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package class_2022_08_3_week;
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// 来自学员问题
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// 给定怪兽的血量为hp
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// 第i回合如果用刀砍，怪兽在这回合会直接掉血，没有后续效果
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// 第i回合如果用毒，怪兽在这回合不会掉血，
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// 但是之后每回合都会掉血，并且所有中毒的后续效果会叠加
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// 给定的两个数组cuts、poisons，两个数组等长，长度都是n
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// 表示你在n回合内的行动，
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// 每一回合的刀砍的效果由cuts[i]表示
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// 每一回合的中毒的效果由poisons[i]表示
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// 如果你在n个回合内没有直接杀死怪兽，意味着你已经无法有新的行动了
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// 但是怪兽如果有中毒效果的话，那么怪兽依然会在hp耗尽的那回合死掉
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// 返回你最快能在多少回合内将怪兽杀死
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// 数据范围 :
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// 1 <= n <= 10的5次方
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// 1 <= hp <= 10的9次方
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// 1 <= cuts[i]、poisons[i] <= 10的9次方
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public class Code02_CutOrPoison {
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// 不算好的方法
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// 为了验证
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public static int fast1(int[] cuts, int[] poisons, int hp) {
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int sum = 0;
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for (int num : poisons) {
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sum += num;
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}
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int[][][] dp = new int[cuts.length][hp + 1][sum + 1];
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return process1(cuts, poisons, 0, hp, 0, dp);
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}
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public static int process1(int[] cuts, int[] poisons, int index, int restHp, int poisonEffect, int[][][] dp) {
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restHp -= poisonEffect;
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if (restHp <= 0) {
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return index + 1;
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}
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// restHp > 0
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if (index == cuts.length) {
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if (poisonEffect == 0) {
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return Integer.MAX_VALUE;
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} else {
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return cuts.length + 1 + (restHp + poisonEffect - 1) / poisonEffect;
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}
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}
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if (dp[index][restHp][poisonEffect] != 0) {
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return dp[index][restHp][poisonEffect];
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}
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int p1 = restHp <= cuts[index] ? (index + 1)
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: process1(cuts, poisons, index + 1, restHp - cuts[index], poisonEffect, dp);
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int p2 = process1(cuts, poisons, index + 1, restHp, poisonEffect + poisons[index], dp);
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int ans = Math.min(p1, p2);
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dp[index][restHp][poisonEffect] = ans;
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return ans;
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}
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// 真正想实现的方法
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// O(N * log(hp))
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public static int fast2(int[] cuts, int[] poisons, int hp) {
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// 怪兽可能的最快死亡回合
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int l = 1;
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// 怪兽可能的最晚死亡回合
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int r = hp + 1;
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int m = 0;
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int ans = Integer.MAX_VALUE;
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while (l <= r) {
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m = l + ((r - l) >> 1);
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if (ok(cuts, poisons, hp, m)) {
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ans = m;
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r = m - 1;
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} else {
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l = m + 1;
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}
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}
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return ans;
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}
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public static boolean ok(int[] cuts, int[] posions, long hp, int limit) {
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int n = Math.min(cuts.length, limit);
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for (int i = 0, j = 1; i < n; i++, j++) {
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hp -= Math.max((long) cuts[i], (long) (limit - j) * (long) posions[i]);
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if (hp <= 0) {
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return true;
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}
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}
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return false;
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}
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// 为了测试
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public static int[] randomArray(int n, int v) {
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int[] ans = new int[n];
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for (int i = 0; i < n; i++) {
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ans[i] = (int) (Math.random() * v) + 1;
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}
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return ans;
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}
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// 为了测试
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public static void main(String[] args) {
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int N = 30;
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int cutV = 20;
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int posionV = 10;
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int hpV = 200;
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int testTimes = 10000;
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System.out.println("测试开始");
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for (int i = 0; i < testTimes; i++) {
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int n = (int) (Math.random() * N) + 1;
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int[] cuts = randomArray(n, cutV);
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int[] posions = randomArray(n, posionV);
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int hp = (int) (Math.random() * hpV) + 1;
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int ans1 = fast1(cuts, posions, hp);
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int ans2 = fast2(cuts, posions, hp);
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if (ans1 != ans2) {
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System.out.println("出错了!");
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}
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}
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System.out.println("测试结束");
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}
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}
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