动态规划|最长公共子序列、最长上升子序列

LIS

百练-2757

package 动态规划;
import java.util.Scanner;
/**
 * 單串
 * @author DELL
 *
 */
public class 最长上升子序列 {
	static int n;
	static int[] data;
	static int[] record;

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		init();
		int max = record[0];
		for (int i = 1; i < n; i++) {
			for (int j = 0; j < i; j++) {// 在左侧寻找
				if (data[j] < data[i]) {
					record[i] = Math.max(record[i], record[j] + 1);
				}
			}
			max = Math.max(record[i], max);
		}
		System.out.println(max);
	}

	private static void init() {
		Scanner sc = new Scanner(System.in);
		n = sc.nextInt();
		data = new int[n];
		record = new int[n];
		for (int i = 0; i < data.length; i++) {
			data[i] = sc.nextInt();
			record[i] = 1;// 初始条件
		}
	}
}

LIS相关题目1

计蒜客-T1722

package DP;

import java.util.Scanner;

public class 利润 {
	static int n;
	static int[] v;
	static int[] dp;// dp[i]表示以第i天结尾时，所能够得到的最大利润和
	static int Max;

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		while (sc.hasNext()) {
			Max = Integer.MIN_VALUE;
			n = sc.nextInt();
			v = new int[n];
			dp = new int[3];
			for (int i = 0; i < n; i++) {
				v[i] = sc.nextInt();
			}
			function();
			System.out.println(Max);
		}
	}

	private static void function() {
		dp[0] = v[0];
		int e = 1;
		for (int i = 1; i < n; i++) {
			if (dp[e ^ 1] < 0)
				dp[e] = v[i];
			else
				dp[e] = dp[e ^ 1] + v[i];
			Max = Math.max(Max, dp[e]);
			e ^= 1;
		}
	}

}

LIS相关题目2

计蒜客-T1227

#include<iostream>
#include<algorithm>
using namespace std;

int n;
int v[100000 + 5];// v[i]表示最后抢的是第i家商店，这种状态下可以得到的最多金钱数

// 在这道题目中，前n家商店所能够得到的最多金钱数目可以表示为：max(v[n-1], v[n])
int main() {
	int t;
	cin >> t;
	while (t--) {
		cin >> n;
		for (int i = 1; i <= n; i++) {
			cin >> v[i];
		}
		for (int i = 3; i <= n; i++) {
			int temp = v[1];
			temp = max(v[i - 3], v[i - 2]);
			v[i] = v[i] + temp;
		}
		int maxV = v[1];
		if (n > 1)
			maxV = max(v[n - 1], v[n]);
		cout << maxV << endl;
	}
	return 0;
}

LCS

POJ-1458
视频讲解

package 动态规划;

import java.util.Scanner;

/**
 * 雙串
 * 
 * @author DELL
 *
 */
public class 最長公共子序列 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		while (sc.hasNext()) {
			String str1 = sc.next();
			String str2 = sc.next();
			int n = str1.length();
			int m = str2.length();
			int[][] dp = new int[n + 1][m + 1];
			for (int i = 1; i < dp.length; i++) {
				for (int j = 1; j < dp[i].length; j++) {
					if (str1.charAt(i - 1) == str2.charAt(j - 1))// str1[i] == str2[j]時
						dp[i][j] = dp[i - 1][j - 1] + 1;
					else
						dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
				}
			}
			System.out.println(dp[n][m]);
		}
	}
}