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# Final state of the string after modification

• Last Updated : 25 Nov, 2020

Given a string S of length n representing n boxes adjacent to each other.

1. A character R at index i represents that i-th box is being pushed towards the right.
2. On the other hand, L at index i represents that i-th box is being pushed towards the left.
3. And a . represents an empty space.

We start with initial configuration, at every time unit, a box being pushed toward right pushes next box toward right and same is true for a box being pushed toward left. The task is to print the final positions of all boxes when no more movements are possible. If there is a substring “R.L”, then middle box is being pushed from both directions and therefore not moved any more.

Examples:

Input: S = “RR.L”
Output: RR.L
The first and second boxes are being toward right. The middle dot is being pushed from both directions, so does not move.

Input: S = “R..R…L.”
Output: RRRRR.LL.
At time unit 1 :
The first box pushes second box.
Third box pushes fourth box.
Second last box pushes third last box, configuration becomes
“RR.RR.LL.”
At time unit 2 :
Second box pushes third box, string becomes
“RRRRR.LL.”

Approach: We can calculate the net force applied on every box. The forces we care about are how close a box is to a leftward R or to a rightward L i.e. the more closer we are, the stronger will be the force.

• Scanning from left to right, force decays by 1 in every iteration, and resets to N if we meet an R again.
• Similarly, from right to left direction, we can find the forces from the right (closeness to L).
• For some box result[i], if the forces are equal then the result is . as both side apply same force to it. Otherwise, our result is implied by whichever force is stronger.

For string S = “R..R…L.”
The forces going from left to right are [7, 6, 5, 7, 6, 5, 4, 0, 0]
The forces going from right to left are [0, 0, 0, 0, -4, -5, -6, -7, 0]
Combining them (taking their arithmetic addition at each index) gives result = [7, 6, 5, 7, 2, 0, -2, -7, 0]
Thus, the final answer is RRRRR.LL.

Below is the implementation of above approach:

## C++

 `// C++ implementation of above approach``#include ``using` `namespace` `std;` `// Function to return final``// positions of the boxes``string pushBoxes(string S)``{``    ``int` `N = S.length();``    ``vector<``int``> force(N, 0);` `    ``// Populate forces going``    ``// from left to right``    ``int` `f = 0;``    ``for``(``int` `i = 0; i < N; i++)``    ``{``        ``if` `(S[i] == ``'R'``)``        ``{``            ``f = N;``        ``}``        ``else` `if` `(S[i] == ``'L'``)``        ``{``            ``f = 0;``        ``}``        ``else``        ``{``            ``f = max(f - 1, 0);``        ``}``        ``force[i] += f;``    ``}` `    ``// Populate forces going from right to left``    ``f = 0;``    ``for``(``int` `i = N - 1; i >= 0; i--)``    ``{``        ``if` `(S[i] == ``'L'``)``        ``{``            ``f = N;``        ``}``        ``else` `if` `(S[i] == ``'R'``)``        ``{``            ``f = 0;``        ``}``        ``else``        ``{``            ``f = max(f - 1, 0);``        ``}``        ``force[i] -= f;``    ``}` `    ``// return final state of boxes``    ``string ans;``    ``for``(``int` `f : force)``    ``{``        ``ans += f == 0 ? ``'.'` `: f > 0 ? ``'R'` `: ``'L'``;``    ``}``    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``string S = ``".L.R...LR..L.."``;``    ` `    ``// Function call to print answer``    ``cout << pushBoxes(S);``}` `// This code is contributed by sanjeev2552`

## Python3

 `# Python3 implementation of above approach` `# Function to return final``# positions of the boxes``def` `pushBoxes(S):` `    ``N ``=` `len``(S)``    ``force ``=` `[``0``] ``*` `N` `    ``# Populate forces going from left to right``    ``f ``=` `0``    ``for` `i ``in` `range``(``0``, N):` `        ``if` `S[i] ``=``=` `'R'``:``            ``f ``=` `N``        ``elif` `S[i] ``=``=` `'L'``:``            ``f ``=` `0``        ``else``:``            ``f ``=` `max``(f ``-` `1``, ``0``)``        ``force[i] ``+``=` `f` `    ``# Populate forces going from right to left``    ``f ``=` `0``    ``for` `i ``in` `range``(N ``-` `1``, ``-``1``, ``-``1``):` `        ``if` `S[i] ``=``=` `'L'``:``            ``f ``=` `N``        ``elif` `S[i] ``=``=` `'R'``:``            ``f ``=` `0``        ``else``:``            ``f ``=` `max``(f ``-` `1``, ``0``)``        ``force[i] ``-``=` `f` `    ``# return final state of boxes``    ``return` `"".join(``'.'` `if` `f ``=``=` `0` `else` `'R'` `if` `f > ``0` `else` `'L'``                   ``for` `f ``in` `force)`  `# Driver code``S ``=` `".L.R...LR..L.."` `# Function call to print answer``print``(pushBoxes(S))`
Output:
```LL.RR.LLRRLL..

```

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