3341. Find Minimum Time to Reach Last Room I
Description
There is a dungeon with n x m rooms arranged as a grid.
You are given a 2D array moveTime of size n x m, where moveTime[i][j] represents the minimum time in seconds after which the room opens and can be moved to. You start from the room (0, 0) at time t = 0 and can move to an adjacent room. Moving between adjacent rooms takes exactly one second.
Return the minimum time to reach the room (n - 1, m - 1).
Two rooms are adjacent if they share a common wall, either horizontally or vertically.
Example 1:
Input: moveTime = [[0,4],[4,4]]
Output: 6
Explanation:
The minimum time required is 6 seconds.
- At time
t == 4, move from room(0, 0)to room(1, 0)in one second. - At time
t == 5, move from room(1, 0)to room(1, 1)in one second.
Example 2:
Input: moveTime = [[0,0,0],[0,0,0]]
Output: 3
Explanation:
The minimum time required is 3 seconds.
- At time
t == 0, move from room(0, 0)to room(1, 0)in one second. - At time
t == 1, move from room(1, 0)to room(1, 1)in one second. - At time
t == 2, move from room(1, 1)to room(1, 2)in one second.
Example 3:
Input: moveTime = [[0,1],[1,2]]
Output: 3
Constraints:
2 <= n == moveTime.length <= 502 <= m == moveTime[i].length <= 500 <= moveTime[i][j] <= 109
Solutions
Solution 1: Dijkstra's Algorithm
We define a two-dimensional array $\textit{dist}$, where $\textit{dist}[i][j]$ represents the minimum time required to reach room $(i, j)$ from the starting point. Initially, we set all elements in the $\textit{dist}$ array to infinity, and then set the $\textit{dist}$ value of the starting point $(0, 0)$ to $0$.
We use a priority queue $\textit{pq}$ to store each state, where each state consists of three values $(d, i, j)$, representing the time $d$ required to reach room $(i, j)$ from the starting point. Initially, we add the starting point $(0, 0, 0)$ to $\textit{pq}$.
In each iteration, we take the front element $(d, i, j)$ from $\textit{pq}$. If $(i, j)$ is the endpoint, we return $d$. If $d$ is greater than $\textit{dist}[i][j]$, we skip this state. Otherwise, we enumerate the four adjacent positions $(x, y)$ of $(i, j)$. If $(x, y)$ is within the map, we calculate the final time $t$ from $(i, j)$ to $(x, y)$ as $t = \max(\textit{moveTime}[x][y], \textit{dist}[i][j]) + 1$. If $t$ is less than $\textit{dist}[x][y]$, we update the value of $\textit{dist}[x][y]$ and add $(t, x, y)$ to $\textit{pq}$.
The time complexity is $O(n \times m \times \log (n \times m))$, and the space complexity is $O(n \times m)$. Here, $n$ and $m$ are the number of rows and columns of the map, respectively.
Python3
class Solution:
def minTimeToReach(self, moveTime: List[List[int]]) -> int:
n, m = len(moveTime), len(moveTime[0])
dist = [[inf] * m for _ in range(n)]
dist[0][0] = 0
pq = [(0, 0, 0)]
dirs = (-1, 0, 1, 0, -1)
while 1:
d, i, j = heappop(pq)
if i == n - 1 and j == m - 1:
return d
if d > dist[i][j]:
continue
for a, b in pairwise(dirs):
x, y = i + a, j + b
if 0 <= x < n and 0 <= y < m:
t = max(moveTime[x][y], dist[i][j]) + 1
if dist[x][y] > t:
dist[x][y] = t
heappush(pq, (t, x, y))
Java
class Solution {
