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| 1 | +//dijkstra |
| 2 | +class Solution { |
| 3 | + fun minimumEffortPath(h: Array<IntArray>): Int { |
| 4 | + val minHeap = PriorityQueue<IntArray> { a, b -> a[2] - b[2] } |
| 5 | + val dirs = intArrayOf(0, 1, 0, -1, 0) |
| 6 | + val n = h.size |
| 7 | + val m = h[0].size |
| 8 | + val visited = Array (n) { BooleanArray (m) } |
| 9 | + |
| 10 | + fun isValid(x: Int, y: Int) = x in (0 until n) && y in (0 until m) |
| 11 | + |
| 12 | + minHeap.add(intArrayOf(0, 0, 0)) |
| 13 | + while (minHeap.isNotEmpty()) { |
| 14 | + val (i, j, e) = minHeap.poll() |
| 15 | + |
| 16 | + if (i == n - 1 && j == m - 1) return e |
| 17 | + visited[i][j] = true |
| 18 | + |
| 19 | + for (k in 0..3) { |
| 20 | + val i2 = i + dirs[k] |
| 21 | + val j2 = j + dirs[k + 1] |
| 22 | + if (isValid(i2, j2) && !visited[i2][j2]) { |
| 23 | + val e2 = Math.abs(h[i][j] - h[i2][j2]) |
| 24 | + minHeap.add(intArrayOf(i2, j2, maxOf(e, e2))) |
| 25 | + } |
| 26 | + } |
| 27 | + } |
| 28 | + |
| 29 | + return 0 |
| 30 | + } |
| 31 | +} |
| 32 | + |
| 33 | +// binary search + dfs to find min effort to reach end from start |
| 34 | +class Solution { |
| 35 | + fun minimumEffortPath(h: Array<IntArray>): Int { |
| 36 | + val dirs = intArrayOf(0, 1, 0, -1, 0) |
| 37 | + val n = h.size |
| 38 | + val m = h[0].size |
| 39 | + var visited = Array (n) { BooleanArray (m) } |
| 40 | + |
| 41 | + fun isValid(x: Int, y: Int) = x in (0 until n) && y in (0 until m) |
| 42 | + |
| 43 | + fun dfs(x: Int, y: Int, k: Int): Boolean { |
| 44 | + if (x == n - 1 && y == m - 1) return true |
| 45 | + |
| 46 | + visited[x][y] = true |
| 47 | + |
| 48 | + for (i in 0..3) { |
| 49 | + val x2 = x + dirs[i] |
| 50 | + val y2 = y + dirs[i + 1] |
| 51 | + if (isValid(x2, y2) && !visited[x2][y2] && Math.abs(h[x][y] - h[x2][y2]) <= k) { |
| 52 | + if (dfs(x2, y2, k)) |
| 53 | + return true |
| 54 | + } |
| 55 | + } |
| 56 | + |
| 57 | + return false |
| 58 | + } |
| 59 | + |
| 60 | + var left = 0 |
| 61 | + var right = 1000000 |
| 62 | + var res = right |
| 63 | + while (left <= right) { |
| 64 | + val mid = (right + left) / 2 |
| 65 | + visited = Array (n) { BooleanArray (m) } |
| 66 | + if (dfs(0, 0, mid)) { |
| 67 | + res = mid |
| 68 | + right = mid - 1 |
| 69 | + } else { |
| 70 | + left = mid + 1 |
| 71 | + } |
| 72 | + } |
| 73 | + |
| 74 | + return res |
| 75 | + } |
| 76 | +} |
| 77 | + |
| 78 | +//MST with kruskals algorith (using DSU) |
| 79 | +class Solution { |
| 80 | + fun minimumEffortPath(h: Array<IntArray>): Int { |
| 81 | + val n = h.size |
| 82 | + val m = h[0].size |
| 83 | + val dsu = DSU(n * m) |
| 84 | + val edges = mutableListOf<IntArray>() |
| 85 | + |
| 86 | + fun c(x: Int, y: Int) = x * m + y |
| 87 | + |
| 88 | + for (i in 0 until n) { |
| 89 | + for (j in 0 until m) { |
| 90 | + if (i + 1 < n) { |
| 91 | + val e = Math.abs(h[i][j] - h[i + 1][j]) |
| 92 | + edges.add(intArrayOf(c(i, j), c(i + 1, j), e)) |
| 93 | + } |
| 94 | + if (j + 1 < m) { |
| 95 | + val e = Math.abs(h[i][j] - h[i][j + 1]) |
| 96 | + edges.add(intArrayOf(c(i, j), c(i, j + 1), e)) |
| 97 | + } |
| 98 | + } |
| 99 | + } |
| 100 | + |
| 101 | + edges.sortWith { a, b -> a[2] - b[2] } |
| 102 | + |
| 103 | + for ((u, v, e) in edges) { |
| 104 | + if (dsu.union(u, v)) { |
| 105 | + if (dsu.find(c(0, 0)) == dsu.find(c(n - 1, m - 1))) { |
| 106 | + return e |
| 107 | + } |
| 108 | + } |
| 109 | + } |
| 110 | + |
| 111 | + return 0 |
| 112 | + } |
| 113 | +} |
| 114 | + |
| 115 | +class DSU(val n: Int) { |
| 116 | + val parent = IntArray (n) { it } |
| 117 | + val size = IntArray (n) { 1 } |
| 118 | + |
| 119 | + fun find(x: Int): Int { |
| 120 | + if (parent[x] != x) |
| 121 | + parent[x] = find(parent[x]) |
| 122 | + return parent[x] |
| 123 | + } |
| 124 | + |
| 125 | + fun union(x: Int, y: Int): Boolean { |
| 126 | + val p1 = find(x) |
| 127 | + val p2 = find(y) |
| 128 | + |
| 129 | + if (p1 == p2) return false |
| 130 | + |
| 131 | + if (size[p1] > size[p2]) { |
| 132 | + parent[p2] = p1 |
| 133 | + size[p1] += size[p2] |
| 134 | + } else { |
| 135 | + parent[p1] = p2 |
| 136 | + size[p2] += size[p1] |
| 137 | + } |
| 138 | + |
| 139 | + return true |
| 140 | + } |
| 141 | +} |
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