# Program to check if a given number is Lucky (all digits are different)

A number is lucky if all digits of the number are different. How to check if a given number is lucky or not.

Examples:

```Input: n = 983
Output: true
All digits are different

Input: n = 9838
Output: false
8 appears twice
```

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The idea is to traverse through every digit of given number and mark the traversed digit as visited. Since total number of digits is 10, we need a boolean array of size only 10 to mark visited digits.

Below is C++ implementation of above idea.

```// C++ program to check if a given number is lucky
#include<iostream>
using namespace std;

// This function returns true if n is lucky
bool isLucky(int n)
{
// Create an array of size 10 and initialize all
// elements as false. This array is used to check
// if a digit is already seen or not.
bool arr[10];
for (int i=0; i<10; i++)
arr[i] = false;

// Traverse through all digits of given number
while (n > 0)
{
// Find the last digit
int digit = n%10;

// If digit is already seen, return false
if (arr[digit])
return false;

// Mark this digit as seen
arr[digit] = true;

// REmove the last digit from number
n = n/10;
}
return true;
}

// Driver program to test above function.
int main()
{
int arr[] = {1291, 897, 4566, 1232, 80, 700};
int n = sizeof(arr)/sizeof(arr[0]);

for (int i=0; i<n; i++)
isLucky(arr[i])? cout << arr[i] << " is Lucky \n":
cout << arr[i] << " is not Lucky \n";
return 0;
}
```

Output:

```1291 is not Lucky
897 is Lucky
4566 is not Lucky
1232 is not Lucky
80 is Lucky
700 is not Lucky```

Time Complexity: O(d) where d is number of digits in input number.
Auxiliary Space: O(1)

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