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package g0801_0900.s0818_race_car;

// #Hard #Dynamic_Programming #2022_03_23_Time_9_ms_(82.90%)_Space_44.2_MB_(70.46%)

import java.util.LinkedList;
import java.util.Queue;

/**
 * 818 - Race Car\.
 *
 * Hard
 *
 * Your car starts at position `0` and speed `+1` on an infinite number line. Your car can go into negative positions. Your car drives automatically according to a sequence of instructions `'A'` (accelerate) and `'R'` (reverse):
 *
 * *   When you get an instruction `'A'`, your car does the following:
 *     *   `position += speed`
 *     *   `speed *= 2`
 * *   When you get an instruction `'R'`, your car does the following:
 *     *   If your speed is positive then `speed = -1`
 *     *   otherwise `speed = 1`Your position stays the same.
 *
 * For example, after commands `"AAR"`, your car goes to positions `0 --> 1 --> 3 --> 3`, and your speed goes to `1 --> 2 --> 4 --> -1`.
 *
 * Given a target position `target`, return _the length of the shortest sequence of instructions to get there_.
 *
 * **Example 1:**
 *
 * **Input:** target = 3
 *
 * **Output:** 2
 *
 * **Explanation:** 
 *
 * The shortest instruction sequence is "AA". 
 *
 * Your position goes from 0 --> 1 --> 3.
 *
 * **Example 2:**
 *
 * **Input:** target = 6
 *
 * **Output:** 5
 *
 * **Explanation:** 
 *
 * The shortest instruction sequence is "AAARA". 
 *
 * Your position goes from 0 --> 1 --> 3 --> 7 --> 7 --> 6.
 *
 * **Constraints:**
 *
 * *   1 <= target <= 104
**/
public class Solution {
    public int racecar(int target) {
        Queue queue = new LinkedList<>();
        queue.add(new int[] {0, 1, 0});
        while (!queue.isEmpty()) {
            int[] arr = queue.poll();
            if (arr[0] == target) {
                return arr[2];
            }
            queue.add(new int[] {arr[0] + arr[1], 2 * arr[1], 1 + arr[2]});
            if ((arr[0] + arr[1]) > target && arr[1] > 0) {
                queue.add(new int[] {arr[0], -1, 1 + arr[2]});
            }
            if ((arr[0]) + arr[1] < target && (arr[1] < 0)) {
                queue.add(new int[] {arr[0], 1, 1 + arr[2]});
            }
        }
        return -1;
    }
}




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