Add solution 1631、1691

Author: halfrost

README.md

@@ -0,0 +1,108 @@
+package leetcode
+
+import (
+	"sort"
+
+	"github.com/halfrost/LeetCode-Go/template"
+)
+
+var dir = [4][2]int{
+	{0, 1},
+	{1, 0},
+	{0, -1},
+	{-1, 0},
+}
+
+// 解法一 DFS + 二分
+func minimumEffortPath(heights [][]int) int {
+	n, m := len(heights), len(heights[0])
+	visited := make([][]bool, n)
+	for i := range visited {
+		visited[i] = make([]bool, m)
+	}
+	low, high := 0, 1000000
+	for low < high {
+		threshold := low + (high-low)>>1
+		if !hasPath(heights, visited, 0, 0, threshold) {
+			low = threshold + 1
+		} else {
+			high = threshold
+		}
+		for i := range visited {
+			for j := range visited[i] {
+				visited[i][j] = false
+			}
+		}
+	}
+	return low
+}
+
+func hasPath(heights [][]int, visited [][]bool, i, j, threshold int) bool {
+	n, m := len(heights), len(heights[0])
+	if i == n-1 && j == m-1 {
+		return true
+	}
+	visited[i][j] = true
+	res := false
+	for _, d := range dir {
+		ni, nj := i+d[0], j+d[1]
+		if ni < 0 || ni >= n || nj < 0 || nj >= m || visited[ni][nj] || res {
+			continue
+		}
+		diff := abs(heights[i][j] - heights[ni][nj])
+		if diff <= threshold && hasPath(heights, visited, ni, nj, threshold) {
+			res = true
+		}
+	}
+	return res
+}
+
+func abs(a int) int {
+	if a < 0 {
+		a = -a
+	}
+	return a
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a < b {
+		return b
+	}
+	return a
+}
+
+// 解法二 并查集
+func minimumEffortPath1(heights [][]int) int {
+	n, m, edges, uf := len(heights), len(heights[0]), []edge{}, template.UnionFind{}
+	uf.Init(n * m)
+	for i, row := range heights {
+		for j, h := range row {
+			id := i*m + j
+			if i > 0 {
+				edges = append(edges, edge{id - m, id, abs(h - heights[i-1][j])})
+			}
+			if j > 0 {
+				edges = append(edges, edge{id - 1, id, abs(h - heights[i][j-1])})
+			}
+		}
+	}
+	sort.Slice(edges, func(i, j int) bool { return edges[i].diff < edges[j].diff })
+	for _, e := range edges {
+		uf.Union(e.v, e.w)
+		if uf.Find(0) == uf.Find(n*m-1) {
+			return e.diff
+		}
+	}
+	return 0
+}
+
+type edge struct {
+	v, w, diff int
+}

leetcode/1631.Path-With-Minimum-Effort/1631. Path With Minimum Effort.go

@@ -0,0 +1,52 @@
+package leetcode
+
+import (
+	"fmt"
+	"testing"
+)
+
+type question1631 struct {
+	para1631
+	ans1631
+}
+
+// para 是参数
+// one 代表第一个参数
+type para1631 struct {
+	heights [][]int
+}
+
+// ans 是答案
+// one 代表第一个答案
+type ans1631 struct {
+	one int
+}
+
+func Test_Problem1631(t *testing.T) {
+
+	qs := []question1631{
+
+		{
+			para1631{[][]int{{1, 2, 2}, {3, 8, 2}, {5, 3, 5}}},
+			ans1631{2},
+		},
+
+		{
+			para1631{[][]int{{1, 2, 3}, {3, 8, 4}, {5, 3, 5}}},
+			ans1631{1},
+		},
+
+		{
+			para1631{[][]int{{1, 2, 1, 1, 1}, {1, 2, 1, 2, 1}, {1, 2, 1, 2, 1}, {1, 2, 1, 2, 1}, {1, 1, 1, 2, 1}}},
+			ans1631{0},
+		},
+	}
+
+	fmt.Printf("------------------------Leetcode Problem 1631------------------------\n")
+
+	for _, q := range qs {
+		_, p := q.ans1631, q.para1631
+		fmt.Printf("【input】:%v      【output】:%v      \n", p, minimumEffortPath(p.heights))
+	}
+	fmt.Printf("\n\n\n")
+}

