<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 <vector>
#include <map>
#include <algorithm>
#include <cmath>
using namespace std;

class Solution {
public:
    int robotSim(vector<int>& commands, vector<vector<int>>& obstacles) {
        int currentDir = 0;
        map<int, vector<int>> X;  // X-coordinate to list of Y-coordinates
        map<int, vector<int>> Y;  // Y-coordinate to list of X-coordinates

        // Build the maps with sorted obstacle coordinates
        for(auto& it: obstacles) {
            X[it[0]].push_back(it[1]);
            Y[it[1]].push_back(it[0]);
        }
        
        for(auto& [key, vec]: X) sort(vec.begin(), vec.end());
        for(auto& [key, vec]: Y) sort(vec.begin(), vec.end());

        int cordinateX = 0;
        int cordinateY = 0;
        int maxDistance = 0; 
        
        for(auto& it: commands) {
            if(it == -2) 
                currentDir = (currentDir - 1 + 4) % 4;  // Turn left
            else if(it == -1) 
                currentDir = (currentDir + 1) % 4;      // Turn right
            else {
                int dx = 0, dy = 0;
                if(currentDir == 0) { // North
                    dy = 1;
                } else if(currentDir == 1) { // East
                    dx = 1;
                } else if(currentDir == 2) { // South
                    dy = -1;
                } else if(currentDir == 3) { // West
                    dx = -1;
                }
                
                for(int step = 0; step < it; ++step) {
                    // Check for obstacles
                    if(currentDir % 2 == 0) { // Moving in X direction
                        if(currentDir == 0 && X.find(cordinateX) != X.end()) {
                            auto& yCoords = X[cordinateX];
                            auto ele = upper_bound(yCoords.begin(), yCoords.end(), cordinateY);
                            if(ele != yCoords.end() && *ele == cordinateY + dy) {
                                break; // Obstacle found in the movement direction
                            }
                        }
                        if(currentDir == 2 && X.find(cordinateX) != X.end()) {
                            auto& yCoords = X[cordinateX];
                            auto ele = lower_bound(yCoords.begin(), yCoords.end(), cordinateY);
                            if(ele != yCoords.begin() && *(--ele) == cordinateY + dy) {
                                break; // Obstacle found in the movement direction
                            }
                        }
                    } else { // Moving in Y direction
                        if(currentDir == 1 && Y.find(cordinateY) != Y.end()) {
                            auto& xCoords = Y[cordinateY];
                            auto ele = upper_bound(xCoords.begin(), xCoords.end(), cordinateX);
                            if(ele != xCoords.end() && *ele == cordinateX + dx) {
                                break; // Obstacle found in the movement direction
                            }
                        }
                        if(currentDir == 3 && Y.find(cordinateY) != Y.end()) {
                            auto& xCoords = Y[cordinateY];
                            auto ele = lower_bound(xCoords.begin(), xCoords.end(), cordinateX);
                            if(ele != xCoords.begin() && *(--ele) == cordinateX + dx) {
                                break; // Obstacle found in the movement direction
                            }
                        }
                    }
                    
                    // Move the robot
                    cordinateX += dx;
                    cordinateY += dy;
                    maxDistance = max(maxDistance, cordinateX * cordinateX + cordinateY * cordinateY);
                }
            }
        }
        return maxDistance;
    }
};

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