Algorithm
Problem Name: 1036. Escape a Large Maze
There is a 1 million by 1 million grid on an XY-plane, and the coordinates of each grid square are (x, y).
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).
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.
Return true if and only if it is possible to reach the target square from the source square through a sequence of valid moves.
Example 1:
Input: blocked = [[0,1],[1,0]], source = [0,0], target = [0,2] Output: false Explanation: The target square is inaccessible starting from the source square because we cannot move. We cannot move north or east because those squares are blocked. We cannot move south or west because we cannot go outside of the grid.
Example 2:
Input: blocked = [], source = [0,0], target = [999999,999999] Output: true Explanation: Because there are no blocked cells, it is possible to reach the target square.
Constraints:
0 <= blocked.length <= 200blocked[i].length == 20 <= xi, yi < 106source.length == target.length == 20 <= sx, sy, tx, ty < 106source != target- It is guaranteed that
sourceandtargetare not blocked.
Code Examples
#1 Code Example with Javascript Programming
Code -
Javascript Programming
const isEscapePossible = function(blocked, source, target) {
const blockedSet = new Set()
for (let el of blocked) {
let key = el[0] + "," + el[1]
blockedSet.add(key)
}
return canVisit(blockedSet, source, target) && canVisit(blockedSet, target, source)
}
function canVisit(blocked, start, end) {
const visited = new Set()
return dfs(blocked, start[0], start[1], end[0], end[1], visited)
}
function dfs(blocked, i, j, m, n, visited) {
visited.add(i + "," + j)
const dirs = [[i - 1, j], [i + 1, j], [i, j + 1], [i, j - 1]]
if ((i == m && j == n) || visited.size >= 20000) {
return true
}
for (let dir of dirs) {
let nextKey = dir[0] + "," + dir[1]
if (
dir[0] >= 0 &&
dir[1] >= 0 &&
dir[0] < 1e6 &&
dir[1] < 1e6 &&
!blocked.has(nextKey) &&
!visited.has(nextKey)
) {
if (dfs(blocked, dir[0], dir[1], m, n, visited)) {
return true
}
}
}
return false
}
Input
Output
#2 Code Example with Python Programming
Code -
Python Programming
class Solution:
def isEscapePossible(self, blocked: List[List[int]], source: List[int], target: List[int]) -> bool:
if not blocked: return True
blocked = set(map(tuple, blocked))
def check(blocked, source, target):
si, sj = source
ti, tj = target
level = 0
q = collections.deque([(si,sj)])
vis = set()
while q:
for _ in range(len(q)):
i,j = q.popleft()
if i == ti and j == tj: return True
for x,y in ((i+1,j),(i-1,j),(i,j+1),(i,j-1)):
if 0<=x<10**6 and 0<=y<10**6 and (x,y) not in vis and (x,y) not in blocked:
vis.add((x,y))
q.append((x,y))
level += 1
if level == len(blocked): break
else:
return False
return True
return check(blocked, source, target) and check(blocked, target, source)
Input
Output