<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:
    char f(char a, int d) {
        if (d == -1) {
            if (a == 'n') return 'e';
            else if (a == 'e') return 's';
            else if (a == 's') return 'w';
            else return 'n';
        } else {
            if (a == 'n') return 'w';
            else if (a == 'w') return 's';
            else if (a == 's') return 'e';
            else return 'n';
        }
    }

    int robotSim(vector<int>& dis, vector<vector<int>>& o) {
        map<int, set<int>> ro;
        map<int, set<int>> cl;

        // Store obstacles
        for (auto it : o) {
            ro[it[0]].insert(it[1]);
            cl[it[1]].insert(it[0]);
        }
        int ans = 0;
        char d = 'n'; // Initial direction north
        int r = 0, c = 0; // Starting coordinates (0, 0)
        int n = dis.size();

        for (int i = 0; i < n; i++) {
            // cout<<d;
            if (dis[i] == -1) {
                d = f(d, -1); // Turn right
            } else if (dis[i] == -2) {
                d = f(d, -2); // Turn left
            } else {
                // Move based on direction
                if (d == 'e') {
                    for (int j = 1; j <= dis[i]; j++) {
                        if (cl[c].find(r+1) == cl[c].end()) {
                            r += 1; // Move north
                            ans = max(ans, r * r + c * c); // Update max distance
                        } else break;
                    }
                } else if (d == 'w') {
                    for (int j = 1; j <= dis[i]; j++) {
                        if (cl[c].find(r-1) == cl[c].end()) {
                            r -= 1; // Move south
                            ans = max(ans, r * r + c * c); // Update max distance
                        } else break;
                    }
                } else if (d == 'n') {
                    for (int j = 1; j <= dis[i]; j++) {
                        if (ro[r].find(c+1) == ro[r].end()) {
                            c += 1; // Move east
                            ans = max(ans, r * r + c * c); // Update max distance
                        } else break;
                    }
                } else if (d == 's') {
                    for (int j = 1; j <= dis[i]; j++) {
                        if (ro[r].find(c-1) == ro[r].end()) {
                            c -= 1; // Move west
                            ans = max(ans, r * r + c * c); // Update max distance
                        } else break;
                    }
                }
            }
            // cout<<r<<" "<<c<<"    ";
        }
        return ans; // Return maximum Euclidean distance
    }
};

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