# Check if sum of array can be made equal to X by removing either the first or last digits of every array element

Last Updated : 04 Apr, 2023

Given an array arr[] consisting of N positive integers and a positive integer X, the task is to check if the sum of the given array can be made equal to X by removing either the first or last digit of every array element. If it is possible to make the sum of array elements equal to X, then print “Yes”. Otherwise, print “No”.

Examples:

Input: arr[] = {545, 433, 654, 23}, X = 134
Output: Yes
Explanation:
Following removal of digits makes the sum of array equal to X:

• Removing the first digit of arr[0] modifies arr[0] to 45.
• Removing the first digit of arr[1] modifies to 33.
• Removing the first digit of arr[2] modifies arr[2] to 54.
• Removing the last digit of arr[3] modifies arr[3] to 2.

The modified array is {45, 33, 54, 2}. Therefore, sum of the modified array = 45 + 33 + 54 + 2 = 134(= X).

Input: arr[] = {54, 22, 76, 432}, X = 48
Output: No

Approach: The given problem can be solved using recursion by generating all possible ways to remove the first or the last digit for every array element. Follow the steps below to solve the given problem.

• Define a recursive function, say makeSumX(arr, S, i, X) that takes the array arr[], the current sum S, the current index i, and the required sum X as the parameters and perform the following operations:
• If the value returned by the function makeSumX(arr, 0, 0, X) is true, then print “Yes”. Otherwise, print “No”.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ` `using` `namespace` `std;`   `// Utility Function to check if the sum` `// of the array elements can be made` `// equal to X by removing either the first` `// or last digits of every array element` `bool` `makeSumX(``int` `arr[], ``int` `X, ``int` `S,` `              ``int` `i, ``int` `N)` `{` `    `  `    ``// Base Case` `    ``if` `(i == N) ` `    ``{` `        ``return` `S == X;` `    ``}`   `    ``// Convert arr[i] to string` `    ``string a = to_string(arr[i]);`   `    ``// Remove last digit` `    ``int` `l = stoi(a.substr(0, a.length() - 1));`   `    ``// Remove first digit` `    ``int` `r = stoi(a.substr(1));`   `    ``// Recursive function call` `    ``bool` `x = makeSumX(arr, X, S + l, i + 1, N);` `    ``bool` `y = makeSumX(arr, X, S + r, i + 1, N);`   `    ``return` `(x || y);` `}`   `// Function to check if sum of given` `// array can be made equal to X or not` `void` `Check(``int` `arr[], ``int` `X, ``int` `N)` `{`   `    ``if` `(makeSumX(arr, X, 0, 0, N))` `    ``{` `        ``cout << ``"Yes"``;` `    ``}` `    ``else` `    ``{` `        ``cout << ``"No"``;` `    ``}` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { 545, 433, 654, 23 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``int` `X = 134;`   `    ``// Function Call` `    ``Check(arr, X, N);`   `    ``return` `0;` `}`   `// This code is contributed by Kingash`

## Java

 `// Java program for the above approach` `import` `java.io.*;` `import` `java.lang.*;` `import` `java.util.*;`   `class` `GFG{`   `// Utility Function to check if the sum` `// of the array elements can be made` `// equal to X by removing either the first` `// or last digits of every array element` `static` `boolean` `makeSumX(``int` `arr[], ``int` `X, ` `                        ``int` `S, ``int` `i)` `{`   `    ``// Base Case` `    ``if` `(i == arr.length) ` `    ``{` `        ``return` `S == X;` `    ``}`   `    ``// Convert arr[i] to string` `    ``String a = Integer.toString(arr[i]);`   `    ``// Remove last digit` `    ``int` `l = Integer.parseInt(` `        ``a.substring(``0``, a.length() - ``1``));`   `    ``// Remove first digit` `    ``int` `r = Integer.parseInt(a.substring(``1``));`   `    ``// Recursive function call` `    ``boolean` `x = makeSumX(arr, X, S + l, i + ``1``);` `    ``boolean` `y = makeSumX(arr, X, S + r, i + ``1``);`   `    ``return` `(x || y);` `}`   `// Function to check if sum of given` `// array can be made equal to X or not` `static` `void` `Check(``int` `arr[], ``int` `X)` `{`   `    ``if` `(makeSumX(arr, X, ``0``, ``0``))` `    ``{` `        ``System.out.println(``"Yes"``);` `    ``}` `    ``else` `    ``{` `        ``System.out.println(``"No"``);` `    ``}` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `    ``int` `arr[] = { ``545``, ``433``, ``654``, ``23` `};` `    ``int` `X = ``134``;`   `    ``// Function Call` `    ``Check(arr, X);` `}` `}`   `// This code is contributed by Kingash`

