From 8133e4d313452203085aaaa41f78f2af923e5a07 Mon Sep 17 00:00:00 2001 From: algorithmzuo Date: Wed, 28 Jun 2023 22:25:10 +0800 Subject: [PATCH] modify code --- .../Code01_SpecialPermutations.java | 69 ++++++++++ .../Code02_PaintingTheWalls.java | 99 +++++++++++++++ .../Code03_FrogHateStoneMinTimes.java | 120 ++++++++++++++++++ .../Code04_ValidArrangementOfPairs.java | 80 ++++++++++++ .../算法和数据结构知识梳理.xmind | Bin 196689 -> 197153 bytes ...养的大厂算法面试题(正在直播) | 50 ++++++++ 6 files changed, 418 insertions(+) create mode 100644 算法周更班/class_2023_06_4_week/Code01_SpecialPermutations.java create mode 100644 算法周更班/class_2023_06_4_week/Code02_PaintingTheWalls.java create mode 100644 算法周更班/class_2023_06_4_week/Code03_FrogHateStoneMinTimes.java create mode 100644 算法周更班/class_2023_06_4_week/Code04_ValidArrangementOfPairs.java diff --git a/算法周更班/class_2023_06_4_week/Code01_SpecialPermutations.java b/算法周更班/class_2023_06_4_week/Code01_SpecialPermutations.java new file mode 100644 index 0000000..c51b123 --- /dev/null +++ b/算法周更班/class_2023_06_4_week/Code01_SpecialPermutations.java @@ -0,0 +1,69 @@ +package class_2023_06_4_week; + +// 给你一个下标从 0 开始的整数数组 nums ,它包含 n 个 互不相同 的正整数 +// 如果 nums 的一个排列满足以下条件,我们称它是一个特别的排列 +// 对于 0 <= i < n - 1 的下标 i +// 要么 nums[i] % nums[i+1] == 0 +// 要么 nums[i+1] % nums[i] == 0 +// 请你返回特别排列的总数目,由于答案可能很大,请将它对 1000000007 取余 后返回 +// 测试链接 : https://leetcode.cn/problems/special-permutations/ +public class Code01_SpecialPermutations { + + public static int specialPerm(int[] nums) { + int n = nums.length; + int[][] dp = new int[1 << n][n]; + for (int i = 0; i < (1 << n); i++) { + for (int j = 0; j < n; j++) { + dp[i][j] = -1; + } + } + return process(nums, n, 0, 0, dp); + } + + public static int mod = 1000000007; + + // a : 4 7 9 2 1 ... 固定数组 + // 0 1 2 3 4 ... + // 4 2 1 9 + // s : 1 1 1 0 1 + // 6 5 4 3 2 1 0 + // p = 2 + // 潜台词 : 之前选的数字,一定相邻两个数,都合法! + // 返回值 : 根据上面的情况,继续把所有数字选完!返回有多少合法的!数量! + // s : 最多14位,2^14 = 16384 + // p : 数组下标,0~13, 14种 + // 16384 * 14 = 229376 * 14 -> 3 211 264 + public static int process(int[] a, int n, int s, int p, int[][] dp) { + if (dp[s][p] != -1) { + return dp[s][p]; + } + // 方法数 + int ans = 0; + // n = 7 + // s : 01111111 + if (s == (1 << n) - 1) { + ans = 1; + } else { + // s : 哪些下标上的数已经选了 + // p : 选的数中,最后一个数来自哪个下标 + // 当前该怎么挑选数字? + // arr[p] (前) 现在 x + // 1) arr[p] % x == 0 + // 2) x % arr[p] == 0 + for (int i = 0; i < n; i++) { + // 0位置的数,能不能做当前 + // 1位置的数,能不能做当前 + // 2位置的数,能不能做当前 + // 3位置的数,能不能做当前 + if (s == 0 // 之前没有选择过数字,当然现在随意 + || + ((s & (1 << i)) == 0 && (a[p] % a[i] == 0 || a[i] % a[p] == 0))) { + ans = (ans + process(a, n, s | (1 << i), i, dp)) % mod; + } + } + } + dp[s][p] = ans; + return ans; + } + +} diff --git a/算法周更班/class_2023_06_4_week/Code02_PaintingTheWalls.java b/算法周更班/class_2023_06_4_week/Code02_PaintingTheWalls.java new file mode 100644 index 0000000..7c6c664 --- /dev/null +++ b/算法周更班/class_2023_06_4_week/Code02_PaintingTheWalls.java @@ -0,0 +1,99 @@ +package class_2023_06_4_week; + +import java.util.Arrays; + +// 给你两个长度为 n 下标从 0 开始的整数数组 cost 和 time +// 分别表示给 n 堵不同的墙刷油漆需要的开销和时间。