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cat-and-mouse-ii.cpp
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cat-and-mouse-ii.cpp
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// Time: O((m * n)^2 * (m + n))
// Space: O((m * n)^2)
class Solution {
private:
enum Result {DRAW, MOUSE, CAT};
public:
bool canMouseWin(vector<string>& grid, int catJump, int mouseJump) {
static const vector<pair<int, int>> directions{{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
const int R = size(grid), C = size(grid[0]);
const int N = R * C;
unordered_set<int> WALLS;
int FOOD = -1, MOUSE_START = -1, CAT_START = -1;
for (int r = 0; r < R; ++r) {
for (int c = 0; c < C; ++c) {
if (grid[r][c] == 'M') {
MOUSE_START = r * C + c;
} else if (grid[r][c] == 'C') {
CAT_START = r * C + c;
} else if (grid[r][c] == 'F') {
FOOD = r * C + c;
} else if (grid[r][c] == '#') {
WALLS.emplace(r * C + c);
}
}
}
vector<vector<vector<int>>> graph(N, vector<vector<int>>(2));
vector<int> jump = {mouseJump, catJump};
for (int r = 0; r < R; ++r) {
for (int c = 0; c < C; ++c) {
if (grid[r][c] == '#') {
continue;
}
int pos = r * C + c;
for (const auto& t : {MOUSE, CAT}) {
for (const auto& [dr, dc] : directions) {
for (int d = 0; d <= jump[t - 1]; ++d) {
int nr = r + dr * d, nc = c + dc * d;
if (!(0 <= nr && nr < R && 0 <= nc && nc < C && grid[nr][nc] != '#')) {
break;
}
graph[pos][t - 1].emplace_back(nr * C + nc);
}
}
}
}
}
vector<vector<vector<int>>> degree(N, vector<vector<int>>(N, vector<int>(2)));
for (int m = 0; m < size(graph); ++m) {
for (int c = 0; c < size(graph); ++c) {
degree[m][c][MOUSE - 1] = size(graph[m][MOUSE - 1]);
degree[m][c][CAT - 1] = size(graph[c][CAT - 1]);
}
}
vector<vector<vector<int>>> color(N, vector<vector<int>>(N, vector<int>(2)));
queue<tuple<int, int, int, int>> q;
for (int i = 0; i < size(graph); ++i) {
if (WALLS.count(i) || i == FOOD) {
continue;
}
color[FOOD][i][CAT - 1] = MOUSE;
q.emplace(FOOD, i, CAT, MOUSE);
color[i][FOOD][MOUSE - 1] = CAT;
q.emplace(i, FOOD, MOUSE, CAT);
for (const auto& t : {MOUSE, CAT}) {
color[i][i][t - 1] = CAT;
q.emplace(i, i, t, CAT);
}
}
while (!empty(q)) {
const auto [i, j, t, c] = q.front(); q.pop();
for (const auto& [ni, nj, nt] : parents(graph, i, j, t)) {
if (color[ni][nj][nt - 1] != DRAW) {
continue;
}
if (nt == c) {
color[ni][nj][nt - 1] = c;
q.emplace(ni, nj, nt, c);
continue;
}
--degree[ni][nj][nt - 1];
if (!degree[ni][nj][nt - 1]) {
color[ni][nj][nt - 1]= c;
q.emplace(ni, nj, nt, c);
}
}
}
return color[MOUSE_START][CAT_START][MOUSE - 1] == MOUSE;
}
private:
vector<tuple<int, int, int>> parents(const vector<vector<vector<int>>>& graph,
int m, int c, int t) {
vector<tuple<int, int, int>> result;
if (t == CAT) {
for (const auto& nm : graph[m][(MOUSE ^ CAT ^ t) - 1]) {
result.emplace_back(nm, c, MOUSE ^ CAT ^ t);
}
} else {
for (const auto& nc : graph[c][(MOUSE ^ CAT ^ t) - 1]) {
result.emplace_back(m, nc, MOUSE ^ CAT ^ t);
}
}
return result;
}
};
// Time: O((m * n)^2 * (m + n))
// Space: O((m * n)^2)
class Solution2 {
private:
enum Result {DRAW, MOUSE, CAT};
public:
