Number of steps required to reach point (x,y) from (0,0) using zig-zag way

Given a coordinate (x, y). The task is to calculate the number of steps required to reach point (x, y) from (0, 0) using zig-zag way and you cannot travel in straight line for more than 1 unit. Also, start moving along Y axis.

For example we can reach the Point denoted by red color in the respective ways as shown in the below diagram:

Examples:

Input: x = 4, y = 4
Output: 8
In the diagram above the line is passing
using 8 steps.

Input: x = 4, y = 3
Output: 9

Input: x = 2, y = 1
Output: 5


Approach: By sketching a small diagram we can see the two cases:

  • Case 1: If x is less than y then answer will always be x + y + 2*((y-x)/2).
  • Case 2: If x is greater than equal to y then answer will always be x + y + 2*(((x-y)+1)/2).

Below is the implementation of the above approach:

C++

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// C++ program to find the number of steps
// required to reach (x, y) from (0, 0) following
// a zig-zag path
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the required position
int countSteps(int x, int y)
{
    if (x < y) {
        return x + y + 2 * ((y - x) / 2);
    }
    else {
        return x + y + 2 * (((x - y) + 1) / 2);
    }
}
  
// Driver Code
int main()
{
    int x = 4, y = 3;
    cout << countSteps(x, y);
  
    return 0;
}

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Java

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// Java program to find the number of steps 
// required to reach (x, y) from (0, 0) following 
// a zig-zag path 
  
class GfG 
{
  
// Function to return the required position 
static int countSteps(int x, int y) 
    if (x < y) 
    
        return x + y + 2 * ((y - x) / 2); 
    
    else 
    
        return x + y + 2 * (((x - y) + 1) / 2); 
    
  
// Driver Code 
public static void main(String[] args) 
    int x = 4, y = 3
    System.out.println(countSteps(x, y)); 
}
  
// This code is contributed by Prerna Saini

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Python3

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# Python3 program to find the number of 
# steps required to reach (x, y) from 
# (0, 0) following a zig-zag path 
    
# Function to return the required position 
def countSteps(x, y): 
   
    if x < y:
        return x + y + 2 * ((y - x) // 2
       
    else:
        return x + y + 2 * (((x - y) + 1) // 2
  
# Driver Code 
if __name__ == "__main__"
   
    x, y = 4, 3 
    print(countSteps(x, y)) 
    
# This code is contributed by Rituraj Jain

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C#

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// C# program to find the number of steps 
// required to reach (x, y) from (0, 0)  
// following a zig-zag path 
using System;
  
class GfG 
{
  
// Function to return the required position 
static int countSteps(int x, int y) 
    if (x < y) 
    
        return x + y + 2 * ((y - x) / 2); 
    
    else
    
        return x + y + 2 * (((x - y) + 1) / 2); 
    
  
// Driver Code 
public static void Main() 
    int x = 4, y = 3; 
    Console.WriteLine(countSteps(x, y)); 
}
  
// This code is contributed by Code_Mech.

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PHP

Output:

9

Time Complexity: O(1)



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