# Queries to check whether all the elements can be made positive by flipping signs exactly K times

Given an integer array arr[], and some queries consisting of an integer K, the task is to determine if its possible to make all the integers positive by flipping signs of integers exactly K times. We can flip the sign of an integer more than once. If possible, then print Yes else print No.

Examples:

Input: arr[] = {-1, 2, -3, 4, 5}, q[] = {1, 2}
Output:
No
Yes
Query 1: Only the sign of either -1 or -3
can be changed and not both.
Query 2: Signs of both the negative numbers
can be changed to positive.

Input: arr[] = {-1, -1, 0, 6}, q[] = {1, 2, 3, 4}
Output:
No
Yes
Yes
Yes

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

Approach: Following will be the algorithm that we will use:

1. Count number of negative integers in the array and store it in a variable cnt.
2. If there is no zero in the array:
• If K ≥ cnt then answer will be Yes.
• If K = cnt and (K – cnt) % 2 = 0 then answer will be Yes.
• Else answer will be No.
3. If there exists a zero in the array then the answer will only be No if K < cnt else the answer is always Yes.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// To store the count of ` `// negative integers ` `int` `cnt_neg; ` ` `  `// Check if zero exists ` `bool` `exists_zero; ` ` `  `// Function to find the count of ` `// negative integers and check ` `// if zero exists in the array ` `void` `preProcess(``int` `arr[], ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(arr[i] < 0) ` `            ``cnt_neg++; ` `        ``if` `(arr[i] == 0) ` `            ``exists_zero = ``true``; ` `    ``} ` `} ` ` `  `// Function that returns true if array ` `// elements can be made positive by ` `// changing signs exactly k times ` `bool` `isPossible(``int` `k) ` `{ ` `    ``if` `(!exists_zero) { ` `        ``if` `(k >= cnt_neg and (k - cnt_neg) % 2 == 0) ` `            ``return` `true``; ` `        ``else` `            ``return` `false``; ` `    ``} ` `    ``else` `{ ` `        ``if` `(k >= cnt_neg) ` `            ``return` `true``; ` `        ``else` `            ``return` `false``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `arr[] = { -1, 2, -3, 4, 5 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``); ` ` `  `    ``// Pre-processing ` `    ``preProcess(arr, n); ` ` `  `    ``int` `queries[] = { 1, 2, 3, 4 }; ` `    ``int` `q = ``sizeof``(queries) / ``sizeof``(``int``); ` ` `  `    ``// Perform queries ` `    ``for` `(``int` `i = 0; i < q; i++) { ` `        ``if` `(isPossible(queries[i])) ` `            ``cout << ``"Yes"` `<< endl; ` `        ``else` `            ``cout << ``"No"` `<< endl; ` `    ``} ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` ` `  ` `  `// To store the count of ` `// negative integers ` `static` `int` `cnt_neg; ` ` `  `// Check if zero exists ` `static` `boolean` `exists_zero; ` ` `  `// Function to find the count of ` `// negative integers and check ` `// if zero exists in the array ` `static` `void` `preProcess(``int` `[]arr, ``int` `n) ` `{ ` `    ``for` `(``int` `i = ``0``; i < n; i++)  ` `    ``{ ` `        ``if` `(arr[i] < ``0``) ` `            ``cnt_neg++; ` `        ``if` `(arr[i] == ``0``) ` `            ``exists_zero = ``true``; ` `    ``} ` `} ` ` `  `// Function that returns true if array ` `// elements can be made positive by ` `// changing signs exactly k times ` `static` `boolean` `isPossible(``int` `k) ` `{ ` `    ``if` `(!exists_zero)  ` `    ``{ ` `        ``if` `(k >= cnt_neg && (k - cnt_neg) % ``2` `== ``0``) ` `            ``return` `true``; ` `        ``else` `            ``return` `false``; ` `    ``} ` `    ``else`  `    ``{ ` `        ``if` `(k >= cnt_neg) ` `            ``return` `true``; ` `        ``else` `            ``return` `false``; ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args)  ` `{ ` `    ``int` `arr[] = { -``1``, ``2``, -``3``, ``4``, ``5` `}; ` `    ``int` `n = arr.length; ` ` `  `    ``// Pre-processing ` `    ``preProcess(arr, n); ` ` `  `    ``int` `queries[] = { ``1``, ``2``, ``3``, ``4` `}; ` `    ``int` `q = arr.length; ` ` `  `    ``// Perform queries ` `    ``for` `(``int` `i = ``0``; i < q; i++)  ` `    ``{ ` `        ``if` `(isPossible(queries[i])) ` `            ``System.out.println( ``"Yes"``); ` `        ``else` `            ``System.out.println( ``"No"``); ` `    ``} ` `} ` `} ` ` `  `// This code is contributed by anuj_67.. `