你有两名油漆匠 +// 一位需要 付费 的油漆匠,刷第 i 堵墙需要花费 time[i] 单位的时间 +// 开销为 cost[i] 单位的钱。 +// 一位 免费 的油漆匠,刷 任意 一堵墙的时间为 1 单位,开销为 0 +// 但是必须在付费油漆匠 工作 时,免费油漆匠才会工作 +// 请你返回刷完 n 堵墙最少开销为多少 +// 测试链接 : https://leetcode.cn/problems/painting-the-walls/ +public class Code02_PaintingTheWalls { + + // 暴力递归 + // 展示了主要的思路 + public static int paintWalls1(int[] cost, int[] time) { + return process1(cost, time, 0, cost.length); + } + + + + + + // 来到i位置的墙,整体还有s面墙需要刷 + // 认为只需要选s面墙即可,剩下的都刷完了 + // 返回刷完所有墙的最少花费 + public static int process1(int[] cost, int[] time, int i, int s) { + if (s <= 0) { + return 0; + } + // s > 0 + if (i == cost.length) { + return Integer.MAX_VALUE; + } else { + // 付费的人,就是不选第i面墙 + int p1 = process1(cost, time, i + 1, s); + // 付费的人,就是选第i面墙 + int p2 = Integer.MAX_VALUE; + int next2 = process1(cost, time, i + 1, s - 1 - time[i]); + if (next2 != Integer.MAX_VALUE) { + p2 = cost[i] + next2; + } + return Math.min(p1, p2); + } + } + + // 暴力递归改记忆化搜索 + public static int paintWalls2(int[] cost, int[] time) { + int n = cost.length; + int[][] dp = new int[n + 1][n + 1]; + for (int i = 0; i <= n; i++) { + Arrays.fill(dp[i], -1); + } + return process2(cost, time, 0, n, dp); + } + + public static int process2(int[] cost, int[] time, int i, int s, int[][] dp) { + if (s <= 0) { + return 0; + } + if (dp[i][s] != -1) { + return dp[i][s]; + } + int ans; + if (i == cost.length) { + ans = Integer.MAX_VALUE; + } else { + int p1 = process2(cost, time, i + 1, s, dp); + int p2 = Integer.MAX_VALUE; + int next2 = process2(cost, time, i + 1, s - 1 - time[i], dp); + if (next2 != Integer.MAX_VALUE) { + p2 = cost[i] + next2; + } + ans = Math.min(p1, p2); + } + dp[i][s] = ans; + return ans; + } + + // 严格位置依赖的动态规划 + 空间压缩 + public static int paintWalls3(int[] cost, int[] time) { + int n = cost.length; + int[] dp = new int[n + 1]; + Arrays.fill(dp, Integer.MAX_VALUE); + dp[0] = 0; + for (int i = n - 1; i >= 0; i--) { + for (int s = n; s >= 1; s--) { + if (s - 1 - time[i] <= 0) { + dp[s] = Math.min(dp[s], cost[i]); + } else if (dp[s - 1 - time[i]] != Integer.MAX_VALUE) { + dp[s] = Math.min(dp[s], cost[i] + dp[s - 1 - time[i]]); + } + } + } + return dp[n]; + } + +} diff --git a/算法周更班/class_2023_06_4_week/Code03_FrogHateStoneMinTimes.java b/算法周更班/class_2023_06_4_week/Code03_FrogHateStoneMinTimes.java new file mode 100644 index 0000000..1b9997f --- /dev/null +++ b/算法周更班/class_2023_06_4_week/Code03_FrogHateStoneMinTimes.java @@ -0,0 +1,120 @@ +package class_2023_06_4_week; + +// 来自华为社招笔试 +// 在河上有一座独木桥,一只青蛙想沿着独木桥从河的一侧跳到另一侧 +// 在桥上有一些石子,青蛙很讨厌踩在这些石子上 +// 由于桥的长度和青蛙一次跳过的距离都是正整数 +// 我们可以把独木桥上青蛙可能到达的点看成数轴上的一串整点:0...L +// 其中L是桥的长度,坐标为 0 的点表示桥的起点,坐标为 L 的点表示桥的终点 +// 青蛙从桥的起点开始,不停的向终点方向跳跃 +// 一次跳跃的距离是 S 到 T 之间的任意正整数(包括S,T) +// 当青蛙跳到或跳过坐标为 L 的点时,就算青蛙已经跳出了独木桥。 +// 题目给出独木桥的长度 L,青蛙跳跃的距离范围[S,T] +// 以及桥上石子的位置 +// 你的任务是确定青蛙要想过河,最少需要踩到的石子数 +// 测试链接 : https://www.luogu.com.cn/problem/P1052 +// 请同学们务必参考如下代码中关于输入、输出的处理 +// 这是输入输出处理效率很高的写法 +// 提交以下的所有代码,并把主类名改成"Main" +// 可以直接通过 +import java.io.BufferedReader; +import java.io.IOException; +import java.io.InputStreamReader; +import java.io.OutputStreamWriter; +import java.io.PrintWriter; +import java.io.StreamTokenizer; +import java.util.Arrays; + +public class Code03_FrogHateStoneMinTimes { + + public static int MAXN = 101; + + public static int MAXL = 100001; + + public static int MAXK = 201; + + public static int[] arr = new int[MAXN]; + + public static int[] distance = new int[MAXN]; + + public static int[] dp = new int[MAXL]; + + public static boolean[] stone = new boolean[MAXL]; + + public static boolean[] reach = new boolean[201]; + + public static int l, s, t, m, cut; + + public static void main(String[] args) throws IOException { + BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); + StreamTokenizer in = new StreamTokenizer(br); + PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out)); + while (in.nextToken() != StreamTokenizer.TT_EOF) { + l = (int) in.nval; + in.nextToken(); + s = (int) in.nval; + in.nextToken(); + t = (int) in.nval; + in.nextToken(); + m = (int) in.nval; + for (int i = 1; i <= m; ++i) { + in.nextToken(); + arr[i] = (int) in.nval; + } + if (s == t) { + int ans = 0; + for (int i = 1; i <= Math.min(l, m); ++i) { + if (arr[i] % s == 0) { + ans++; + } + } + out.println(ans); + } else { // s < t + Arrays.sort(arr, 1, m + 1); + // 可以直接给一个保守的距离,不需要算 + // 因为s和t,不大,<= 10 + cut = reduce(s, t); + for (int i = 1; i <= m; i++) { + distance[i] = distance[i - 1] + Math.min(arr[i] - arr[i - 1], cut); + stone[distance[i]] = true; + } + l = Math.min(l, distance[m] + cut); + Arrays.fill(dp, 1, l + 1, MAXN); + for (int i = 1; i <= l; i++) { + for (int j = Math.max(i - t, 0); j <= i - s; j++) { + dp[i] = Math.min(dp[i], dp[j] + (stone[i] ? 1 : 0)); + } + } + int ans = MAXN; + for (int i = distance[m] + 1; i <= l; i++) { + ans = Math.min(ans, dp[i]); + } + out.println(ans); + } + out.flush(); + } + } + + // 一旦s和t定了,那么距离多远就可以缩减 + public static int reduce(int s, int t) { + Arrays.fill(reach, false); + int cnt = 0; + int ans = 0; + for (int i = 0; i < MAXK; i++) { + for (int j = i + s; j < Math.min(i + t + 1, MAXK); j++) { + reach[j] = true; + } + if (!reach[i]) { + cnt = 0; + } else { + cnt++; + } + if (cnt == t) { + ans = i; + break; + } + } + return ans; + } + +} diff --git a/算法周更班/class_2023_06_4_week/Code04_ValidArrangementOfPairs.java b/算法周更班/class_2023_06_4_week/Code04_ValidArrangementOfPairs.java new file mode 100644 index 0000000..8cfb906 --- /dev/null +++ b/算法周更班/class_2023_06_4_week/Code04_ValidArrangementOfPairs.java @@ -0,0 +1,80 @@ +package class_2023_06_4_week; + +import java.util.ArrayList; +import java.util.HashMap; +import java.util.LinkedList; + +// 欧拉路径问题 +// 给你一个下标从 0 开始的二维整数数组 pairs +// 其中 pairs[i] = [starti, endi] +// 如果 pairs 的一个重新排列 +// 满足对每一个下标 i ( 1 <= i < pairs.length ) +// 都有 endi-1 == starti , +// 那么我们就认为这个重新排列是 pairs 的一个 合法重新排列 +// 请你返回 任意一个 pairs 的合法重新排列 +// 注意:数据保证至少存在一个 pairs 的合法重新排列 +// 测试链接 : https://leetcode.cn/problems/valid-arrangement-of-pairs/ +public class Code04_ValidArrangementOfPairs { + + // 欧拉路 : 从图中某个点出发,遍历整个图,每条边通过且只通过一次 + // 欧拉回路 : 起点和终点相同的欧拉路 + // 怎么判断是否存在欧拉路 + // 1) 判断联通性,用dfs或者并查集来检查 + // 2) 无向连通图存在欧拉路的判断 + // 在无向图中 : 一个点上连接边的数量,称为这个点的度数, + // 度数为奇数,称这个点为奇点;度数为偶数,称这个点为偶点。 + // 如果图中的点都是偶点,则存在欧拉回路,任意点都可以成为起点或终点 + // 如果图中只有两个奇点,则存在欧拉路,其中一个奇点是起点,另一个是终点 + // 3) 有向连通图存在欧拉路的判断 + // 在有向图中 : 分为出度和入度,出度记为+1,入度记为-1, + // 那么每个点自己的入度与出度相加后的值,叫做该点的度数 + // 一个有向图存在欧拉回路的条件 : + // 必须该图中所有点的度数为0,起点可以为任意点 + // 一个有向图存在欧拉路的条件 : + // 只有一个点度数为+1,只有一个点度数为-1,其他点度数为0 + // 并且起点是度数+1的点,终点是度数-1的点 + // 如上的判断,非常容易写代码,只要了解图结构,代码都不难,不再赘述 + // 本题目既有有向图欧拉路的判断,但重点是欧拉路的第二个常考类型 : + // 怎么输出一个欧拉路 + // 实在没有什么难度,就是利用剪枝的dfs,代码硬记,也没多少 + public static int[][] validArrangement(int[][] pairs) { + HashMap> graph = new HashMap<>(); + HashMap degrees = new HashMap<>(); + for (int[] pair : pairs) { + graph.putIfAbsent(pair[0], new LinkedList<>()); + graph.putIfAbsent(pair[1], new LinkedList<>()); + degrees.putIfAbsent(pair[0], 0); + degrees.putIfAbsent(pair[1], 0); + } + for (int[] pair : pairs) { + graph.get(pair[0]).add(pair[1]); + degrees.put(pair[0], degrees.get(pair[0]) + 1); + degrees.put(pair[1], degrees.get(pair[1]) - 1); + } + int from = pairs[0][0]; + for (Integer cur : degrees.keySet()) { + if (degrees.get(cur) == 1) { + from = cur; + break; + } + } + ArrayList record = new ArrayList<>(); + dfs(from, graph, record); + int n = record.size(); + int[][] ans = new int[n][2]; + for (int i = n - 1, j = 0; j < n; i--, j++) { + ans[i] = record.get(j); + } + return ans; + } + + public static void dfs(int from, HashMap> graph, ArrayList record) { + LinkedList next = graph.get(from); + while (!next.isEmpty()) { + int to = next.poll(); + dfs(to, graph, record); + record.add(new int[] { from, to }); + } + } + +} diff --git a/算法课堂笔记/算法和数据结构知识梳理.xmind b/算法课堂笔记/算法和数据结构知识梳理.xmind index 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