# Nth term of a sequence formed by sum of current term with product of its largest and smallest digit

Given two numbers **N** and **K**, where K represents the starting term of the sequence. The task is to find the **Nth term** of a sequence formed by sum of current term with product of largest and smallest digit of current term, i.e.,

A

_{N+1}= A_{N}+ max(digits of A_{N}) * min(digits of A_{N})

**Examples:**

Input:K = 1, N = 5

Output:50

Explanation:

A_{1}= 1

A_{2}= A_{1}+ minDigit( A_{1}) * maxDigit( A_{1}) = 1 + min(1) * max(1) = 1 + 1*1 = 2

A_{3}= A_{2}+ minDigit( A_{2}) * maxDigit( A_{2}) = 2 + min(2) * max(2) = 2 + 2*2 = 6

A_{4}= A_{3}+ minDigit( A_{3}) * maxDigit( A_{3}) = 6 + min(6) * max(6) = 6 + 6*6 = 42

A_{5}= A_{4}+ minDigit( A_{4}) * maxDigit( A_{4}) = 42 + min(4, 2) * max(4, 2) = 42 + 2*4 = 50

Input:K = 487, N = 2

Output:519

Explanation:

A_{1}= 487

A_{2}= A_{1}+ minDigit( A_{1}) * maxDigit( a_{1}) = 487 + min(4, 8, 7) * max(4, 8, 7) = 487 + 4*8 = 519

**Approach:**

Let us try to see some observations,

When K = 1, the sequence becomes: 1, 2, 6, 42, 50, 50, 50, …

When K = 2, the sequence becomes: 2, 6, 42, 50, 50, 50, …

.

.

When K = 5, the sequence becomes: 5, 30, 30, 30, 30, 30, …

.

.

Similarly, When K = 10, the sequence becomes: 10, 10, 10, 10, 10, 10, …

From the above examples, it can be observed that the sequence eventually stops increasing after an integer has at least one digit becomes 0. If any digit becomes 0, then the minimum digit would be always 0 and after that, all the integers in the sequence remain the same.

So the approach is to find the terms of the sequence till any 0 is encountered in the digits of the current term,

Below is the implementation of the above approach.

## C++

`// C++ program for the above approach. ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find integer ` `int` `find(` `int` `K, ` `int` `N) ` `{ ` ` ` ` ` `// because 1st integer is K itself ` ` ` `N--; ` ` ` ` ` `while` `(N--) { ` ` ` `int` `curr_term = K; ` ` ` ` ` `// Initialize min_d and max_d ` ` ` `int` `min_d = 9; ` ` ` `int` `max_d = 0; ` ` ` ` ` `while` `(curr_term > 0) { ` ` ` `int` `r = curr_term % 10; ` ` ` ` ` `// updating min_d and max_d ` ` ` `min_d = min(min_d, r); ` ` ` `max_d = max(max_d, r); ` ` ` ` ` `curr_term = curr_term / 10; ` ` ` `} ` ` ` ` ` `// break if min digit is 0 ` ` ` `if` `(min_d == 0) { ` ` ` `break` `; ` ` ` `} ` ` ` ` ` `K = K + min_d * max_d; ` ` ` `} ` ` ` ` ` `return` `K; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `K = 487; ` ` ` `int` `N = 2; ` ` ` ` ` `cout << find(K, N) << endl; ` ` ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program for the above approach. ` `import` `java.util.*; ` ` ` `class` `GFG{ ` ` ` `// Function to find integer ` `static` `int` `find(` `int` `K, ` `int` `N) ` `{ ` ` ` ` ` `// Because 1st integer is K itself ` ` ` `N--; ` ` ` ` ` `while` `(N-- != ` `0` `) ` ` ` `{ ` ` ` `int` `curr_term = K; ` ` ` ` ` `// Initialize min_d and max_d ` ` ` `int` `min_d = ` `9` `; ` ` ` `int` `max_d = ` `0` `; ` ` ` ` ` `while` `(curr_term > ` `0` `) ` ` ` `{ ` ` ` `int` `r = curr_term % ` `10` `; ` ` ` ` ` `// Updating min_d and max_d ` ` ` `min_d = Math.min(min_d, r); ` ` ` `max_d = Math.max(max_d, r); ` ` ` ` ` `curr_term = curr_term / ` `10` `; ` ` ` `} ` ` ` ` ` `// Break if min digit is 0 ` ` ` `if` `(min_d == ` `0` `) ` ` ` `{ ` ` ` `break` `; ` ` ` `} ` ` ` `K = K + min_d * max_d; ` ` ` `} ` ` ` `return` `K; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `K = ` `487` `; ` ` ` `int` `N = ` `2` `; ` ` ` ` ` `System.out.print(find(K, N) + ` `"\n"` `); ` `} ` `} ` ` ` `// This code is contributed by 29AjayKumar ` |

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## Python3

`# Python3 program for the above approach. ` ` ` `# Function to find integer ` `def` `find(K, N): ` ` ` ` ` `# Because 1st integer is K itself ` ` ` `N ` `=` `N ` `-` `1` ` ` ` ` `for` `i ` `in` `range` `(` `0` `, N): ` ` ` `curr_term ` `=` `K ` ` ` ` ` `# Initialize min_d and max_d ` ` ` `min_d ` `=` `9` ` ` `max_d ` `=` `0` ` ` ` ` `while` `curr_term > ` `0` `: ` ` ` `r ` `=` `int` `(curr_term ` `%` `10` `) ` ` ` ` ` `# Updating min_d and max_d ` ` ` `min_d ` `=` `min` `(min_d, r) ` ` ` `max_d ` `=` `max` `(max_d, r) ` ` ` ` ` `curr_term ` `=` `int` `(curr_term ` `/` `10` `) ` ` ` ` ` `# Break if min digit is 0 ` ` ` `if` `min_d ` `=` `=` `0` `: ` ` ` `break` ` ` ` ` `K ` `=` `K ` `+` `min_d ` `*` `max_d ` ` ` `return` `K ` ` ` `# Driver code ` `K ` `=` `487` `N ` `=` `2` ` ` `print` `(find(K, N)) ` ` ` `# This code is contributed by ishayadav181 ` |

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## C#

`// C# program for the above approach. ` `using` `System; ` ` ` `class` `GFG{ ` ` ` `// Function to find integer ` `static` `int` `find(` `int` `K, ` `int` `N) ` `{ ` ` ` ` ` `// Because 1st integer is K itself ` ` ` `N--; ` ` ` ` ` `while` `(N-- != 0) ` ` ` `{ ` ` ` `int` `curr_term = K; ` ` ` ` ` `// Initialize min_d and max_d ` ` ` `int` `min_d = 9; ` ` ` `int` `max_d = 0; ` ` ` ` ` `while` `(curr_term > 0) ` ` ` `{ ` ` ` `int` `r = curr_term % 10; ` ` ` ` ` `// Updating min_d and max_d ` ` ` `min_d = Math.Min(min_d, r); ` ` ` `max_d = Math.Max(max_d, r); ` ` ` ` ` `curr_term = (` `int` `)(curr_term / 10); ` ` ` `} ` ` ` ` ` `// Break if min digit is 0 ` ` ` `if` `(min_d == 0) ` ` ` `{ ` ` ` `break` `; ` ` ` `} ` ` ` ` ` `K = K + min_d * max_d; ` ` ` `} ` ` ` `return` `K; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `K = 487; ` ` ` `int` `N = 2; ` ` ` ` ` `Console.Write(find(K, N)); ` `} ` `} ` ` ` `// This code is contributed by Code_Mech ` |

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**Output:**

519

**Time Complexity:** O(N)

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