# Next greater number on the basis of precedence of digits

Given a number num containing n digits. The problem is to find the next greater number using the same set of digits in num on the basis of the given precedence of digits. For example the precedence of digits is given as 1, 6, 4, 5, 2, 9, 8, 0, 7, 3 which simply means 1 < 6 < 4 < 5 < 2 < 9 < 8 < 0 < 7 < 3. If next greater number cannot be formed then print the original number.

Examples:

```Input : num = "231447"
pre[] = {1, 6, 7, 5, 2, 9, 8, 0, 4, 3}
Output : 237144
According to the precedence of digits 1 is
being considered as the smallest digit and 3
is being considered as the largest digit.

Input : num = "471"
pre[] = {1, 6, 7, 5, 2, 9, 8, 0, 4, 3}
Output : 471
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Following are the steps:

1. Create a priority[] array of size ’10’. With the help of precedence array pre[] assign a priority number to each digit in priority[] where ‘1’ is being considered as smallest priority and ’10’ as the highest priority.
2. Using the STL C++ next_permutation with a manually defined compare function find the next greater permutation.
3. .

 `// C++ implementation to find the next greater number ` `// on the basis of precedence of digits ` `#include ` ` `  `using` `namespace` `std; ` ` `  `#define DIGITS 10 ` ` `  `// priority[] to store the priority of digits ` `// on the basis of pre[] array. Here '1' is being ` `// considered as the smallest priority as '10' as ` `// the highest priority ` `int` `priority[DIGITS]; ` ` `  `// comparator function used for finding the ` `// the next greater permutation ` `struct` `compare { ` `  ``bool` `operator()(``char` `x, ``char` `y) { ` `    ``return` `priority[x - ``'0'``] < priority[y - ``'0'``]; ` `  ``} ` `}; ` ` `  `// function to find the next greater number ` `// on the basis of precedence of digits ` `void` `nextGreater(``char` `num[], ``int` `n, ``int` `pre[]) { ` `  ``memset``(priority, 0, ``sizeof``(priority)); ` ` `  `  ``// variable to assgin priorities to digits ` `  ``int` `assign = 1; ` ` `  `  ``// assigning priorities to digits on ` `  ``// the basis of pre[] ` `  ``for` `(``int` `i = 0; i < DIGITS; i++) { ` `    ``priority[pre[i]] = assign; ` `    ``assign++; ` `  ``} ` ` `  `  ``// find the next greater permutation of 'num' ` `  ``// using the compare() function ` `  ``bool` `a = next_permutation(num, num + n, compare()); ` ` `  `  ``// if the next greater permutation does not exists ` `  ``// then store the original number back to 'num' ` `  ``// using 'pre_permutation'. ` `  ``if` `(a == ``false``) ` `    ``prev_permutation(num, num + n, compare()); ` `} ` ` `  `// Driver program to test above ` `int` `main() { ` `  ``char` `num[] = ``"231447"``; ` `  ``int` `n = ``strlen``(num); ` `  ``int` `pre[] = {1, 6, 7, 5, 2, 9, 8, 0, 4, 3}; ` `  ``nextGreater(num, n, pre); ` `  ``cout << ``"Next Greater: "` `<< num; ` `  ``return` `0; ` `} `

Output:

```Next Greater: 237144
```

Time Complexity: O(n).
Auxiliary Space: O(1).

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