leetcode/1631.Path-With-Minimum-Effort/1631. Path With Minimum Effort_test.go

@@ -0,0 +1,170 @@
+# [1631. Path With Minimum Effort](https://leetcode.com/problems/path-with-minimum-effort/)
+
+## 题目
+
+You are a hiker preparing for an upcoming hike. You are given `heights`, a 2D array of size `rows x columns`, where `heights[row][col]` represents the height of cell `(row, col)`. You are situated in the top-left cell, `(0, 0)`, and you hope to travel to the bottom-right cell, `(rows-1, columns-1)` (i.e., **0-indexed**). You can move **up**, **down**, **left**, or **right**, and you wish to find a route that requires the minimum **effort**.
+
+A route's **effort** is the **maximum absolute difference** in heights between two consecutive cells of the route.
+
+Return *the minimum **effort** required to travel from the top-left cell to the bottom-right cell.*
+
+**Example 1:**
+
+![https://assets.leetcode.com/uploads/2020/10/04/ex1.png](https://assets.leetcode.com/uploads/2020/10/04/ex1.png)
+
+```
+Input: heights = [[1,2,2],[3,8,2],[5,3,5]]
+Output: 2
+Explanation: The route of [1,3,5,3,5] has a maximum absolute difference of 2 in consecutive cells.
+This is better than the route of [1,2,2,2,5], where the maximum absolute difference is 3.
+```
+
+**Example 2:**
+
+![https://assets.leetcode.com/uploads/2020/10/04/ex2.png](https://assets.leetcode.com/uploads/2020/10/04/ex2.png)
+
+```
+Input: heights = [[1,2,3],[3,8,4],[5,3,5]]
+Output: 1
+Explanation: The route of [1,2,3,4,5] has a maximum absolute difference of 1 in consecutive cells, which is better than route [1,3,5,3,5].
+```
+
+**Example 3:**
+
+![https://assets.leetcode.com/uploads/2020/10/04/ex3.png](https://assets.leetcode.com/uploads/2020/10/04/ex3.png)
+
+```
+Input: heights = [[1,2,1,1,1],[1,2,1,2,1],[1,2,1,2,1],[1,2,1,2,1],[1,1,1,2,1]]
+Output: 0
+Explanation: This route does not require any effort.
+```
+
+**Constraints:**
+
+- `rows == heights.length`
+- `columns == heights[i].length`
+- `1 <= rows, columns <= 100`
+- `1 <= heights[i][j] <= 10^6`
+
+## 题目大意
+
+你准备参加一场远足活动。给你一个二维 `rows x columns` 的地图 `heights` ，其中 `heights[row][col]` 表示格子 `(row, col)` 的高度。一开始你在最左上角的格子 `(0, 0)` ，且你希望去最右下角的格子 `(rows-1, columns-1)` （注意下标从 0 开始编号）。你每次可以往 上，下，左，右 四个方向之一移动，你想要找到耗费 体力 最小的一条路径。一条路径耗费的 体力值 是路径上相邻格子之间 高度差绝对值 的 最大值 决定的。请你返回从左上角走到右下角的最小 体力消耗值 。
+
+## 解题思路
+
+- 此题和第 778 题解题思路完全一致。在第 778 题中求的是最短连通时间。此题求的是连通路径下的最小体力值。都是求的最小值，只是 2 个值的意义不同罢了。
+- 按照第 778 题的思路，本题也有多种解法。第一种解法是 DFS + 二分。先将题目变换一个等价问法。题目要求找到最小体力消耗值，也相当于问是否存在一个体力消耗值 x，只要大于等于 x，一定能连通。利用二分搜索来找到这个临界值。体力消耗值是有序的，此处满足二分搜索的条件。题目给定柱子高度是 [1,10^6]，所以体力值一定在 [0,10^6-1] 这个区间内。判断是否取中值的条件是用 DFS 或者 BFS 搜索 (0,0) 点和 (N-1, N-1) 点之间是否连通。时间复杂度：O(mnlogC)，其中 m 和 n 分别是地图的行数和列数，C 是格子的最大高度。C 最大为 10^6，所以 logC 常数也很小。空间复杂度 O(mn)。
+- 第二种解法是并查集。将图中所有边按照权值从小到大进行排序，并依次加入并查集中。直到加入一条权值为 x 的边以后，左上角到右下角连通了。最小体力消耗值也就找到了。注意加入边的时候，只加入 `i-1` 和 `i` ，`j-1` 和 `j` 这 2 类相邻的边。因为最小体力消耗意味着不走回头路。上下左右四个方向到达一个节点，只可能从上边和左边走过来。从下边和右边走过来肯定是浪费体力了。时间复杂度：O(mnlog(mn))，其中 m 和 n 分别是地图的行数和列数，图中的边数为 O(mn)。空间复杂度 O(mn)，即为存储所有边以及并查集需要的空间。
+
+## 代码
+
+```go
+package leetcode
+
+import (
+	"sort"
+
+	"github.com/halfrost/LeetCode-Go/template"
+)
+
+var dir = [4][2]int{
+	{0, 1},
+	{1, 0},
+	{0, -1},
+	{-1, 0},
+}
+
+// 解法一 DFS + 二分
+func minimumEffortPath(heights [][]int) int {
+	n, m := len(heights), len(heights[0])
+	visited := make([][]bool, n)
+	for i := range visited {
+		visited[i] = make([]bool, m)
+	}
+	low, high := 0, 1000000
+	for low < high {
+		threshold := low + (high-low)>>1
+		if !hasPath(heights, visited, 0, 0, threshold) {
+			low = threshold + 1
+		} else {
+			high = threshold
+		}
+		for i := range visited {
+			for j := range visited[i] {
+				visited[i][j] = false
+			}
+		}
+	}
+	return low
+}
+
+func hasPath(heights [][]int, visited [][]bool, i, j, threshold int) bool {
+	n, m := len(heights), len(heights[0])
+	if i == n-1 && j == m-1 {
+		return true
+	}
+	visited[i][j] = true
+	res := false
+	for _, d := range dir {
+		ni, nj := i+d[0], j+d[1]
+		if ni < 0 || ni >= n || nj < 0 || nj >= m || visited[ni][nj] || res {
+			continue
+		}
+		diff := abs(heights[i][j] - heights[ni][nj])
+		if diff <= threshold && hasPath(heights, visited, ni, nj, threshold) {
+			res = true
+		}
+	}
+	return res
+}
+
+func abs(a int) int {
+	if a < 0 {
+		a = -a
+	}
+	return a
+}
+
+func min(a, b int) int {
+	if a < b {
+		return a
+	}
+	return b
+}
+
+func max(a, b int) int {
+	if a < b {
+		return b
+	}
+	return a
+}
+
+// 解法二 并查集
+func minimumEffortPath1(heights [][]int) int {
+	n, m, edges, uf := len(heights), len(heights[0]), []edge{}, template.UnionFind{}
+	uf.Init(n * m)
+	for i, row := range heights {
+		for j, h := range row {
+			id := i*m + j
+			if i > 0 {
+				edges = append(edges, edge{id - m, id, abs(h - heights[i-1][j])})
+			}
+			if j > 0 {
+				edges = append(edges, edge{id - 1, id, abs(h - heights[i][j-1])})
+			}
+		}
+	}
+	sort.Slice(edges, func(i, j int) bool { return edges[i].diff < edges[j].diff })
+	for _, e := range edges {
+		uf.Union(e.v, e.w)
+		if uf.Find(0) == uf.Find(n*m-1) {
+			return e.diff
+		}
+	}
+	return 0
+}
+
+type edge struct {
+	v, w, diff int
+}
+```

