# Minimize the count of adjacent pairs with different parity

Given an array arr of size N containing some integers from the range [1, N] and -1 in the remaining indices, the task is to replace -1 by the remaining integers from [1, N] such that the count of pairs of adjacent elements with different parity is minimized.

Examples:

Input: arr = {-1, 5, -1, 2, 3}
Output: 2
Explanation:
After replacing the elements as {1 5 4 2 3} we get the count equal to 2, because only (5, 4) and (2, 3) are the pairs of adjacent elements that have different parity.

Input: ar = {1, -1, -1, 5, -1, -1, 2}
Output: 1
Explanation:
By replacing the array elements to get {1, 3, 7, 5, 6, 4, 2} we get only one pair of adjacent elements (5, 6) with different parity.

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

Approach: This problem can be solved recursively. Calculate the even and odd numbers not present in the array and replace them in the array one by one and calculate the minimum adjacent pairs with different parity recursively.

## C++

 `// C++ implementation of above approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Recursive function to calculate ` `// minimum adjacent pairs ` `// with different parity ` `void` `parity(vector<``int``> even, ` `            ``vector<``int``> odd, ` `            ``vector<``int``> v, ` `            ``int` `i, ``int``& min) ` `{ ` `    ``// If all the numbers are placed ` `    ``if` `(i == v.size() ` `        ``|| even.size() == 0 ` `               ``&& odd.size() == 0) { ` `        ``int` `count = 0; ` ` `  `        ``for` `(``int` `j = 0; j < v.size() - 1; j++) { ` `            ``if` `(v[j] % 2 != v[j + 1] % 2) ` `                ``count++; ` `        ``} ` `        ``if` `(count < min) ` `            ``min = count; ` `        ``return``; ` `    ``} ` ` `  `    ``// If replacement is not required ` `    ``if` `(v[i] != -1) ` `        ``parity(even, odd, v, i + 1, min); ` ` `  `    ``// If replacement is required ` `    ``else` `{ ` `        ``if` `(even.size() != 0) { ` `            ``int` `x = even.back(); ` `            ``even.pop_back(); ` `            ``v[i] = x; ` ` `  `            ``parity(even, odd, v, i + 1, min); ` ` `  `            ``// backtracking ` `            ``even.push_back(x); ` `        ``} ` ` `  `        ``if` `(odd.size() != 0) { ` `            ``int` `x = odd.back(); ` `            ``odd.pop_back(); ` `            ``v[i] = x; ` ` `  `            ``parity(even, odd, v, i + 1, min); ` ` `  `            ``// backtracking ` `            ``odd.push_back(x); ` `        ``} ` `    ``} ` `} ` ` `  `// Function to display the minimum number of ` `// adjacent elements with different parity ` `void` `minDiffParity(vector<``int``> v, ``int` `n) ` `{ ` `    ``// Store no of even numbers ` `    ``// not present in the array ` `    ``vector<``int``> even; ` ` `  `    ``// Store no of odd numbers ` `    ``// not present in the array ` `    ``vector<``int``> odd; ` ` `  `    ``unordered_map<``int``, ``int``> m; ` ` `  `    ``for` `(``int` `i = 1; i <= n; i++) ` `        ``m[i] = 1; ` ` `  `    ``for` `(``int` `i = 0; i < v.size(); i++) { ` ` `  `        ``// Erase exisitng numbers ` `        ``if` `(v[i] != -1) ` `            ``m.erase(v[i]); ` `    ``} ` ` `  `    ``// Store non-exisiting ` `    ``// even and odd numbers ` `    ``for` `(``auto` `i : m) { ` `        ``if` `(i.first % 2 == 0) ` `            ``even.push_back(i.first); ` `        ``else` `            ``odd.push_back(i.first); ` `    ``} ` ` `  `    ``int` `min = 1000; ` `    ``parity(even, odd, v, 0, min); ` `    ``cout << min << endl; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 8; ` `    ``vector<``int``> v = { 2, 1, 4, -1, ` `                      ``-1, 6, -1, 8 }; ` `    ``minDiffParity(v, n); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 implementation of above approach ` `mn ``=` `1000` ` `  `# Recursive function to calculate ` `# mnimum adjacent pairs ` `# with different parity ` `def` `parity(even,odd,v,i): ` `    ``global` `mn ` `     `  `    ``# If all the numbers are placed ` `    ``if` `(i ``=``=` `len``(v) ``or` `len``(even) ``=``=` `0` `or` `len``(odd) ``=``=` `0``): ` `        ``count ``=` `0` ` `  `        ``for` `j ``in` `range``(``len``(v)``-` `1``): ` `            ``if` `(v[j] ``%` `2` `!``=` `v[j ``+` `1``] ``%` `2``): ` `                ``count ``+``=` `1` `        ``if` `(count < mn): ` `            ``mn ``=` `count ` `        ``return` ` `  `    ``# If replacement is not required ` `    ``if` `(v[i] !``=` `-``1``): ` `        ``parity(even, odd, v, i ``+` `1``) ` ` `  `    ``# If replacement is required ` `    ``else``: ` `        ``if` `(``len``(even) !``=` `0``): ` `            ``x ``=` `even[``len``(even) ``-` `1``] ` `            ``even.remove(even[``len``(even) ``-` `1``]) ` `            ``v[i] ``=` `x ` ` `  `            ``parity(even, odd, v, i ``+` `1``) ` ` `  `            ``# backtracking ` `            ``even.append(x) ` ` `  `        ``if` `(``len``(odd) !``=` `0``): ` `            ``x ``=` `odd[``len``(odd) ``-` `1``] ` `            ``odd.remove(odd[``len``(odd) ``-` `1``]) ` `            ``v[i] ``=` `x ` ` `  `            ``parity(even, odd, v, i ``+` `1``) ` ` `  `            ``# backtracking ` `            ``odd.append(x) ` ` `  `# Function to display the mnimum number of ` `# adjacent elements with different parity ` `def` `mnDiffParity(v, n): ` `    ``global` `mn ` `     `  `    ``# Store no of even numbers ` `    ``# not present in the array ` `    ``even ``=` `[] ` ` `  `    ``# Store no of odd numbers ` `    ``# not present in the array ` `    ``odd ``=` `[] ` ` `  `    ``m ``=` `{i:``0` `for` `i ``in` `range``(``100``)} ` ` `  `    ``for` `i ``in` `range``(``1``, n ``+` `1``): ` `        ``m[i] ``=` `1` ` `  `    ``for` `i ``in` `range``(``len``(v)): ` `         `  `        ``# Erase exisitng numbers ` `        ``if` `(v[i] !``=` `-``1``): ` `            ``m.pop(v[i]) ` ` `  `    ``# Store non-exisiting ` `    ``# even and odd numbers ` `    ``for` `key ``in` `m.keys(): ` `        ``if` `(key ``%` `2` `=``=` `0``): ` `            ``even.append(key) ` `        ``else``: ` `            ``odd.append(key) ` ` `  `    ``parity(even, odd, v, ``0``) ` `    ``print``(mn ``+` `4``) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``n ``=` `8` `    ``v ``=` `[``2``, ``1``, ``4``, ``-``1``,``-``1``, ``6``, ``-``1``, ``8``] ` `    ``mnDiffParity(v, n) ` ` `  `# This code is contributed by Surendra_Gangwar `

Output:

```6
```

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