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Commit a220e4c

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第464场周赛T1~T4 (4)
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public class Solution3658 {
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public int gcdOfOddEvenSums(int n) {
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long sumOdd = 0, sumEven = 0;
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int odd = 1, even = 2;
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for (int i = 0; i < n; i++) {
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sumOdd += odd;
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sumEven += even;
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odd += 2;
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even += 2;
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}
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return (int) getGCD(sumOdd, sumEven);
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}
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private long getGCD(long num1, long num2) {
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return num1 == 0 ? num2 : getGCD(num2 % num1, num1);
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}
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}
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/*
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3658. 奇数和与偶数和的最大公约数
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https://leetcode.cn/problems/gcd-of-odd-and-even-sums/description/
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第 464 场周赛 T1。
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给你一个整数 n。请你计算以下两个值的 最大公约数(GCD):
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- sumOdd:前 n 个奇数的总和。
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- sumEven:前 n 个偶数的总和。
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返回 sumOdd 和 sumEven 的 GCD。
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提示:
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1 <= n <= 1000
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模拟 / 数学。
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sumOdd = n^2
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sumEven = n(n+1)
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最大公约数为 n。
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时间复杂度 O(1)。
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*/
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import java.util.HashMap;
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import java.util.Map;
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public class Solution3659 {
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public boolean partitionArray(int[] nums, int k) {
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int n = nums.length;
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if (n % k != 0) return false;
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Map<Integer, Integer> mp = new HashMap<>();
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int max_cnt = 0;
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for (int v : nums) {
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max_cnt = Math.max(max_cnt, mp.merge(v, 1, Integer::sum));
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}
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return max_cnt <= n / k;
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}
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}
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/*
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3659. 数组元素分组
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https://leetcode.cn/problems/partition-array-into-k-distinct-groups/description/
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第 464 场周赛 T2。
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给你一个整数数组 nums 和一个整数 k。
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请你判断是否可以将 nums 中的所有元素分成一个或多个组,使得:
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- 每个组 恰好 包含 k 个 不同的 元素。
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- nums 中的每个元素 必须 被分配到 恰好一个 组中。
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如果可以完成这样的分组,返回 true;否则,返回 false。
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提示:
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1 <= nums.length <= 10^5
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1 <= nums[i] <= 10^5
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1 <= k <= nums.length
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构造。n 必须能整除 k,且频次最高元素不能超过 k。
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时间复杂度 O(n)。
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*/
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public class Solution3660 {
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public int[] maxValue(int[] nums) {
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int n = nums.length;
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int[] preMax = new int[n];
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preMax[0] = nums[0];
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for (int i = 1; i < n; i++) {
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preMax[i] = Math.max(preMax[i - 1], nums[i]);
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}
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int sufMin = Integer.MAX_VALUE;
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int mx = 0;
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for (int i = n - 1; i >= 0; i--) {
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if (preMax[i] <= sufMin) {
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mx = preMax[i]; // 无法跳到 [i+1,n-1] 中,只能跳到 [0,i] 中的最大值
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}
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sufMin = Math.min(sufMin, nums[i]);
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nums[i] = mx;
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}
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return nums;
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}
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}
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/*
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3660. 跳跃游戏 9
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https://leetcode.cn/problems/jump-game-ix/description/
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第 464 场周赛 T3。
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给你一个整数数组 nums。
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从任意下标 i 出发,你可以根据以下规则跳跃到另一个下标 j:
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- 仅当 nums[j] < nums[i] 时,才允许跳跃到下标 j,其中 j > i。
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- 仅当 nums[j] > nums[i] 时,才允许跳跃到下标 j,其中 j < i。
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对于每个下标 i,找出从 i 出发且可以跳跃 任意 次,能够到达 nums 中的 最大值 是多少。
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返回一个数组 ans,其中 ans[i] 是从下标 i 出发可以到达的最大值。
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提示:
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1 <= nums.length <= 10^5
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1 <= nums[i] <= 10^9
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结论 + 动态规划。
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题目很绕。翻译一下就是 如果左边比右边大,可以从右跳到左,也可以从左跳到右;
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设 f(i) 表示前 i 个元素的最大值,g(i) 表示第 i 到第 n 个元素的最小值。
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每个 f(i) <= g(i+1) 的位置就把整个序列分成了很多段,每一段的答案就是当前段的最大值。
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时间复杂度 O(n)。
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rating 2173 (clist.by)
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*/
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import java.util.Arrays;
