - 24.0) < TOLERANCE || abs(op1 - op2 - 24.0) < TOLERANCE || abs(op1 * op2 - 24.0) < TOLERANCE || op2 && abs(op1 / op2 - 24.0) < TOLERANCE) return true; return false;}// Function which applies all the possible operations// in between all the parameters and call the function// which check if given number can result in 24 or notbool isNumber24PossibleUtil(double op1, double op2, double op3){ // Applying operation between two operands reduces // the count of operands to two if (isNumber24PossibleUtil(op1 + op2, op3) || isNumber24PossibleUtil(op1 - op2, op3) || isNumber24PossibleUtil(op1 * op2, op3) || op2 && isNumber24PossibleUtil(op1 / op2, op3)) return true; if (isNumber24PossibleUtil(op1, op2 + op3) || isNumber24PossibleUtil(op1, op2 - op3) || isNumber24PossibleUtil(op1, op2 * op3) || op3 && isNumber24PossibleUtil(op1, op2 / op3)) return true; return false;}// Function takes given array as arr parameter// and apply all possible operation in every// consecutive elements and check if the remaining// 3 parameters can be used for obtaining 24 or notbool isNumber24Possible(int arr[]){ // Apply every operation between first two operands if (isNumber24PossibleUtil(arr[0] + arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] - arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] * arr[1], arr[2], arr[3]) || arr[1] && isNumber24PossibleUtil(arr[0] / arr[1], arr[2], arr[3])) return true; // Between second and third operands if (isNumber24PossibleUtil(arr[0], arr[1] + arr[2], arr[3]) || isNumber24PossibleUtil(arr[0], arr[1] - arr[2], arr[3]) || isNumber24PossibleUtil(arr[0], arr[1] * arr[2], arr[3]) || arr[2] && isNumber24PossibleUtil(arr[0], arr[1] / arr[2], arr[3])) return true; // Between third and fourth operands if (isNumber24PossibleUtil(arr[0], arr[1], arr[2] + arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] - arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] * arr[3]) || arr[3] && isNumber24PossibleUtil(arr[0], arr[1], arr[2] / arr[3])) return true; return false;}// Driver Codeint main(){ // Given Input int arr[] = { 3, 6, 8, 2 }; // Function Call if (isNumber24Possible(arr)) { cout << "Possible" << endl; } else { cout << "Not Possible" << endl; } return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{ // Division operation might loose some// precision consider 0.001 as tolerance.static double TOLERANCE = 0.001;// This function is used to check whether// given two number can reduce to 24 using// any of the 4 operationsstatic boolean isNumber24PossibleUtil(double op1, double op2){ // Check if any of the operation result to 24 if (Math.abs(op1 + op2 - 24.0) < TOLERANCE || Math.abs(op1 - op2 - 24.0) < TOLERANCE || Math.abs(op1 * op2 - 24.0) < TOLERANCE || op2 != 0 && Math.abs(op1 / op2 - 24.0) < TOLERANCE) return true; return false;}// Function which applies all the possible operations// in between all the parameters and call the function// which check if given number can result in 24 or notstatic boolean isNumber24PossibleUtil(double op1, double op2, double op3){ // Applying operation between two operands reduces // the count of operands to two if (isNumber24PossibleUtil(op1 + op2, op3) || isNumber24PossibleUtil(op1 - op2, op3) || isNumber24PossibleUtil(op1 * op2, op3) || op2 != 0 && isNumber24PossibleUtil(op1 / op2, op3)) return true; if (isNumber24PossibleUtil(op1, op2 + op3) || isNumber24PossibleUtil(op1, op2 - op3) || isNumber24PossibleUtil(op1, op2 * op3) || op3 != 0 && isNumber24PossibleUtil(op1, op2 / op3)) return true; return false;}// Function takes given array as arr parameter// and apply all possible operation in every// consecutive elements and check if the remaining// 3 parameters can be used for obtaining 24 or notstatic boolean isNumber24Possible(int arr[]){ // Apply every operation between first two operands if (isNumber24PossibleUtil(arr[0] + arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] - arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] * arr[1], arr[2], arr[3]) || arr[1] != 0 && isNumber24PossibleUtil(arr[0] / arr[1], arr[2], arr[3])) return true; // Between second and third operands if (isNumber24PossibleUtil(arr[0], arr[1] + arr[2], arr[3]) || isNumber24PossibleUtil(arr[0], arr[1] - arr[2], arr[3]) || isNumber24PossibleUtil(arr[0], arr[1] * arr[2], arr[3]) || arr[2] != 