## Python3

 `# Python3 implementation of the approach  ` ` `  `# To store the count of  ` `# negative integers  ` `cnt_neg ``=` `0``;  ` ` `  `# Check if zero exists  ` `exists_zero ``=` `None``;  ` ` `  `# Function to find the count of  ` `# negative integers and check  ` `# if zero exists in the array  ` `def` `preProcess(arr, n) :  ` `    ``global` `cnt_neg ` `     `  `    ``for` `i ``in` `range``(n) : ` `        ``if` `(arr[i] < ``0``) : ` `            ``cnt_neg ``+``=` `1``; ` `         `  `        ``if` `(arr[i] ``=``=` `0``) : ` `            ``exists_zero ``=` `True``;  ` ` `  `# Function that returns true if array  ` `# elements can be made positive by  ` `# changing signs exactly k times  ` `def` `isPossible(k) :  ` ` `  `    ``if` `(``not` `exists_zero) : ` `        ``if` `(k >``=` `cnt_neg ``and` `(k ``-` `cnt_neg) ``%` `2` `=``=` `0``) : ` `            ``return` `True``;  ` `        ``else` `: ` `            ``return` `False``;  ` `     `  `    ``else` `: ` `        ``if` `(k >``=` `cnt_neg) :  ` `            ``return` `True``;  ` `        ``else` `: ` `            ``return` `False``;  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``arr ``=` `[ ``-``1``, ``2``, ``-``3``, ``4``, ``5` `];  ` `    ``n ``=` `len``(arr);  ` ` `  `    ``# Pre-processing  ` `    ``preProcess(arr, n);  ` ` `  `    ``queries ``=` `[ ``1``, ``2``, ``3``, ``4` `];  ` `    ``q ``=` `len``(queries);  ` ` `  `    ``# Perform queries  ` `    ``for` `i ``in` `range``(q) : ` `        ``if` `(isPossible(queries[i])) : ` `            ``print``(``"Yes"``);  ` `        ``else` `: ` `            ``print``(``"No"``);  ` ` `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// To store the count of ` `// negative integers ` `static` `int` `cnt_neg; ` ` `  `// Check if zero exists ` `static` `bool` `exists_zero ; ` ` `  `// Function to find the count of ` `// negative integers and check ` `// if zero exists in the array ` `static` `void` `preProcess(``int` `[]arr, ``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++)  ` `    ``{ ` `        ``if` `(arr[i] < 0) ` `            ``cnt_neg++; ` `        ``if` `(arr[i] == 0) ` `            ``exists_zero = ``true``; ` `    ``} ` `} ` ` `  `// Function that returns true if array ` `// elements can be made positive by ` `// changing signs exactly k times ` `static` `bool` `isPossible(``int` `k) ` `{ ` `    ``if` `(!exists_zero)  ` `    ``{ ` `        ``if` `(k >= cnt_neg && (k - cnt_neg) % 2 == 0) ` `            ``return` `true``; ` `        ``else` `            ``return` `false``; ` `    ``} ` `    ``else` `    ``{ ` `        ``if` `(k >= cnt_neg) ` `            ``return` `true``; ` `        ``else` `            ``return` `false``; ` `    ``} ` `} ` ` `  `// Driver code ` `static` `public` `void` `Main () ` `{ ` `     `  `    ``int` `[]arr = { -1, 2, -3, 4, 5 }; ` `    ``int` `n = arr.Length; ` `     `  `    ``// Pre-processing ` `    ``preProcess(arr, n); ` `     `  `    ``int` `[]queries = { 1, 2, 3, 4 }; ` `    ``int` `q = arr.Length; ` `     `  `    ``// Perform queries ` `    ``for` `(``int` `i = 0; i < q; i++)  ` `    ``{ ` `        ``if` `(isPossible(queries[i])) ` `            ``Console.WriteLine( ``"Yes"``); ` `        ``else` `            ``Console.WriteLine( ``"No"``); ` `    ``} ` `} ` `} ` ` `  `// This code is contributed by ajit... `

Output:

```No
Yes
No
Yes
```

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