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import java.util.Comparator;
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public class Solution3661 {
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private int[][] a;
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private int[] walls;
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private int[][] memo;
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public int maxWalls(int[] robots, int[] distance, int[] walls) {
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int n = robots.length;
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this.walls = walls;
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a = new int[n][2];
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for (int i = 0; i < n; i++) {
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a[i][0] = robots[i];
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a[i][1] = distance[i];
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}
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Arrays.sort(a, Comparator.comparingInt(p -> p[0]));
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Arrays.sort(walls);
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memo = new int[n][2];
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for (int[] row : memo) {
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Arrays.fill(row, -1); // -1 表示没有计算过
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}
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return dfs(n - 1, 1);
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}
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private int dfs(int i, int j) {
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if (i < 0) return 0;
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// 之前计算过
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if (memo[i][j] != -1) return memo[i][j];
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// 往左射
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int leftX = a[i][0] - a[i][1];
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if (i > 0) {
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leftX = Math.max(leftX, a[i - 1][0] + 1); // 不能到达左边那个机器人
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}
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int left = lowerBound(walls, leftX);
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int cur = lowerBound(walls, a[i][0] + 1);
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int res = dfs(i - 1, 0) + cur - left; // [left, cur-1] 中的墙都能摧毁
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// 往右射
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int rightX = a[i][0] + a[i][1];
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if (i + 1 < a.length) {
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int x2 = a[i + 1][0];
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if (j == 0) { // 右边那个机器人往左射
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x2 -= a[i + 1][1];
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}
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rightX = Math.min(rightX, x2 - 1); // 不能到达右边那个机器人(或者他往左射到的墙)
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}
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int right = lowerBound(walls, rightX + 1);
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cur = lowerBound(walls, a[i][0]);
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res = Math.max(res, dfs(i - 1, 1) + right - cur); // [cur, right-1] 中的墙都能摧毁
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return memo[i][j] = res; // 记忆化
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}
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private int lowerBound(int[] a, int key) {
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int l = 0, r = a.length;
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while (l < r) {
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int m = l + (r - l) / 2;
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if (a[m] >= key) r = m;
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else l = m + 1;
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}
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return l;
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}
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}
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/*
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3661. 可以被机器人摧毁的最大墙壁数目
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https://leetcode.cn/problems/maximum-walls-destroyed-by-robots/description/
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第 464 场周赛 T4。
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一条无限长的直线上分布着一些机器人和墙壁。给你整数数组 robots ,distance 和 walls:
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- robots[i] 是第 i 个机器人的位置。
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- distance[i] 是第 i 个机器人的子弹可以行进的 最大 距离。
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- walls[j] 是第 j 堵墙的位置。
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每个机器人有 一颗 子弹,可以向左或向右发射,最远距离为 distance[i] 米。
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子弹会摧毁其射程内路径上的每一堵墙。机器人是固定的障碍物:如果子弹在到达墙壁前击中另一个机器人,它会 立即 在该机器人处停止,无法继续前进。
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返回机器人可以摧毁墙壁的 最大 数量。
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注意:
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- 墙壁和机器人可能在同一位置;该位置的墙壁可以被该位置的机器人摧毁。
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- 机器人不会被子弹摧毁。
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提示:
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1 <= robots.length == distance.length <= 10^5
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1 <= walls.length <= 10^5
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1 <= robots[i], walls[j] <= 10^9
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1 <= distance[i] <= 10^5
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robots 中的所有值都是 互不相同 的
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walls 中的所有值都是 互不相同 的
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记忆化搜索 + 二分。
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时间复杂度 O(nlogn + mlogm + nlogm),其中 n 是 robots 的长度,m 是 walls 的长度。
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rating 2505 (clist.by)
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*/
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import org.junit.jupiter.api.Assertions;
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import org.junit.jupiter.api.Test;
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public class Solution3658Tests {
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private final Solution3658 solution3658 = new Solution3658();
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@Test
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public void example1() {
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int n = 4;
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int expected = 4;
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Assertions.assertEquals(expected, solution3658.gcdOfOddEvenSums(n));
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}
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@Test
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public void example2() {
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int n = 5;
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int expected = 5;
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Assertions.assertEquals(expected, solution3658.gcdOfOddEvenSums(n));
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}
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}
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import org.junit.jupiter.api.Assertions;