0 && isNumber24PossibleUtil(arr[0], arr[1] / arr[2], arr[3])) return true; // Between third and fourth operands if (isNumber24PossibleUtil(arr[0], arr[1], arr[2] + arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] - arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] * arr[3]) || arr[3] != 0 && isNumber24PossibleUtil(arr[0], arr[1], arr[2] / arr[3])) return true; return false;} // Driver Codepublic static void main(String[] args){ // Given Input int arr[] = { 3, 6, 8, 2 }; // Function Call if (isNumber24Possible(arr)) { System.out.print("Possible"); } else { System.out.print("Not Possible"); }}}// This code is contributed by code_hunt |
Python3
# Python3 program for the above approach# Division operation might loose some# precision consider 0.001 as tolerance.TOLERANCE = 0.001# This function is used to check whether# given two number can reduce to 24 using# any of the 4 operationsdef isNumber24PossibleUtill(op1, op2): # Check if any of the operation result to 24 if (abs(op1 + op2 - 24.0) < TOLERANCE or abs(op1 - op2 - 24.0) < TOLERANCE or abs(op1 * op2 - 24.0) < TOLERANCE or op2 and abs(op1 / op2 - 24.0) < TOLERANCE): return True return False# Function which applies all the possible operations# in between all the parameters and call the function# which check if given number can result in 24 or notdef isNumber24PossibleUtil(op1, op2, op3): # Applying operation between two operands reduces # the count of operands to two if ((isNumber24PossibleUtill(op1 + op2, op3)) or (isNumber24PossibleUtill(op1 - op2, op3)) or (isNumber24PossibleUtill(op1 * op2, op3)) or (op2 and isNumber24PossibleUtill(op1 / op2, op3))): return True if (isNumber24PossibleUtill(op1, op2 + op3) or isNumber24PossibleUtill(op1, op2 - op3) or isNumber24PossibleUtill(op1, op2 * op3) or op3 and isNumber24PossibleUtill(op1, op2 / op3)): return True return False# Function takes given array as arr parameter# and apply all possible operation in every# consecutive elements and check if the remaining# 3 parameters can be used for obtaining 24 or notdef isNumber24Possible(arr): # Apply every operation between first two operands if (isNumber24PossibleUtil(arr[0] + arr[1], arr[2], arr[3]) or isNumber24PossibleUtil(arr[0] - arr[1], arr[2], arr[3]) or isNumber24PossibleUtil(arr[0] * arr[1], arr[2], arr[3]) or arr[1] and isNumber24PossibleUtil(arr[0] / arr[1], arr[2], arr[3])): return True # Between second and third operands if (isNumber24PossibleUtil(arr[0], arr[1] + arr[2], arr[3]) or isNumber24PossibleUtil(arr[0], arr[1] - arr[2], arr[3]) or isNumber24PossibleUtil(arr[0], arr[1] * arr[2], arr[3]) or arr[2] and isNumber24PossibleUtil(arr[0], arr[1] / arr[2], arr[3])): return True # Between third and fourth operands if (isNumber24PossibleUtil(arr[0], arr[1], arr[2] + arr[3]) or isNumber24PossibleUtil(arr[0], arr[1], arr[2] - arr[3]) or isNumber24PossibleUtil(arr[0], arr[1], arr[2] * arr[3]) or arr[3] and isNumber24PossibleUtil(arr[0], arr[1], arr[2] / arr[3])): return True return False# Driver Code# Given Inputarr = [ 3, 6, 8, 2 ]# Function Callif (isNumber24Possible(arr)): print("Possible")else: print("Not Possible")# This code is contributed by sanjoy_62 |
C#
using System;public class GFG { static double TOLERANCE = 0.001; // This function is used to check whether // given two number can reduce to 24 using // any of the 4 operations static bool isNumber24PossibleUtil(double op1, double op2) { // Check if any of the operation result to 24 if (Math.Abs(op1 + op2 - 24.0) < TOLERANCE || Math.Abs(op1 - op2 - 24.0) < TOLERANCE || Math.Abs(op1 * op2 - 24.0) < TOLERANCE || op2 != 0 && Math.Abs(op1 / op2 - 24.0) < TOLERANCE) return true; return false; } // Function which applies all the possible operations // in between all the parameters and call the function // which check if given number can result in 24 or not static bool isNumber24PossibleUtil(double op1, double op2, double op3) { // Applying operation between two operands reduces // the count of operands to two if (isNumber24PossibleUtil(op1 + op2, op3) || isNumber24PossibleUtil(op1 - op2, op3) || isNumber24PossibleUtil(op1 * op2, op3) || op2 != 0 && isNumber24PossibleUtil(op1 / op2, op3)) return true; if (isNumber24PossibleUtil(op1, op2 + op3) || isNumber24PossibleUtil(op1, op2 - op3) || isNumber24PossibleUtil(op1, op2 * op3) || op3 != 0 && isNumber24PossibleUtil(op1, op2 / op3)) return true; return false; } // Function takes given array as arr parameter // and apply all possible operation in every // consecutive elements and check if the remaining // 3 parameters can be used for obtaining 24 or not static bool isNumber24Possible(int[] arr) { // Apply every operation between first two operands if (isNumber24PossibleUtil(arr[0] + arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] - arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] * arr[1], arr[2], arr[3]) || arr[1] != 0 && isNumber24PossibleUtil( arr[0] / arr[1], arr[2], arr[3])) return true; // Between second and third operands if (isNumber24PossibleUtil(arr[0], arr[1] + arr[2], arr[3]) || isNumber24PossibleUtil( arr[0], arr[1] - arr[2], arr[3]) || isNumber24PossibleUtil( arr[0], arr[1] * arr[2], arr[3]) || arr[2] != 0 && isNumber24PossibleUtil( arr[0], arr[1] / arr[2], arr[3])) return true; // Between third and fourth operands if (isNumber24PossibleUtil(arr[0], arr[1], arr[2] + arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] - arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] * arr[3]) || arr[3] != 0 && isNumber24PossibleUtil( arr[0], arr[1], arr[2] / arr[3])) return true; return false; } static public void Main() { int[] arr = { 3, 6, 8, 2 }; // Function Call if (isNumber24Possible(arr)) { Console.WriteLine("Possible"); } else { Console.WriteLine("Not Possible"); } }}// This code is contributed by maddler. |
Javascript
<script>// JavaScript program to implement above approach// Division operation might loose some// precision consider 0.001 as tolerance.const TOLERANCE = 0.001// This function is used to check whether// given two number can reduce to 24 using// any of the 4 operationsfunction isNumber24PossibleUtill(op1, op2){ // Check if any of the operation result to 24 if (Math.abs(op1 + op2 - 24.0) < TOLERANCE || Math.abs(op1 - op2 - 24.0) < TOLERANCE || Math.abs(op1 * op2 - 24.0) < TOLERANCE || op2 && Math.abs(op1 / op2 - 24.0) < TOLERANCE) return true return false}// Function which applies all the possible operations// in between all the parameters and call the function// which check if given number can result in 24 or notfunction isNumber24PossibleUtil(op1, op2, op3){ // Applying operation between two operands reduces // the count of operands to two if ((isNumber24PossibleUtill(op1 + op2, op3)) || (isNumber24PossibleUtill(op1 - op2, op3)) || (isNumber24PossibleUtill(op1 * op2, op3)) || (op2 && isNumber24PossibleUtill(op1 / op2, op3))) return true if (isNumber24PossibleUtill(op1, op2 + op3) || isNumber24PossibleUtill(op1, op2 - op3) || isNumber24PossibleUtill(op1, op2 * op3) || op3 && isNumber24PossibleUtill(op1, op2 / op3)) return true return false}// Function takes given array as arr parameter// and apply all possible operation in every// consecutive elements and check if the remaining// 3 parameters can be used for obtaining 24 or notfunction isNumber24Possible(arr){ // Apply every operation between first two operands if (isNumber24PossibleUtil(arr[0] + arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] - arr[1], arr[2], arr[3]) || isNumber24PossibleUtil(arr[0] * arr[1], arr[2], arr[3]) || arr[1] && isNumber24PossibleUtil(arr[0] / arr[1], arr[2], arr[3])) return true // Between second and third operands if (isNumber24PossibleUtil(arr[0], arr[1] + arr[2], arr[3]) || isNumber24PossibleUtil(arr[0], arr[1] - arr[2], arr[3]) || isNumber24PossibleUtil(arr[0], arr[1] * arr[2], arr[3]) || arr[2] && isNumber24PossibleUtil(arr[0], arr[1] / arr[2], arr[3])) return true // Between third and fourth operands if (isNumber24PossibleUtil(arr[0], arr[1], arr[2] + arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] - arr[3]) || isNumber24PossibleUtil(arr[0], arr[1], arr[2] * arr[3]) || arr[3] && isNumber24PossibleUtil(arr[0], arr[1], arr[2] / arr[3])) return true return false}// Driver Code// Given Inputlet arr = [ 3, 6, 8, 2 ]// Function Callif (isNumber24Possible(arr)) document.write("Possible","</br>")else document.write("Not Possible","</br>")// This code is contributed by shinjanpatra</script> |
Output
Possible
Time Complexity: O(42 × 4!)
Auxiliary Space: O(1)
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