Create 1728.Cat-and-Mouse-II.cpp

Author: wisdompeak

BFS/1728.Cat-and-Mouse-II/1728.Cat-and-Mouse-II.cpp

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+class Solution {
+ int memo[9][9][9][9][3];
+ pair<int,int>mouse;
+ pair<int,int>cat;
+ pair<int,int>food; 
+ int catJump;
+ int mouseJump;
+public:
+ bool canMouseWin(vector<string>& grid, int catJump, int mouseJump) 
+ {
+ int m = grid.size();
+ int n = grid[0].size();
+ queue<array<int,5>>q;
+ this->catJump = catJump;
+ this->mouseJump = mouseJump;
+
+ for (int i=0; i<m; i++)
+ for (int j=0; j<n; j++)
+ {
+ if (grid[i][j]=='M')
+ mouse = {i,j};
+ if (grid[i][j]=='C')
+ cat = {i,j};
+ if (grid[i][j]=='F')
+ food = {i,j};
+ }
+ 
+ for (int i=0; i<m; i++)
+ for (int j=0; j<n; j++)
+ {
+ if (grid[i][j]=='#') continue;
+ if (i==food.first && j==food.second) continue;
+ memo[food.first][food.second][i][j][1] = 1; // mouse win
+ memo[food.first][food.second][i][j][2] = 1; // mouse win
+ memo[i][j][food.first][food.second][1] = 2; // cat win 
+ memo[i][j][food.first][food.second][2] = 2; // cat win 
+ q.push({food.first, food.second, i, j, 1}); 
+ q.push({food.first, food.second, i, j, 2}); 
+ q.push({i, j, food.first, food.second, 1}); 
+ q.push({i, j, food.first, food.second, 2}); 
+ }
+ 
+ for (int i=0; i<m; i++)
+ for (int j=0; j<n; j++)
+ {
+ if (grid[i][j]=='#') continue;
+ memo[i][j][i][j][1] = 2; // cat win
+ memo[i][j][i][j][2] = 2; // cat win 
+ q.push({i, j, i, j, 1}); 
+ q.push({i, j, i, j, 2}); 
+ }
+ 
+ int step = 0;
+ while (!q.empty())
+ { 
+ step++;
+ if (step>2000) return true;
+ int len = q.size();
+ while (len--)
+ {
+ int mx = q.front()[0];
+ int my = q.front()[1];
+ int cx = q.front()[2];
+ int cy = q.front()[3];
+ int t = q.front()[4]; 
+ int status = memo[mx][my][cx][cy][t];
+ q.pop();
+ // cout<<mx<<" "<<my<<" "<<cx<<" "<<cy<<":"<<t<<":"<<memo[mx][my][cx][cy][t]<<endl;
+ 
+ for (auto nextNode: findAllParents(grid,mx,my,cx,cy,t))
+ {
+ int mx2 = nextNode[0];
+ int my2 = nextNode[1];
+ int cx2 = nextNode[2];
+ int cy2 = nextNode[3]; 
+ int t2 = nextNode[4];
+
+ if (memo[mx2][my2][cx2][cy2][t2]!=0) continue; // has been determined
+
+ if (t2==status) // immediate win, (m2,c2,t2)->(m,c,t)
+ {
+ memo[mx2][my2][cx2][cy2][t2] = status;
+ q.push({mx2,my2,cx2,cy2,t2});
+ }
+ else if (allChildrenWin(grid, mx2,my2,cx2,cy2,t2)) // eventually lose
+ {
+ memo[mx2][my2][cx2][cy2][t2] = (t2==1)? 2:1;
+ q.push({mx2,my2,cx2,cy2,t2}); 
+ } 
+ } 
+ }
+ }
+ 
+ cout<<memo[mouse.first][mouse.second][cat.first][cat.second][1]<<endl;
+ return memo[mouse.first][mouse.second][cat.first][cat.second][1]==1; 
+ }
+ 
+ vector<vector<int>> findAllParents(vector<string>& grid, int mx, int my, int cx, int cy, int t)
+ {
+ int m = grid.size();
+ int n = grid[0].size();
+ auto dir = vector<pair<int,int>>({{1,0},{-1,0},{0,1},{0,-1}});
+ vector<vector<int>>neighbours;
+ if (t==1)
+ {
+ for (int k=0; k<4; k++)
+ for (int a = 0; a<=catJump; a++)
+ {
+ int cx2 = cx+dir[k].first*a;
+ int cy2 = cy+dir[k].second*a;
+ if (cx2<0||cx2>=m||cy2<0||cy2>=n) break;
+ if (grid[cx2][cy2]=='#') break;
+ neighbours.push_back({mx,my,cx2,cy2,2});
+ }
+ }
+ else
+ {
+ for (int k=0; k<4; k++)
+ for (int a = 0; a<=mouseJump; a++)
+ {
+ int mx2 = mx+dir[k].first*a;
+ int my2 = my+dir[k].second*a;
+ if (mx2<0||mx2>=m||my2<0||my2>=n) break;
+ if (grid[mx2][my2]=='#') break;
+ neighbours.push_back({mx2,my2,cx,cy,1});
+ }
+ }
+ return neighbours;
+ }
+ 
+ bool allChildrenWin(vector<string>& grid, int mx, int my, int cx, int cy, int t)
+ {
+ int m = grid.size();
+ int n = grid[0].size();
+ auto dir = vector<pair<int,int>>({{1,0},{-1,0},{0,1},{0,-1}});
+ 
+ if (t==1)
+ {
+ for (int k=0; k<4; k++)
+ for (int a = 0; a<=mouseJump; a++)
+ {
+ int mx2 = mx+dir[k].first*a;
+ int my2 = my+dir[k].second*a;
+ if (mx2<0||mx2>=m||my2<0||my2>=n) break;
+ if (grid[mx2][my2]=='#') break;
+ if (memo[mx2][my2][cx][cy][2]!=2)
+ return false;
+ } 
+ }
+ else if (t==2)
+ {
+ for (int k=0; k<4; k++)
+ for (int a = 0; a<=catJump; a++)
+ {
+ int cx2 = cx+dir[k].first*a;
+ int cy2 = cy+dir[k].second*a;
+ if (cx2<0||cx2>=m||cy2<0||cy2>=n) break;
+ if (grid[cx2][cy2]=='#') break;
+ if (memo[mx][my][cx2][cy2][1]!=1)
+ return false;
+ }
+ }
+ return true;
+ } 
+};