## Python3

 `# Python3 program for the above approach`   `# Utility Function to check if the sum` `# of the array elements can be made` `# equal to X by removing either the first` `# or last digits of every array element` `def` `makeSumX(arr, X, S, i):` `  `  `      ``# Base Case` `    ``if` `i ``=``=` `len``(arr):` `        ``return` `S ``=``=` `X`   `    ``# Convert arr[i] to string` `    ``a ``=` `str``(arr[i])` `    `  `    ``# Remove last digit` `    ``l ``=` `int``(a[:``-``1``])` `    `  `    ``# Remove first digit` `    ``r ``=` `int``(a[``1``:])`   `    ``# Recursive function call` `    ``x ``=` `makeSumX(arr, X, S ``+` `l, i ``+` `1``)` `    ``y ``=` `makeSumX(arr, X, S ``+` `r, i ``+` `1``)`   `    ``return` `x | y`   `# Function to check if sum of given` `# array can be made equal to X or not` `def` `Check(arr, X):`   `    ``if` `(makeSumX(arr, X, ``0``, ``0``)):` `      ``print``(``"Yes"``)` `    ``else``:` `      ``print``(``"No"``)`     `# Driver Code`   `arr ``=` `[``545``, ``433``, ``654``, ``23``]` `X ``=` `134`   `Check(arr, X)`

## C#

 `// C# program for the above approach` `using` `System;` `using` `System.Collections.Generic;  `   `class` `GFG{` `    `  `// Utility Function to check if the sum` `// of the array elements can be made` `// equal to X by removing either the first` `// or last digits of every array element` `static` `bool` `makeSumX(``int``[] arr, ``int` `X, ` `                     ``int` `S, ``int` `i)` `{` `    `  `    ``// Base Case` `    ``if` `(i == arr.Length) ` `    ``{` `        ``return` `S == X;` `    ``}`   `    ``// Convert arr[i] to string` `    ``string` `a = Convert.ToString(arr[i]);`   `    ``// Remove last digit` `    ``int` `l = Int32.Parse(` `        ``a.Substring(0, a.Length - 1));`   `    ``// Remove first digit` `    ``int` `r = Int32.Parse(a.Substring(1));`   `    ``// Recursive function call` `    ``bool` `x = makeSumX(arr, X, S + l, i + 1);` `    ``bool` `y = makeSumX(arr, X, S + r, i + 1);`   `    ``return` `(x || y);` `}`   `// Function to check if sum of given` `// array can be made equal to X or not` `static` `void` `Check(``int``[] arr, ``int` `X)` `{` `    ``if` `(makeSumX(arr, X, 0, 0))` `    ``{` `        ``Console.Write(``"Yes"``);` `    ``}` `    ``else` `    ``{` `        ``Console.Write(``"No"``);` `    ``}` `}`   `// Driver Code` `public` `static` `void` `Main()` `{` `    ``int``[] arr = { 545, 433, 654, 23 };` `    ``int` `X = 134;`   `    ``// Function Call` `    ``Check(arr, X);` `}` `}`   `// This code is contributed by sanjoy_62`

## Javascript

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Output:

`Yes`

Time Complexity: O(2N)
Auxiliary Space: O(N)