<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:
    int robotSim(vector<int>& commands, vector<vector<int>>& obstacles) {
        map<int, set<int>> obsX, obsY;
        bool needAdd = false;
        for (vector<int> ob: obstacles) {
            if (ob[0] == 0 && ob[1] == 0) {
                needAdd = true;
            } else {
                obsX[ob[0]].insert(ob[1]);
                obsY[ob[1]].insert(ob[0]);
            }
        }

        int pos[] = {0,0};
        int dir[] = {0,1};
        unsigned furthest = 0;
        unsigned dist;
        for (int cmd: commands) {
            dist = processCmd(pos, dir, cmd, obsX, obsY, needAdd);
            furthest = dist > furthest ? dist : furthest;
        }
        return furthest;
    }

    unsigned processCmd(int (&pos) [], int (&dir) [], int cmd, map<int, set<int>> &obsX, map<int, set<int>> &obsY, bool &needAdd) {
        if ((dir[0] == -1 && cmd == -2) || (dir[0] == 1 && cmd == -1)) {
            dir[0] = 0;
            dir[1] = -1;
        } else if ((dir[0] == -1 && cmd == -1) || (dir[0] == 1 && cmd == -2)) {
            dir[0] = 0;
            dir[1] = 1;
        } else if ((dir[1] == -1 && cmd == -1) || (dir[1] == 1 && cmd == -2)) {
            dir[0] = -1;
            dir[1] = 0;
        } else if ((dir[1] == -1 && cmd == -2) || (dir[1] == 1 && cmd == -1)) {
            dir[0] = 1;
            dir[1] = 0;
        } else {
            int newPos;
            if (dir[0]) {
                newPos = pos[0] + cmd * dir[0];
                if (dir[0] == 1) {
                    auto upper = obsY[pos[1]].upper_bound(pos[0]);
                    if (upper != obsY[pos[1]].end() && newPos >= *upper) newPos = *upper - 1;
                } else {
                    auto lower = obsY[pos[1]].lower_bound(pos[0]);
                    if (lower != obsY[pos[1]].begin()) {
                        --lower;
                        if (newPos <= *lower)  newPos = *lower + 1;
                    }
                }
                pos[0] = newPos;
            } else {
                newPos = pos[1] + cmd * dir[1];
                if (dir[1] == 1) {
                    auto upper = obsX[pos[0]].upper_bound(pos[1]);
                    if (upper != obsX[pos[0]].end() && newPos >= *upper) newPos = *upper - 1;
                } else {
                    auto lower = obsX[pos[0]].lower_bound(pos[1]);
                    if (lower != obsX[pos[0]].begin()) {
                        --lower;
                        if (newPos <= *lower)  newPos = *lower + 1;
                    }
                }
                pos[1] = newPos;
            }
            if (needAdd) {
                obsX[0].insert(0);
                obsY[0].insert(0);
                needAdd = false;
            }
        }
        return pos[0]*pos[0] + pos[1]*pos[1];
    }
};
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