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

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++

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// C++ implementation of the approach
#include <bits/stdc++.h>
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;
}

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Java

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// 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..

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Python3

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# 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

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C#

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// 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...

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Output:

No
Yes
No
Yes


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Improved By : vt_m, jit_t, AnkitRai01