LeetCode: Escape a Large Maze – Prepare For Coder Interview

Escape a Large Maze

Similar Problems:

In a 1 million by 1 million grid, the coordinates of each grid square are (x, y) with 0 <= x, y < 10^6.

We start at the source square and want to reach the target square. Each move, we can walk to a 4-directionally adjacent square in the grid that isn’t in the given list of blocked squares.

Return true if and only if it is possible to reach the target square through a sequence of 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 can't walk outside the grid.

Example 2:

Input: blocked = [], source = [0,0], target = [999999,999999]
Output: true
Explanation: 
Because there are no blocked cells, it's possible to reach the target square.

Note:

0 <= blocked.length <= 200
blocked[i].length == 2
0 <= blocked[i][j] < 10^6
source.length = target.length = 2
0 <= source[i][j], target[i][j] < 10^6
source != target

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

Solution: DFS

// Basic Ideas: DFS
//
// Key Observations:
//   For a cell, if four directions are blocked, this cell is blocked
//   If there is a blocked loop around source or target, we may not be able to find a route
//   The maximum are of blocked region is limited, given at 200 nodes in blocked list
//
// Notice: what if both source and target are inside one blocked loop?
//
// Complexity: Time ?, Space ?
import "math"
type MyNode struct {
        i, j int
}

func dfs(i int, j int, target []int, blocks map[MyNode]bool, seen map[MyNode]bool) bool {
    bound := int(math.Pow(10, 6))
    // position is valid
    if i<0 || i>=bound || j<0 || j>=bound {
        return false
    }
    node := MyNode{i:i, j:j}
    if blocks[node] || seen[node] {
        return false
    }
    // find target
    if i == target[0] && j == target[1] {
        return true
    }
    // move out of the blocked region
    if len(seen) >= 20000 {
        return true
    }
    seen[node] = true
    return dfs(i+1, j, target, blocks, seen) || dfs(i-1, j, target, blocks, seen) || 
            dfs(i, j+1, target, blocks, seen) || dfs(i, j-1, target, blocks, seen)
}

func isEscapePossible(blocked [][]int, source []int, target []int) bool {
    blocks := map[MyNode]bool{}
    for _, node := range blocked {
        blocks[MyNode{i:node[0], j:node[1]}] = true
    }
    if blocks[MyNode{i:source[0], j:source[1]}] || blocks[MyNode{i:target[0], j:target[1]}] {
        return false
    }
    return dfs(source[0], source[1], target, blocks, map[MyNode]bool{}) && dfs(target[0], target[1], source, blocks, map[MyNode]bool{})
}

Solution: BFS

// https://code.dennyzhang.com/escape-a-large-maze
// Basic Ideas: BFS
//
// Key Observations:
//   For a cell, if four directions are blocked, this cell is blocked
//   If there is a blocked loop around source or target, we may not be able to find a route
//   The maximum are of blocked region is limited, given at 200 nodes in blocked list
//
// Notice: what if both source and target are inside one blocked loop?
//
// Complexity: Time ?, Space ?
import "math"
type MyNode struct {
        i, j int
}

func bfs(source []int, target []int, blocks map[MyNode]bool, maxRegion int) bool {
    bound := int(math.Pow(10, 6))
    seen := map[MyNode]bool{}
    seen[MyNode{source[0], source[1]}] = true
    queue := [][]int{source}
    for len(queue) > 0 {
        l := [][]int{}
        for _, node := range queue {
            // get nexts
            for _, offset := range [][]int{[]int{1, 0}, []int{-1, 0}, []int{0, 1},[]int{0, -1}} {
                i2, j2 := node[0]+offset[0], node[1]+offset[1]
                if i2<0 || i2>=bound || j2<0 || j2>=bound {
                    continue
                }
                node2 := MyNode{i:i2, j:j2}
                if blocks[node2] || seen[node2] {
                    continue
                }
                if i2==target[0] && j2==target[1] {
                    return true
                }
                seen[node2] = true
                l = append(l, []int{i2, j2})
            }
        }
        queue = l
        if len(seen) > maxRegion {
            return true
        }
    }
    return false
}

func isEscapePossible(blocked [][]int, source []int, target []int) bool {
    blocks := map[MyNode]bool{}
    for _, node := range blocked {
        blocks[MyNode{i:node[0], j:node[1]}] = true
    }
    if blocks[MyNode{i:source[0], j:source[1]}] || blocks[MyNode{i:target[0], j:target[1]}] {
        return false
    }
    maxRegion := (len(blocked)*(len(blocked)-1))/2
    return bfs(source, target, blocks, maxRegion) && bfs(target, source, blocks, maxRegion)
}

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