最長單調遞增子序列問題
題目:設計一個 O( n ^ 2 )複雜度的算法,找出由 n 個數組成的序列的最長單調遞增子序列。
import java.util.Scanner;
public class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
while (scanner.hasNext()) {
int n = scanner.nextInt();
int[] nums = new int[n + 1];// 數列數據
int[] sub_len = new int[n + 1];// sub_len[i]表示從i到n的最長遞增序列的長度
int[] sub_index = new int[n + 1];// sub_index[i]表示第i個數據的後面一個數據的下標
for (int i = 1; i <= n; i++) {
nums[i] = scanner.nextInt();
sub_len[i] = 1;
sub_index[i] = 0;
}
for (int i = n - 1; i >= 1; i--) {
int max = 0, p = 0;// 臨時變量
for (int j = i + 1; j <= n; j++) {
if (nums[i] < nums[j] && sub_len[j] > max) {
max = sub_len[j];
p = j;
}
if (p != 0) {
sub_len[i] = sub_len[p] + 1;
sub_index[i] = p;
}
}
}
int max = 0, p = 0;
for (int i = 1; i <= n; i++) {
if (sub_len[i] > max) {
max = sub_len[i];
p = i;
}
}
System.out.println("最長長度:" + max);
System.out.print("最長遞增序列:");
while (p != 0) {
System.out.print(nums[p] + " ");
p = sub_index[p];
}
System.out.println();
}
scanner.close();
}
}