1. 爬樓梯
   MIOJ 爬樓梯

package mioj.day4.ClimbStairs;

import java.util.Scanner;

/**
 * @author: chuanyi@88.com
 * @description: mioj: 爬樓梯 https://code.mi.com/problem/list/view?id=10&cid=14
 * @date: 2020/10/24 20:27
 */
public class Main {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        while (scanner.hasNext()) {
            int num = scanner.nextInt();
            long start = System.currentTimeMillis();
            System.out.println("1.climbStairsRecursive result: " + climbStairsRecursive(num));
            long time1 = System.currentTimeMillis();
            System.out.println("1.climbStairsRecursive time cost:" + (time1 - start) + " ms");
            System.out.println("2.climbStairsRecursiveImproved result: " + climbStairsRecursiveImproved(num));
            long time2 = System.currentTimeMillis();
            System.out.println("2.climbStairsRecursiveImproved time cost:" + (time2 - time1) + " ms");
            System.out.println("3.climbStairsIterative result: " + climbStairsIterative(num));
            long time3 = System.currentTimeMillis();
            System.out.println("3.climbStairsIterative time cost:" + (time3 - time2) + " ms");
            System.out.println("4.climbStairsDp result: " + climbStairsDp(num));
            long time4 = System.currentTimeMillis();
            System.out.println("4.climbStairsDp time cost:" + (time4 - time3) + " ms");
            System.out.println("5.climbStairsSlippedWindow result: " + climbStairsSlippedWindow(num));
            long time5 = System.currentTimeMillis();
            System.out.println("5.climbStairsSlippedWindow time cost:" + (time5 - time4) + " ms");


        }
    }

    /**
     * 遞歸做法
     *
     * @param num
     * @return
     */
    private static int climbStairsRecursive(int num) {
        if (num < 1) {
            return 0;
        }
        if (num <= 2) {
            return num;
        }
        return climbStairsRecursive(num - 1)
                + climbStairsRecursive(num - 2);
    }

    /**
     * 遞歸做法存儲改進版.有人叫它備忘錄??法
     *
     * @param num
     * @return
     */
    private static int climbStairsRecursiveImproved(int num) {
        if (num < 1) {
            return 0;
        }
        if (num <=2){
            return num;
        }
        int[] count = new int[num+1];//注意第一下標丟棄不用
        return climbStairsRecursive(num - 1, count)
                + climbStairsRecursive(num - 2, count);
    }

    private static int climbStairsRecursive(int num, int[] count) {
        if (num <= 2) {
            count[num] = num;
        } else {
            count[num] = climbStairsRecursive(num - 1, count)
                    + climbStairsRecursive(num - 2, count);
        }
        return count[num];
    }

    /**
     * 迭代
     *
     * @param num
     * @return
     */
    private static int climbStairsIterative(int num) {
        if (num < 1) {
            return 0;
        }
        int cur = 1;
        int pre = 0;
        for (int i = 0; i < num; i++) {
            int temp = cur;
            cur += pre;
            pre = temp;
        }
        return cur;
    }


    /**
     * 動態(tài)規(guī)劃法
     * @param num
     * @return
     */
    private static int climbStairsDp(int num){
        if (num < 1){
            return 0;
        }
        if (num <= 2){
            return num;
        }
        int[] count = new int[num+1];//這里下標從1開始使用扑眉，比較容易理解和表示
        count[1] = 1;
        count[2] = 2;
        for (int i = 3; i <= num; i++) {
            count[i] = count[i -1] + count[i - 2];
        }
        return count[num];
    }

    /**
     * 每個結果只和上一個和上上一個結果有關，所以每次只保留這兩個結果即可
     * @param num
     * @return
     * 3
     * count 1 2 3
     * cur 1 1 2 2
     * pre 1 1 1
     * prepre 0 1 1
     * temp 1 1 2
     * temp2 1 1 1
     *
     *
     *
     */
    private static int climbStairsSlippedWindow(int num){
        if (num < 1){
            return 0;
        }
        if (num <= 2){
            return num;
        }
        int count = 0;
        int cur = 0;
        int pre = 1;
        int prepre = 0;
        while (count < num){
            cur = pre + prepre;
            prepre  = pre;
            pre = cur;

            count ++;
        }
        return cur;

    }
}

參考: (爬樓梯問題)[https://blog.csdn.net/wu2304211/article/details/52717578?utm_medium=distribute.pc_relevant.none-task-blog-BlogCommendFromMachineLearnPai2-1.channel_param&depth_1-utm_source=distribute.pc_relevant.none-task-blog-BlogCommendFromMachineLearnPai2-1.channel_param]