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import org.junit.jupiter.api.Test;
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public class Solution3659Tests {
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private final Solution3659 solution3659 = new Solution3659();
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@Test
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public void example1() {
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int[] nums = {1, 2, 3, 4};
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int k = 2;
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Assertions.assertTrue(solution3659.partitionArray(nums, k));
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}
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@Test
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public void example2() {
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int[] nums = {3, 5, 2, 2};
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int k = 2;
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Assertions.assertTrue(solution3659.partitionArray(nums, k));
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}
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@Test
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public void example3() {
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int[] nums = {1, 5, 2, 3};
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int k = 3;
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Assertions.assertFalse(solution3659.partitionArray(nums, k));
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}
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}
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import org.junit.jupiter.api.Assertions;
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import org.junit.jupiter.api.Test;
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public class Solution3660Tests {
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private final Solution3660 solution3660 = new Solution3660();
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@Test
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public void example1() {
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int[] nums = {2, 1, 3};
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int[] expected = {2, 2, 3};
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Assertions.assertArrayEquals(expected, solution3660.maxValue(nums));
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}
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@Test
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public void example2() {
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int[] nums = {2, 3, 1};
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int[] expected = {3, 3, 3};
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Assertions.assertArrayEquals(expected, solution3660.maxValue(nums));
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}
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}
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import org.junit.jupiter.api.Assertions;
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import org.junit.jupiter.api.Test;
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public class Solution3661Tests {
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private final Solution3661 solution3661 = new Solution3661();
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@Test
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public void example1() {
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int[] robots = {4};
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int[] distance = {3};
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int[] walls = {1, 10};
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int expected = 1;
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Assertions.assertEquals(expected, solution3661.maxWalls(robots, distance, walls));
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}
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@Test
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public void example2() {
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int[] robots = {10, 2};
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int[] distance = {5, 1};
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int[] walls = {5, 2, 7};
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int expected = 3;
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Assertions.assertEquals(expected, solution3661.maxWalls(robots, distance, walls));
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}
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@Test
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public void example3() {
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int[] robots = {1, 2};
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int[] distance = {100, 1};
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int[] walls = {10};
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int expected = 0;
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Assertions.assertEquals(expected, solution3661.maxWalls(robots, distance, walls));
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}
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// 补充用例
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@Test
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public void example4() {
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// https://leetcode.cn/problems/maximum-walls-destroyed-by-robots/submissions/655939484/
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int[] robots = {31, 36, 18, 39, 10, 21, 40, 69, 57, 51, 19, 32, 50, 53, 3, 28, 9, 59, 46, 22, 13, 63, 33, 14, 25, 52, 64, 5, 44, 17, 68, 45};
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int[] distance = {5, 3, 4, 6, 3, 4, 2, 4, 6, 5, 4, 3, 1, 4, 3, 4, 5, 3, 1, 3, 2, 2, 4, 1, 3, 2, 4, 2, 2, 1, 4, 6};
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int[] walls = {10, 41, 54, 6, 7, 33, 14, 30, 9, 12, 38, 27, 39, 52, 42, 46, 45, 17, 2, 15, 55, 44, 4, 18, 20, 34, 28, 51, 11, 13, 37, 31, 23, 24, 5, 56, 22, 57, 35, 29, 32, 26, 48, 47, 16, 43, 36, 25, 53, 19, 40, 49, 21, 1, 50, 3, 8};
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int expected = 56;
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Assertions.assertEquals(expected, solution3661.maxWalls(robots, distance, walls));
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}
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@Test
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public void example5() {
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// https://leetcode.cn/problems/maximum-walls-destroyed-by-robots/submissions/655951952/
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int[] robots = {12, 6, 34, 28, 58, 10, 42, 4, 55, 48, 3, 7, 26, 40, 54, 17, 32, 23, 56, 43, 31, 1, 24};
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int[] distance = {2, 5, 1, 6, 3, 8, 6, 4, 5, 6, 9, 3, 3, 8, 6, 3, 5, 7, 5, 7, 5, 7, 7};
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int[] walls = {25, 37, 48, 94, 56, 55, 30, 28, 40, 35, 15, 97, 12, 6, 85, 14, 52, 60, 27, 71, 5, 19, 73, 9, 92, 32, 11, 63, 13, 8, 39, 88, 44, 79, 7, 17, 78, 93, 33, 80, 26, 46, 68, 47, 95, 24, 36, 49, 90, 70, 64, 18, 57, 50, 66, 51, 54, 2, 21, 86, 16, 61, 91, 75, 58, 38, 65, 45, 29, 69, 3, 53, 1, 87, 83, 59, 23, 10, 62, 76, 43, 96, 77, 31, 4, 34, 42, 67, 89, 41, 82, 72, 22, 20, 81, 84, 74};
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int expected = 61;
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Assertions.assertEquals(expected, solution3661.maxWalls(robots, distance, walls));
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}
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}

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