<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 {
    int findSmaller(vector<int> &v,int num){
        int low=0,high=v.size()-1;
        int ans=-1e9;
        while(low<=high){
            int mid=(low+high)/2;
            if(v[mid]<num){
                ans=v[mid];
                low=mid+1;
            } else high=mid-1;
        }
        return ans;
    }
    int findLarger(vector<int> &v,int num){
        int low=0,high=v.size()-1;
        int ans=1e9;
        while(low<=high){
            int mid=(low+high)/2;
            if(v[mid]<=num)low=mid+1; 
            else {
                ans=v[mid];
                high=mid-1;
            }
        }
        return ans;
    }
public:
    int robotSim(vector<int>& commands, vector<vector<int>>& obstacles) {
        map<int,vector<int>> mapX,mapY;
        for(auto it:obstacles){
            mapX[it[0]].push_back(it[1]);
            mapY[it[1]].push_back(it[0]);
        }
        for(auto &it:mapX) sort(it.second.begin(),it.second.end());
        for(auto &it:mapY) sort(it.second.begin(),it.second.end());
        int dir=0;
        int x=0,y=0;
        int ans=0;
        for(auto it:commands){
            if(it==-1) dir=(dir+3)%4;
            else if(it==-2) dir=(dir+1)%4;
            else{
                if(dir==0 || dir==2){
                    if(mapX.find(x)==mapX.end()){
                        if(dir==0) y+=it;
                        if(dir==2) y-=it;
                    } else if(dir==0){
                        int num=findLarger(mapX[x],y);
                        y=min(y+it,num-1);
                    } else{
                        int num=findSmaller(mapX[x],y);
                        y=max(y-it,num+1);
                    }
                } else {
                    if(mapY.find(y)==mapY.end()){
                        if(dir==1) x-=it;
                        else x+=it;
                    }else if(dir==3){
                        int num=findLarger(mapY[y],x);
                        x=min(x+it,num-1);
                    } else{
                        int num=findSmaller(mapY[y],x);
                        x=max(x-it,num+1);
                    }
                }
                ans=max(ans,x*x+y*y);
            }
        }
        return ans;
    }
};
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