# Minimize moves to reach a target point from origin by moving horizontally or diagonally in right direction

Given source **(X1, Y1)** as **(0, 0)** and a target **(X2,** **Y2)** on a 2-D plane. In one step, either of **(X1+1, Y1+1)** or **(X1+1, Y1)** can be visited from **(X1, Y1)**. The task is to calculate the **minimum** moves required to reach the target using given moves. If the target can’t be reached, print **“-1”**.

**Examples: **

Input:X2 = 1, Y2 = 0Output:1Explanation:Take 1 step from (X1, Y1) to (X1+1, Y1), i.e., (0,0) -> (1,0). So number of moves to reach target is 1.

Input:X2 = 47, Y2 = 11Output:47

**Naive Approach:** The naive approach to solve this problem is to check all combination of (X+1, Y) and (X+1, Y+1) moves needed to reach the target and print the least among them.

**Efficient Approach: **Based on given conditions about movement, following points can be observed:

- If Y2 > X2, then we cannot the target since in every move it must that X increases by 1.
- If Y2 < X2, then we can either move diagonally Y2 times, and then (X2-Y2) times horizontally, or vice versa.
- If Y2 = X2, then we can move either X2 times diagonally or Y2 moves diagonally

The task can be solved using the above observations. If **Y2 > X2**, then the target can **never** be reached with given moves, else always a minimum of **X2 moves** are necessary.

Below is the implementation of the above approach-:

## C++

`// C++ Implementation of the approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find minimum moves` `int` `minimum_Moves(` `int` `x, ` `int` `y)` `{` ` ` `// If y > x, target can never be reached` ` ` `if` `(x < y) {` ` ` `return` `-1;` ` ` `}` ` ` `// In all other case answer will be X` ` ` `else` `{` ` ` `return` `x;` ` ` `}` `}` `// Driver Code` `int` `main()` `{` ` ` `long` `long` `int` `X2 = 47, Y2 = 11;` ` ` `cout << minimum_Moves(X2, Y2) << endl;` `}` |

## Java

`// Java program for the above approach` `import` `java.io.*;` `import` `java.lang.*;` `import` `java.util.*;` `class` `GFG {` ` ` `// Function to find minimum moves` ` ` `static` `long` `minimum_Moves(` `long` `x, ` `long` `y)` ` ` `{` ` ` ` ` `// If y > x, target can never be reached` ` ` `if` `(x < y) {` ` ` `return` `-` `1` `;` ` ` `}` ` ` `// In all other case answer will be X` ` ` `else` `{` ` ` `return` `x;` ` ` `}` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `long` `X2 = ` `47` `, Y2 = ` `11` `;` ` ` `System.out.println(minimum_Moves(X2, Y2));` ` ` `}` `}` `// This code is contributed by hrithikgarg03188` |

## Python

`# Pyhton Implementation of the approach` `# Function to find minimum moves` `def` `minimum_Moves(x, y):` ` ` ` ` `# If y > x, target can never be reached` ` ` `if` `(x < y):` ` ` `return` `-` `1` ` ` `# In all other case answer will be X` ` ` `else` `:` ` ` `return` `x` `# Driver Code` `X2 ` `=` `47` `Y2 ` `=` `11` `print` `(minimum_Moves(X2, Y2))` `# This code is contributed by samim2000.` |

## C#

`// C# Implementation of the approach` `using` `System;` `class` `GFG {` ` ` `// Function to find minimum moves` ` ` `static` `int` `minimum_Moves(` `int` `x, ` `int` `y)` ` ` `{` ` ` ` ` `// If y > x, target can never be reached` ` ` `if` `(x < y) {` ` ` `return` `-1;` ` ` `}` ` ` `// In all other case answer will be X` ` ` `else` `{` ` ` `return` `x;` ` ` `}` ` ` `}` ` ` `// Driver Code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `X2 = 47, Y2 = 11;` ` ` `Console.WriteLine(minimum_Moves(X2, Y2));` ` ` `}` `}` `// This code is contributed by ukasp.` |

## Javascript

`<script>` ` ` `// JavaScript code for the above approach` ` ` `// Function to find minimum moves` ` ` `function` `minimum_Moves(x, y)` ` ` `{` ` ` ` ` `// If y > x, target can never be reached` ` ` `if` `(x < y)` ` ` `{` ` ` `return` `-1;` ` ` `}` ` ` `// In all other case answer will be X` ` ` `else` ` ` `{` ` ` `return` `x;` ` ` `}` ` ` `}` ` ` `// Driver Code` ` ` `let X2 = 47, Y2 = 11;` ` ` `document.write(minimum_Moves(X2, Y2) + ` `'<br>'` `);` ` ` `// This code is contributed by Potta Lokesh` ` ` `</script>` |

**Output**

47

* Time Complexity*: O(1)

*: O(1)*

**Auxiliary Space**