<p>A robot on an infinite XY-plane starts at point <code>(0, 0)</code> facing north. The robot receives an array of integers <code>commands</code>, which represents a sequence of moves that it needs to execute. There are only three possible types of instructions the robot can receive:</p>

<ul>
	<li><code>-2</code>: Turn left <code>90</code> degrees.</li>
	<li><code>-1</code>: Turn right <code>90</code> degrees.</li>
	<li><code>1 &lt;= k &lt;= 9</code>: Move forward <code>k</code> units, one unit at a time.</li>
</ul>

<p>Some of the grid squares are <code>obstacles</code>. The <code>i<sup>th</sup></code> obstacle is at grid point <code>obstacles[i] = (x<sub>i</sub>, y<sub>i</sub>)</code>. If the robot runs into an obstacle, it will stay in its current location (on the block adjacent to the obstacle) and move onto the next command.</p>

<p>Return the <strong>maximum squared Euclidean distance</strong> that the robot reaches at any point in its path (i.e. if the distance is <code>5</code>, return <code>25</code>).</p>

<p><strong>Note:</strong></p>

<ul>
	<li>There can be an obstacle at <code>(0, 0)</code>. If this happens, the robot will ignore the obstacle until it has moved off the origin. However, it will be unable to return to <code>(0, 0)</code> due to the obstacle.</li>
	<li>North means +Y direction.</li>
	<li>East means +X direction.</li>
	<li>South means -Y direction.</li>
	<li>West means -X direction.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">commands = [4,-1,3], obstacles = []</span></p>

<p><strong>Output:</strong> <span class="example-io">25</span></p>

<p><strong>Explanation: </strong></p>

<p>The robot starts at <code>(0, 0)</code>:</p>

<ol>
	<li>Move north 4 units to <code>(0, 4)</code>.</li>
	<li>Turn right.</li>
	<li>Move east 3 units to <code>(3, 4)</code>.</li>
</ol>

<p>The furthest point the robot ever gets from the origin is <code>(3, 4)</code>, which squared is <code>3<sup>2</sup> + 4<sup>2 </sup>= 25</code> units away.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">commands = [4,-1,4,-2,4], obstacles = [[2,4]]</span></p>

<p><strong>Output:</strong> <span class="example-io">65</span></p>

<p><strong>Explanation:</strong></p>

<p>The robot starts at <code>(0, 0)</code>:</p>

<ol>
	<li>Move north 4 units to <code>(0, 4)</code>.</li>
	<li>Turn right.</li>
	<li>Move east 1 unit and get blocked by the obstacle at <code>(2, 4)</code>, robot is at <code>(1, 4)</code>.</li>
	<li>Turn left.</li>
	<li>Move north 4 units to <code>(1, 8)</code>.</li>
</ol>

<p>The furthest point the robot ever gets from the origin is <code>(1, 8)</code>, which squared is <code>1<sup>2</sup> + 8<sup>2</sup> = 65</code> units away.</p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">commands = [6,-1,-1,6], obstacles = [[0,0]]</span></p>

<p><strong>Output:</strong> <span class="example-io">36</span></p>

<p><strong>Explanation:</strong></p>

<p>The robot starts at <code>(0, 0)</code>:</p>

<ol>
	<li>Move north 6 units to <code>(0, 6)</code>.</li>
	<li>Turn right.</li>
	<li>Turn right.</li>
	<li>Move south 5 units and get blocked by the obstacle at <code>(0,0)</code>, robot is at <code>(0, 1)</code>.</li>
</ol>

<p>The furthest point the robot ever gets from the origin is <code>(0, 6)</code>, which squared is <code>6<sup>2</sup> = 36</code> units away.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= commands.length &lt;= 10<sup>4</sup></code></li>
	<li><code>commands[i]</code> is either <code>-2</code>, <code>-1</code>, or an integer in the range <code>[1, 9]</code>.</li>
	<li><code>0 &lt;= obstacles.length &lt;= 10<sup>4</sup></code></li>
	<li><code>-3 * 10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 3 * 10<sup>4</sup></code></li>
	<li>The answer is guaranteed to be less than <code>2<sup>31</sup></code>.</li>
</ul>

#include <string>
#include <utility>
#include <vector>

class Solution {
  public:
    int robotSim(std::vector<int>& commands,
                 std::vector<std::vector<int>>& obstacles) {
        std::pair<int, int> coord = std::make_pair(0, 0);
        // state => NORTH | SOUTH | EAST | WEST
        std::string state = "NORTH";
        int max_dist = 0;

        for (const auto& command : commands) {
            std::string next_state = state;

            if (command == -1 || command == -2) {
                next_state = get_state_after_pivot(state, command);
            }

            std::pair<int, int> next_coord = coord;

            for (int i = 0; i < command; i++) {
                next_coord =
                    get_coord_after_state_update(next_coord, next_state, 1);
                bool is_obstacle = false;

                for (const auto& obstacle : obstacles) {
                    if (obstacle[0] == next_coord.first &&
                        obstacle[1] == next_coord.second) {
                        is_obstacle = true;
                        break;
                    }
                }

                if (is_obstacle) {
                    // revert the step
                    next_coord = get_coord_after_state_update(next_coord,
                                                              next_state, -1);
                    break;
                }
            }

            coord = next_coord;
            state = next_state;

            max_dist = std::max(max_dist, approx_dist(coord));
        }

        return max_dist;
    }

    std::string get_state_after_pivot(std::string state, int pivot) {
        if (state == "NORTH") {
            if (pivot == -2) {
                return "WEST";
            }

            return "EAST";
        }

        if (state == "SOUTH") {
            if (pivot == -2) {
                return "EAST";
            }

            return "WEST";
        }

        if (state == "EAST") {
            if (pivot == -2) {
                return "NORTH";
            }

            return "SOUTH";
        }

        // NOTE: State is WEST
        if (pivot == -2) {
            return "SOUTH";
        }

        return "NORTH";
    }

    std::pair<int, int>
    get_coord_after_state_update(std::pair<int, int> current,
                                 std::string direction, int steps) {
        if (direction == "NORTH")
            return std::make_pair(current.first, current.second + steps);

        if (direction == "SOUTH")
            return std::make_pair(current.first, current.second - steps);

        if (direction == "EAST")
            return std::make_pair(current.first + steps, current.second);

        return std::make_pair(current.first - steps, current.second);
    }

    int approx_dist(std::pair<int, int> coord) {
        return coord.first * coord.first + coord.second * coord.second;
    }
};

32888