bool canMouseWin(vector<string>& grid, int catJump, int mouseJump) {
static const vector<pair<int, int>> directions{{0, 1}, {1, 0}, {0, -1}, {-1, 0}};
const int R = size(grid), C = size(grid[0]);
const int N = R * C;
unordered_set<int> WALLS;
int FOOD = -1, MOUSE_START = -1, CAT_START = -1;
for (int r = 0; r < R; ++r) {
for (int c = 0; c < C; ++c) {
if (grid[r][c] == 'M') {
MOUSE_START = r * C + c;
} else if (grid[r][c] == 'C') {
CAT_START = r * C + c;
} else if (grid[r][c] == 'F') {
FOOD = r * C + c;
} else if (grid[r][c] == '#') {
WALLS.emplace(r * C + c);
}
}
}
vector<vector<vector<int>>> graph(N, vector<vector<int>>(2));
vector<int> jump = {mouseJump, catJump};
for (int r = 0; r < R; ++r) {
for (int c = 0; c < C; ++c) {
if (grid[r][c] == '#') {
continue;
}
int pos = r * C + c;
for (const auto& t : {MOUSE, CAT}) {
for (const auto& [dr, dc] : directions) {
for (int d = 0; d <= jump[t - 1]; ++d) {
int nr = r + dr * d, nc = c + dc * d;
if (!(0 <= nr && nr < R && 0 <= nc && nc < C && grid[nr][nc] != '#')) {
break;
}
graph[pos][t - 1].emplace_back(nr * C + nc);
}
}
}
}
}
vector<vector<vector<int>>> degree(N, vector<vector<int>>(N, vector<int>(2)));
for (int m = 0; m < size(graph); ++m) {
for (int c = 0; c < size(graph); ++c) {
// degree[m][c][MOUSE - 1] = size(graph[m][MOUSE - 1]);
degree[m][c][CAT - 1] = size(graph[c][CAT - 1]);
}
}
vector<vector<vector<int>>> color(N, vector<vector<int>>(N, vector<int>(2)));
queue<tuple<int, int, int>> q1;
// queue<tuple<int, int, int>> q2;
for (int i = 0; i < size(graph); ++i) {
if (WALLS.count(i) || i == FOOD) {
continue;
}
color[FOOD][i][CAT - 1] = MOUSE;
q1.emplace(FOOD, i, CAT);
color[i][FOOD][MOUSE - 1] = CAT;
// q2.emplace(i, FOOD, MOUSE);
for (const auto& t : {MOUSE, CAT}) {
color[i][i][t - 1] = CAT;
// q2.emplace(i, i, t);
}
}
while (!empty(q1)) {
const auto [i, j, t] = q1.front(); q1.pop();
for (const auto& [ni, nj, nt] : parents(graph, i, j, t)) {
if (color[ni][nj][nt - 1] != DRAW) {
continue;
}
if (t == CAT) {
color[ni][nj][nt - 1] = MOUSE;
q1.emplace(ni, nj, nt);
continue;
}
--degree[ni][nj][nt - 1];
if (!degree[ni][nj][nt - 1]) {
color[ni][nj][nt - 1] = MOUSE;
q1.emplace(ni, nj, nt);
}
}
}
// while (!empty(q2)) {
// const auto [i, j, t] = q2.front(); q2.pop();
// for (const auto& [ni, nj, nt] : parents(graph, i, j, t)) {
// if (color[ni][nj][nt - 1] != DRAW) {
// continue;
// }
// if (t == MOUSE) {
// color[ni][nj][nt - 1] = CAT;
// q2.emplace(ni, nj, nt);
// continue;
// }
// --degree[ni][nj][nt - 1];
// if (!degree[ni][nj][nt - 1]) {
// color[ni][nj][nt - 1] = CAT;
// q2.emplace(ni, nj, nt);
// }
// }
// }
return color[MOUSE_START][CAT_START][MOUSE - 1] == MOUSE;
}
private:
vector<tuple<int, int, int>> parents(const vector<vector<vector<int>>>& graph,
int m, int c, int t) {
vector<tuple<int, int, int>> result;
if (t == CAT) {
for (const auto& nm : graph[m][(MOUSE ^ CAT ^ t) - 1]) {
result.emplace_back(nm, c, MOUSE ^ CAT ^ t);
}
} else {
for (const auto& nc : graph[c][(MOUSE ^ CAT ^ t) - 1]) {
result.emplace_back(m, nc, MOUSE ^ CAT ^ t);
}
}
return result;
}
};