<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>

class Solution {
public:

    struct pair_hash {
        template <class T1, class T2>
        size_t operator() (const pair<T1, T2>& p) const {
            auto hash1 = hash<T1>{}(p.first);
            auto hash2 = hash<T2>{}(p.second);
            return hash1 ^ (hash2 << 1); // Combine the two hashes
        }
    };
    int robotSim(vector<int>& commands, vector<vector<int>>& obstacles) {
        unordered_map<pair<int,int>, bool, pair_hash> obst_loc;
        unordered_map<char, unordered_map<char, char>> next_dir;
        unordered_map<char, pair<int, int>> next_move;

        // for left turn          // for right turn
        next_dir['L']['N'] = 'W'; next_dir['R']['N'] = 'E';
        next_dir['L']['W'] = 'S'; next_dir['R']['E'] = 'S';
        next_dir['L']['S'] = 'E'; next_dir['R']['S'] = 'W';
        next_dir['L']['E'] = 'N'; next_dir['R']['W'] = 'N';

        next_move['N'].first = 0;  next_move['N'].second = 1;
        next_move['W'].first = -1; next_move['W'].second = 0;
        next_move['S'].first = 0;  next_move['S'].second = -1;
        next_move['E'].first = 1;  next_move['E'].second = 0;

        for(auto & obst : obstacles){
            int x = obst[0];
            int y = obst[1];
            obst_loc[{x,y}] = true;
        }

        int curr_x = 0, curr_y = 0;
        int next_x = 0, next_y = 0;
        int max_sqrt_dist = 0, curr_sqrt_dist = 0;
        char curr_dir = 'N';
        for(int cmd : commands){
            if(cmd == -1){
                curr_dir = next_dir['R'][curr_dir];
            }else if(cmd == -2){
                curr_dir = next_dir['L'][curr_dir];
            }else{
                for(int step = 0; step < cmd; step++){
                    next_x = curr_x + next_move[curr_dir].first;
                    next_y = curr_y + next_move[curr_dir].second;
                    if(obst_loc.find(make_pair(next_x,next_y)) == obst_loc.end()){
                        curr_x = next_x;
                        curr_y = next_y;
                        curr_sqrt_dist = curr_x*curr_x + curr_y*curr_y;
                        max_sqrt_dist = max(curr_sqrt_dist, max_sqrt_dist);
                    }else{
                        break;
                    }
                }
            }
        }

        return max_sqrt_dist;
    }
};
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