Algorithm

Maintain Takahashi’s current coordinate in a variable position, initialized to 0. Process the moves in input order. For each move, add X_i if D_i is R, and subtract X_i if D_i is L. Immediately after each update, print the resulting value of position. There is no need to store the input in an array; each line can be processed as it is read.

Correctness Proof

Consider the invariant that, before each iteration, position equals Takahashi’s coordinate after all previously completed moves.

• Base case: Before any moves, Takahashi is at coordinate 0, and position is initialized to 0, so the invariant holds.
• Inductive step: If the i-th move is R, the new coordinate is the old coordinate plus X_i. If it is L, the new coordinate is the old coordinate minus X_i. The program performs exactly this update, so the invariant remains true after the iteration.

By induction, the value printed after the i-th move is Takahashi’s coordinate immediately after that move. Since the program processes every move exactly once and in the given order, it prints the required N coordinates in the correct order.

Complexity

• Time: O(N)
• Auxiliary space: O(1)

The input is processed sequentially, and each output line is written immediately, so no array is used to store the full input or output. There is no tie-breaking because there is no choice or ordering criterion to resolve.