leetcode/1631.Path-With-Minimum-Effort/README.md

@@ -0,0 +1,42 @@
+package leetcode
+
+import "sort"
+
+func maxHeight(cuboids [][]int) int {
+	n := len(cuboids)
+	for i := 0; i < n; i++ {
+		sort.Ints(cuboids[i]) // 立方体三边内部排序
+	}
+	// 立方体排序，先按最短边，再到最长边
+	sort.Slice(cuboids, func(i, j int) bool {
+		if cuboids[i][0] != cuboids[j][0] {
+			return cuboids[i][0] < cuboids[j][0]
+		}
+		if cuboids[i][1] != cuboids[j][1] {
+			return cuboids[i][1] < cuboids[j][1]
+		}
+		return cuboids[i][2] < cuboids[j][2]
+	})
+	res := 0
+	dp := make([]int, n)
+	for i := 0; i < n; i++ {
+		dp[i] = cuboids[i][2]
+		res = max(res, dp[i])
+	}
+	for i := 1; i < n; i++ {
+		for j := 0; j < i; j++ {
+			if cuboids[j][0] <= cuboids[i][0] && cuboids[j][1] <= cuboids[i][1] && cuboids[j][2] <= cuboids[i][2] {
+				dp[i] = max(dp[i], dp[j]+cuboids[i][2])
+			}
+		}
+		res = max(res, dp[i])
+	}
+	return res
+}
+
+func max(x, y int) int {
+	if x > y {
+		return x
+	}
+	return y
+}