public int minTimeToReach(int[][] moveTime) {
int n = moveTime.length;
int m = moveTime[0].length;
int[][] dist = new int[n][m];
for (var row : dist) {
Arrays.fill(row, Integer.MAX_VALUE);
}
dist[0][0] = 0;
PriorityQueue<int[]> pq = new PriorityQueue<>((a, b) -> a[0] - b[0]);
pq.offer(new int[] {0, 0, 0});
int[] dirs = {-1, 0, 1, 0, -1};
while (true) {
int[] p = pq.poll();
int d = p[0], i = p[1], j = p[2];
if (i == n - 1 && j == m - 1) {
return d;
}
if (d > dist[i][j]) {
continue;
}
for (int k = 0; k < 4; k++) {
int x = i + dirs[k];
int y = j + dirs[k + 1];
if (x >= 0 && x < n && y >= 0 && y < m) {
int t = Math.max(moveTime[x][y], dist[i][j]) + 1;
if (dist[x][y] > t) {
dist[x][y] = t;
pq.offer(new int[] {t, x, y});
}
}
}
}
}
}
C++
class Solution {
public:
int minTimeToReach(vector<vector<int>>& moveTime) {
int n = moveTime.size();
int m = moveTime[0].size();
vector<vector<int>> dist(n, vector<int>(m, INT_MAX));
dist[0][0] = 0;
priority_queue<array<int, 3>, vector<array<int, 3>>, greater<>> pq;
pq.push({0, 0, 0});
int dirs[5] = {-1, 0, 1, 0, -1};
while (1) {
auto [d, i, j] = pq.top();
pq.pop();
if (i == n - 1 && j == m - 1) {
return d;
}
if (d > dist[i][j]) {
continue;
}
for (int k = 0; k < 4; ++k) {
int x = i + dirs[k];
int y = j + dirs[k + 1];
if (x >= 0 && x < n && y >= 0 && y < m) {
int t = max(moveTime[x][y], dist[i][j]) + 1;
if (dist[x][y] > t) {
dist[x][y] = t;
pq.push({t, x, y});
}
}
}
}
}
};
Go
func minTimeToReach(moveTime [][]int) int {
n, m := len(moveTime), len(moveTime[0])
dist := make([][]int, n)
for i := range dist {
dist[i] = make([]int, m)
for j := range dist[i] {
dist[i][j] = math.MaxInt32
}
}
dist[0][0] = 0
pq := &hp{}
heap.Init(pq)
heap.Push(pq, tuple{0, 0, 0})
dirs := []int{-1, 0, 1, 0, -1}
for {
p := heap.Pop(pq).(tuple)
d, i, j := p.dis, p.x, p.y
if i == n-1 && j == m-1 {
return d
}
if d > dist[i][j] {
continue
}
for k := 0; k < 4; k++ {
x, y := i+dirs[k], j+dirs[k+1]
if x >= 0 && x < n && y >= 0 && y < m {
t := max(moveTime[x][y], dist[i][j]) + 1
if dist[x][y] > t {
dist[x][y] = t
heap.Push(pq, tuple{t, x, y})
}
}
}
}
}
type tuple struct{ dis, x, y int }
type hp []tuple
func (h hp) Len() int { return len(h) }
func (h hp) Less(i, j int) bool { return h[i].dis < h[j].dis }
func (h hp) Swap(i, j int) { h[i], h[j] = h[j], h[i] }
func (h *hp) Push(v any) { *h = append(*h, v.(tuple)) }
func (h *hp) Pop() (v any) { a := *h; *h, v = a[:len(a)-1], a[len(a)-1]; return }
TypeScript
function minTimeToReach(moveTime: number[][]): number {
const n = moveTime.length;
const m = moveTime[0].length;
const dist = Array.from({ length: n }, () => Array(m).fill(Infinity));
dist[0][0] = 0;
type Node = [number, number, number];
const pq = new PriorityQueue<Node>((a, b) => a[0] - b[0]);
pq.enqueue([0, 0, 0]);
const dirs = [-1, 0, 1, 0, -1];
while (!pq.isEmpty()) {
const [d, i, j] = pq.dequeue();
if (d > dist[i][j]) continue;
if (i === n - 1 && j === m - 1) return d;
for (let k = 0; k < 4; ++k) {
const x = i + dirs[k];
const y = j + dirs[k + 1];
if (x >= 0 && x < n && y >= 0 && y < m) {
const t = Math.max(moveTime[x][y], d) + 1;
if (t < dist[x][y]) {
dist[x][y] = t;
pq.enqueue([t, x, y]);
}
}
}
}
return -1;
}