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package class48;
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import java.util.Arrays;
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// 来自学员问题
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// 比如{ 5, 3, 1, 4 }
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// 全部数字对是：(5,3)、(5,1)、(5,4)、(3,1)、(3,4)、(1,4)
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// 数字对的差值绝对值： 2、4、1、2、1、3
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// 差值绝对值排序后：1、1、2、2、3、4
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// 给定一个数组arr，和一个正数k
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// 返回arr中所有数字对差值的绝对值，第k小的是多少
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// arr = { 5, 3, 1, 4 }, k = 4
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// 返回2
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public class Code01_MinKthPairMinusABS {
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// 暴力解，生成所有数字对差值绝对值，排序，拿出第k个，k从1开始
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public static int kthABS1(int[] arr, int k) {
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int n = arr.length;
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int m = ((n - 1) * n) >> 1;
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if (m == 0 || k < 1 || k > m) {
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return -1;
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}
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int[] abs = new int[m];
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int size = 0;
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for (int i = 0; i < n; i++) {
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for (int j = i + 1; j < n; j++) {
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abs[size++] = Math.abs(arr[i] - arr[j]);
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}
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}
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Arrays.sort(abs);
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return abs[k - 1];
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}
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// 二分 + 不回退
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public static int kthABS2(int[] arr, int k) {
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int n = arr.length;
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if (n < 2 || k < 1 || k > ((n * (n - 1)) >> 1)) {
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return -1;
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}
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Arrays.sort(arr);
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// 0 ~ 大-小 二分
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// l ~ r
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int left = 0;
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int right = arr[n - 1] - arr[0];
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int mid = 0;
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int rightest = -1;
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while (left <= right) {
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mid = (left + right) / 2;
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// 数字对差值的绝对值<=mid的数字对个数，是不是 < k个的！
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if (valid(arr, mid, k)) {
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rightest = mid;
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left = mid + 1;
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} else {
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right = mid - 1;
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}
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}
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return rightest + 1;
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}
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// 假设arr中的所有数字对，差值绝对值<=limit的个数为x
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// 如果 x < k，达标，返回true
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// 如果 x >= k，不达标，返回false
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public static boolean valid(int[] arr, int limit, int k) {
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int x = 0;
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for (int l = 0, r = 1; l < arr.length; r = Math.max(r, ++l)) {
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while (r < arr.length && arr[r] - arr[l] <= limit) {
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r++;
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}
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x += r - l - 1;
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}
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return x < k;
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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 < ans.length; i++) {
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ans[i] = (int) (Math.random() * v);
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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 size = 100;
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int value = 100;
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int testTime = 10000;
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System.out.println("测试开始");
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for (int i = 0; i < testTime; i++) {
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int n = (int) (Math.random() * size);
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int k = (int) (Math.random() * (n * (n - 1) / 2)) + 1;
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int[] arr = randomArray(n, value);
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int ans1 = kthABS1(arr, k);
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int ans2 = kthABS2(arr, k);
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if (ans1 != ans2) {
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System.out.print("arr : ");
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for (int num : arr) {
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System.out.print(num + " ");
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}
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System.out.println();
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System.out.println("k : " + k);
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System.out.println("ans1 : " + ans1);
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System.out.println("ans2 : " + ans2);
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System.out.println("出错了！");
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break;
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}
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}
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System.out.println("测试结束");
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long start;
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long end;
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int n = 500000;
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int v = 50000000;
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int[] arr = randomArray(n, v);
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int k = (int) (Math.random() * (n * (n - 1) / 2)) + 1;
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start = System.currentTimeMillis();
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kthABS2(arr, k);
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end = System.currentTimeMillis();
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System.out.println("大数据量运行时间（毫秒）：" + (end - start));
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}
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}
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