# Minimum moves to reach target on a infinite line | Set 2

Given a target position on infinite number line, (-infinity to +infinity). Starting form 0 you have to reach the target by moving as described : In ith move you can take i steps forward or backward. Find the minimum number of moves required to reach the target.

Examples :

```Input : target = 3
Output : 2
Explanation:
On the first move we step from 0 to 1.
On the second step we step from 1 to 3.

Input: target = 2
Output: 3
Explanation:
On the first move we step from 0 to 1.
On the second move we step  from 1 to -1.
On the third move we step from -1 to 2.
```

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

Approach :
Idea is similar to discussed in O(n) approach here.
Keep adding sum = 1 + 2 + .. + n >= target. Solving this quadratic equation gives the smallest n such that sum >= target, i.e solving for n in n(n+1) / 2 – target >= 0 gives smallest n.
If sum == target, answer is n. Now next case where sum is greater than target. Find the difference by how much steps index is ahead of target, i.e sum – target.
Case 1 : Difference is even then answer is n, (because there will always a move flipping which will lead to target).
Case 2 : Difference is odd, then take one more step, i.e add n+1 to sum and now again take the difference. If difference is even the n+1 is the answer else take one more move and this will certainly make the difference even then answer will be n + 2.

Explanation : Since difference is odd. Target is either odd or even.
case 1 : n is even (1 + 2 + 3 + … + n), then adding n + 1 makes the difference even.
case 2 : n is odd then adding n + 1 doesn’t makes difference even so take one more move, i.e., n+2.

## C++

 `// CPP code to find minimum moves ` `// to reach target ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find minimum steps ` `// to reach target ` `int` `StepstoReachTarget(``int` `target) ` `{ ` `    ``// Handling negatives ` `    ``// by symmetry ` `    ``target = ``abs``(target); ` ` `  `    ``// Keep moving while sum is ` `    ``// smaller i.e calculating n ` `    ``int` `n = ``ceil``((-1.0 + ``sqrt``(1 + 8.0 * target)) / 2); ` `    ``int` `sum = n * (n + 1) / 2; ` ` `  `    ``if` `(sum == target) ` `        ``return` `n; ` ` `  `    ``int` `d = sum - target; ` ` `  `    ``// case 1 : d is even ` `    ``if` `((d & 1) == 0) ` `        ``return` `n; ` ` `  `    ``// d is odd ` `    ``else` `        ``return` `n + ((n & 1) ? 2 : 1); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `target = 5; ` `    ``cout << StepstoReachTarget(target); ` `    ``return` `0; ` `} `

## Java

 `// Java code to find minimum moves ` `// to reach target ` `import` `java.lang.*; ` ` `  `class` `GFG { ` `     `  `    ``// Function to find minimum steps ` `    ``// to reach target ` `    ``static` `int` `StepstoReachTarget(``int` `target) ` `    ``{ ` `         `  `        ``// Handling negatives ` `        ``// by symmetry ` `        ``target = Math.abs(target); ` ` `  `        ``// Keep moving while sum is ` `        ``// smaller i.e calculating n ` `        ``int` `n = (``int``)Math.ceil((-``1.0` `+  ` `              ``(``int``)Math.sqrt(``1` `+ ``8.0` `* ` `                         ``target)) / ``2``); ` `                          `  `        ``int` `sum = n * (n + ``1``) / ``2``; ` ` `  `        ``if` `(sum == target) ` `            ``return` `n; ` ` `  `        ``int` `d = sum - target; ` ` `  `        ``// case 1 : d is even ` `        ``if` `((d & ``1``) == ``0``) ` `            ``return` `n; ` ` `  `        ``// d is odd ` `        ``else` `            ``return` `n + ((n & ``1``) != ``0`  `                           ``? ``2` `: ``1``); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] arg) ` `    ``{ ` `        ``int` `target = ``5``; ` `        ``System.out.println( ` `             ``StepstoReachTarget(target)); ` `    ``} ` `} ` ` `  `// This code is contributed by ` `// Smitha Dinesh Semwal `

## Python3

 `# Python code to find minimum  ` `# moves to reach target ` `import` `math ` ` `  `# Function to find minimum  ` `# steps to reach target ` `def` `StepstoReachTarget(target) : ` ` `  `    ``# Handling negatives ` `    ``# by symmetry ` `    ``target ``=` `abs``(target) ` ` `  `    ``# Keep moving while sum is ` `    ``# smaller i.e calculating n ` `    ``n ``=` `math.ceil((``-``1.0` `+` `math.sqrt(``1` `+` `                    ``8.0` `*` `target)) ``/` `2``) ` `    ``sum` `=` `n ``*` `(n ``+` `1``) ``/` `2` ` `  `    ``if` `(``sum` `=``=` `target) : ` `        ``return` `n ` ` `  `    ``d ``=` `sum` `-` `target ` ` `  `    ``# case 1 : d is even ` `    ``if` `((d ``and` `1``) ``=``=` `0``) : ` `        ``return` `n ` ` `  `    ``# d is odd ` `    ``else` `: ` `        ``if``(n & ``1``) : ` `            ``return` `n ``+` `2` `        ``return` `n ``+` `1` ` `  `# Driver code ` `target ``=` `5` `print` `(StepstoReachTarget(target)) ` ` `  `# This code is contributed by  ` `# Manish Shaw(manishshaw1) `

## C#

 `// C# code to find minimum moves ` `// to reach target ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// Function to find minimum steps ` `    ``// to reach target ` `    ``static` `int` `StepstoReachTarget(``int` `target) ` `    ``{ ` `         `  `        ``// Handling negatives ` `        ``// by symmetry ` `        ``target = Math.Abs(target); ` ` `  `        ``// Keep moving while sum is ` `        ``// smaller i.e calculating n ` `        ``int` `n = (``int``)Math.Ceiling((-1.0 +  ` `                  ``(``int``)Math.Sqrt(1 + 8.0 * ` `                            ``target)) / 2); ` `                         `  `        ``int` `sum = n * (n + 1) / 2; ` ` `  `        ``if` `(sum == target) ` `            ``return` `n; ` ` `  `        ``int` `d = sum - target; ` ` `  `        ``// case 1 : d is even ` `        ``if` `((d & 1) == 0) ` `            ``return` `n; ` ` `  `        ``// d is odd ` `        ``else` `            ``return` `n + ((n & 1) != 0 ` `                        ``? 2 : 1); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `target = 5; ` `        ``Console.Write( ` `            ``StepstoReachTarget(target)); ` `    ``} ` `} ` ` `  `// This code is contributed by nitin mittal. `

## PHP

 ` `

Output :

```5
```

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