90 lines
2.3 KiB
Java
90 lines
2.3 KiB
Java
package DynamicProgramming;
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import java.util.Scanner;
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/** @author Afrizal Fikri (https://github.com/icalF) */
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public class LongestIncreasingSubsequence {
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public static void main(String[] args) {
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Scanner sc = new Scanner(System.in);
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int n = sc.nextInt();
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int arr[] = new int[n];
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for (int i = 0; i < n; i++) {
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arr[i] = sc.nextInt();
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}
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System.out.println(LIS(arr));
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System.out.println(findLISLen(arr));
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sc.close();
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}
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private static int upperBound(int[] ar, int l, int r, int key) {
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while (l < r - 1) {
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int m = (l + r) >>> 1;
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if (ar[m] >= key) r = m;
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else l = m;
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}
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return r;
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}
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private static int LIS(int[] array) {
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int N = array.length;
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if (N == 0) return 0;
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int[] tail = new int[N];
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// always points empty slot in tail
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int length = 1;
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tail[0] = array[0];
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for (int i = 1; i < N; i++) {
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// new smallest value
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if (array[i] < tail[0]) tail[0] = array[i];
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// array[i] extends largest subsequence
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else if (array[i] > tail[length - 1]) tail[length++] = array[i];
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// array[i] will become end candidate of an existing subsequence or
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// Throw away larger elements in all LIS, to make room for upcoming grater elements than
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// array[i]
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// (and also, array[i] would have already appeared in one of LIS, identify the location and
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// replace it)
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else tail[upperBound(tail, -1, length - 1, array[i])] = array[i];
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}
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return length;
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}
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/** @author Alon Firestein (https://github.com/alonfirestein) */
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// A function for finding the length of the LIS algorithm in O(nlogn) complexity.
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public static int findLISLen(int a[]) {
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int size = a.length;
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int arr[] = new int[size];
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arr[0] = a[0];
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int lis = 1;
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for (int i = 1; i < size; i++) {
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int index = binarySearchBetween(arr, lis, a[i]);
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arr[index] = a[i];
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if (index > lis) lis++;
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}
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return lis;
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}
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// O(logn)
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private static int binarySearchBetween(int[] t, int end, int key) {
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int left = 0;
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int right = end;
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if (key < t[0]) return 0;
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if (key > t[end]) return end + 1;
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while (left < right - 1) {
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int middle = (left + right) / 2;
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if (t[middle] < key) left = middle;
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else right = middle;
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}
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return right;
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}
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}
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