111 lines
5.8 KiB
C++
111 lines
5.8 KiB
C++
#include <vector>
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#include <iostream>
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#include <set>
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#include <queue>
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/**
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* 1036. Escape a Large Maze
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* There is a 1 million by 1 million grid on an XY-plane, and the coordinates of each grid square are (x, y).
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* We start at the source = [sx, sy] square and want to reach the target = [tx, ty] square. There is also an array of blocked squares, where each blocked[i] = [xi, yi] represents a blocked square with coordinates (xi, yi).
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* Each move, we can walk one square north, east, south, or west if the square is not in the array of blocked squares. We are also not allowed to walk outside of the grid.
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* Return true if and only if it is possible to reach the target square from the source square through a sequence of valid moves.
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*/
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class Solution {
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private:
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inline static int dX[4] = {0, 1, 0, -1};
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inline static int dY[4] = {1, 0, -1, 0};
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public:
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// blocked -> m, map size -> n (10^6)
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// O(m^2 * log(m))
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static bool isEscapePossible(const std::vector<std::vector<int>>& blocked, const std::vector<int>& source, const std::vector<int>& target) {
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std::set<std::pair<int, int>> s;
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// O(m * log(m))
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for (const auto& i : blocked) {
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s.insert(std::make_pair(i[0], i[1]));
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}
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// bfs, from source
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{
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std::queue<std::pair<int, int>> q;
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std::set<std::pair<int, int>> vis;
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q.push(std::make_pair(source[0], source[1]));
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vis.insert(q.front());
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// iterate at most 100 * 100 = 10^4 times.
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// because 200 obstacles could block a 100 x 100 area
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// no! it is not a square, but a triangle sized 200 * 200 / 2 = 20000!
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// even when using borders.
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// O(m^2 * log(m))
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int i = 0;
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for (; i < 20002 && !q.empty(); ++i) {
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auto current = q.front();
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q.pop();
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// reached ???
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if (current.first == target[0] && current.second == target[1])
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return true;
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// O(log(m))
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for (int j = 0; j < 4; ++j) {
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auto next = std::make_pair(current.first + dX[j], current.second + dY[j]);
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if (next.first < 0 || next.second < 0 || next.first >= 1000000 || next.second >= 1000000 || vis.count(next) || s.count(next))
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continue;
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q.push(next);
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vis.insert(next);
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}
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// std::cout << "q.size = " << q.size() << std::endl;
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// std::cout << "vis.size = " << vis.size() << "\n\n";
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}
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// source is impossible to reach target!
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if (i < 20002)
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return false;
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}
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// bfs, from target
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{
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std::queue<std::pair<int, int>> q;
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std::set<std::pair<int, int>> vis;
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q.push(std::make_pair(target[0], target[1]));
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// ditto
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// O(m^2 * log(m))
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int i = 0;
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for (; i < 20002 && !q.empty(); ++i) {
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auto current = q.front();
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q.pop();
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// reached ???
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if (current.first == source[0] && current.second == source[1])
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return true;
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// O(log(m))
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for (int j = 0; j < 4; ++j) {
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auto next = std::make_pair(current.first + dX[j], current.second + dY[j]);
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if (next.first < 0 || next.second < 0 || next.first >= 1000000 || next.second >= 1000000 || vis.count(next) || s.count(next))
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continue;
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q.push(next);
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vis.insert(next);
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}
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}
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// target is impossible to reach source!
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if (i < 20002)
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return false;
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}
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// it is now impossible for obstacles to block all paths.
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return true;
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}
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};
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int main() {
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std::cout << Solution::isEscapePossible({{100004,100036},{100005,100037},{100006,100038},{100007,100039},{100008,100040},{100009,100041},{100010,100042},{100011,100043},{100012,100044},{100013,100045},{100014,100046},{100015,100047},{100016,100048},{100017,100049},{100018,100050},{100019,100051},{100020,100052},{100021,100053},{100022,100054},{100023,100055},{100024,100056},{100025,100057},{100026,100058},{100027,100059},{100028,100060},{100029,100061},{100030,100062},{100031,100063},{100032,100064},{100033,100065},{100034,100066},{100035,100067},{100036,100068},{100037,100069},{100038,100070},{100039,100071},{100040,100072},{100041,100073},{100042,100074},{100043,100075},{100044,100074},{100045,100073},{100046,100072},{100047,100071},{100048,100070},{100049,100069},{100050,100068},{100051,100067},{100052,100066},{100053,100065},{100054,100064},{100055,100063},{100056,100062},{100057,100061},{100058,100060},{100059,100059},{100060,100058},{100061,100057},{100062,100056},{100063,100055},{100064,100054},{100065,100053},{100066,100052},{100067,100051},{100068,100050},{100069,100049},{100070,100048},{100071,100047},{100072,100046},{100073,100045},{100074,100044},{100075,100043},{100076,100042},{100077,100041},{100078,100040},{100079,100039},{100080,100038},{100081,100037},{100082,100036},{100083,100035},{100082,100034},{100081,100033},{100080,100032},{100079,100031},{100078,100030},{100077,100029},{100076,100028},{100075,100027},{100074,100026},{100073,100025},{100072,100024},{100071,100023},{100070,100022},{100069,100021},{100068,100020},{100067,100019},{100066,100018},{100065,100017},{100064,100016},{100063,100015},{100062,100014},{100061,100013},{100060,100012},{100059,100011},{100058,100010},{100057,100009},{100056,100008},{100055,100007},{100054,100006},{100053,100005},{100052,100004},{100051,100003},{100050,100002},{100049,100001},{100048,100000},{100047,99999},{100046,99998},{100045,99997},{100044,99996},{100043,99995},{100042,99996},{100041,99997},{100040,99998},{100039,99999},{100038,100000},{100037,100001},{100036,100002},{100035,100003},{100034,100004},{100033,100005},{100032,100006},{100031,100007},{100030,100008},{100029,100009},{100028,100010},{100027,100011},{100026,100012},{100025,100013},{100024,100014},{100023,100015},{100022,100016},{100021,100017},{100020,100018},{100019,100019},{100018,100020},{100017,100021},{100016,100022},{100015,100023},{100014,100024},{100013,100025},{100012,100026},{100011,100027},{100010,100028},{100009,100029},{100008,100030},{100007,100031},{100006,100032},{100005,100033},{100004,100034}},
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{100043,100035},
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{999939,999987});
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return 0;
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}
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