Given four numbers M, N, A and B, the task is to check whether M and N can be made equal to each other by doing any of the below operations:
- M can be increased by A and N can be decreased by B
- Leave both of them as it is.
Examples:
Input: M = 2, N = 8, A = 3, B = 3
Output: Yes
Explanation:
After first Operation:
M can be increased by A. Therefore, M = 2 + 3 = 5
N can be decreased by B. Therefore, N = 8 – 3 = 5
Finally, M = N = 5.Input: M = 6, N = 4, A = 2, B = 1
Output: No
Approach: On careful observation, it can be observed that since we are increasing M and decreasing N, they can be made equal only when M is less than N. Therefore when M is less than N, there are two cases at each step:
- M can be increased by A and N can be decreased by B.
- Leave both of them as it is.
Another observation which can be made is that when M is increased and N is decreased, the absolute distance between M and N is reduced by the factor of A + B. For example:
Let M = 2, N = 14, A = 3 and B = 3.
- In step 1, M = 5 and N = 11. The absolute distance between M and N got reduced by 6. That is, initially, the absolute distance was 12(14 – 2). After performing the given step, the absolute distance became 6(11 – 5).
- In step 2, M = 8 and N = 8. The absolute distance between M and N again got reduced by 6 thereby making M and N equal.
From the above example, we can come to the conclusion that this problem can be solved in a constant time only by checking if the absolute distance between M and N is a multiple of (A + B) or not.
- If it is a multiple, then M and N can be made equal.
- Else, they cannot be made equal.
Below is the implementation of the above approach:
// C++ program to check if two numbers // can be made equal by increasing // the first by a and decreasing // the second by b #include <bits/stdc++.h> using namespace std;
// Function to whether the numbers // can be made equal or not bool checkEqualNo( int m, int n, int a, int b)
{ if (m <= n) {
// Check whether the numbers can reach
// an equal point or not
if ((n - m) % (a + b) == 0) {
return true ;
}
else {
return false ;
}
}
else {
// M and N cannot be made equal by
// increasing M and decreasing N when
// M is already greater than N
return false ;
}
} // Driver code int main()
{ int M = 2, N = 8;
int A = 3, B = 3;
if (checkEqualNo(M, N, A, B))
cout << "Yes" << endl;
else
cout << "No" << endl;
return 0;
} |
// Java program to check if two numbers // can be made equal by increasing // the first by a and decreasing // the second by b class GFG
{ // Function to whether the numbers
// can be made equal or not
static boolean checkEqualNo( int m, int n, int a, int b)
{
if (m <= n) {
// Check whether the numbers can reach
// an equal point or not
if ((n - m) % (a + b) == 0 ) {
return true ;
}
else {
return false ;
}
}
else {
// M and N cannot be made equal by
// increasing M and decreasing N when
// M is already greater than N
return false ;
}
}
// Driver code
public static void main (String[] args)
{
int M = 2 , N = 8 ;
int A = 3 , B = 3 ;
if (checkEqualNo(M, N, A, B) == true )
System.out.println( "Yes" );
else
System.out.println( "No" );
}
} // This code is contributed by Yash_R |
# Python3 program to check if two numbers # can be made equal by increasing # the first by a and decreasing # the second by b # Function to whether the numbers # can be made equal or not def checkEqualNo(m, n, a, b) :
if (m < = n) :
# Check whether the numbers can reach
# an equal point or not
if ((n - m) % (a + b) = = 0 ) :
return True ;
else :
return False ;
else :
# M and N cannot be made equal by
# increasing M and decreasing N when
# M is already greater than N
return False ;
# Driver code if __name__ = = "__main__" :
M = 2 ; N = 8 ;
A = 3 ; B = 3 ;
if (checkEqualNo(M, N, A, B)) :
print ( "Yes" );
else :
print ( "No" );
# This code is contributed by Yash_R |
// C# program to check if two numbers // can be made equal by increasing // the first by a and decreasing // the second by b using System;
class GFG
{ // Function to whether the numbers
// can be made equal or not
static bool checkEqualNo( int m, int n, int a, int b)
{
if (m <= n) {
// Check whether the numbers can reach
// an equal point or not
if ((n - m) % (a + b) == 0) {
return true ;
}
else {
return false ;
}
}
else {
// M and N cannot be made equal by
// increasing M and decreasing N when
// M is already greater than N
return false ;
}
}
// Driver code
public static void Main (String[] args)
{
int M = 2;
int N = 8;
int A = 3;
int B = 3;
if (checkEqualNo(M, N, A, B) == true )
Console.WriteLine( "Yes" );
else
Console.WriteLine( "No" );
}
} // This code is contributed by Yash_R |
Yes
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