JAVA算法：求解跳跃游戏（Jump Game）

JAVA求解跳跃游戏（Jump Game）

原题链接：https://leetcode.com/problems/jump-game/description/ JUMP GAME
原题链接：https://leetcode.com/problems/jump-game-ii/description/ JUMP GAMEII

这两个是一类问题

问题描述：给定一个非负整数数组，给定的初始化位置在数组的起始位置。数组中的每个元素代表着你能都在此位置跳跃的最大的距离。你的目标是用最少的跳跃数达到数组的末尾。

假设条件：你可以假设你总是有可能到达数组的末尾。

给出的一个举例为
For example:
Given array A = [2,3,1,1,4]

The minimum number of jumps to reach the last index is 2. (Jump 1 step from index 0 to 1, then 3 steps to the last index.)

算法设计—1

public static int canJump (int[] nums) {
	    if (nums.length == 1) {//当数组中只有一个元素时，返回0。
	        return 0;
	    }

	    int step = 0;//在开始之前初始化 step = 0 
	    int position = 0;// 从当前的step开始的位置初始化为0
	    int reachable = 0;// 从当前的step可以到达的最远的位置
	    int furthest = 0;// 下一步可以达到的最远的位置, 在下一轮次循环中，它是新的reachable的值

	    
	    while (position <= reachable) {// 一次循环代表一步, 从step==0开始
	        furthest = Math.max(furthest, position + nums[position]);// 求出一个最大值
	        if (furthest >= nums.length - 1) {//能够到达数组的结束（末尾）
	            return step + 1; // step+1
	        }
	        if (position == reachable) {//本次跳跃结束
	            if (furthest <= reachable) {//不能到达
	                return -1; //返回 -1
	            } else {// 添加本次的step，更新 reachable的值
	                ++step;
	                reachable = furthest;
	            }
	        }
	        ++position;//继续
	    }
	    return -1;
	}

算法设计—2

public static int canJump(int[] nums) {
// If nums.length < 2, means that we do not
// need to move at all.
if (nums == null || nums.length < 2) {
return 0;
}

    // First set up current region, which is
    // from 0 to nums[0].
    int l = 0;
    int r = nums[0];
    // Since the length of nums is greater than
    // 1, we need at least 1 step.
    int step = 1;

    // We go through all elements in the region.
    while (l <= r) {

        // If the right of current region is greater
        // than nums.length - 1, that means we are done.
        if (r >= nums.length - 1) {
            return step;
        }

        // We should know how far can we reach in current
        // region.
        int max = Integer.MIN_VALUE;
        for (; l <= r; l++) {
            max = Math.max(max, l + nums[l]);
        }

        // If we can reach far more in this round, we update
        // the boundary of current region, and also add a step.
        if (max > r) {
            l = r;
            r = max;
            step++;
        }
    }

    // We can not finish the job.
    return -1;
}

可以自己编写一个main方法进行测试。

算法设计 -3

package com.bean.algorithm.dp;

public class JumpGame55_4 {

	public int minStepJump(int arr[]) 
    { 
        if (arr.length <= 1) 
            return 0; 
  
        // 如果不能再跳跃时返回 -1 
        if (arr[0] == 0) 
            return -1; 
  
        // 初始化 
        int maxReach = arr[0]; 
        int step = arr[0]; 
        int jump = 1; 
  
  
        // 开始遍历数组元素 
        for (int i = 1; i < arr.length; i++) 
        { 
            // check是否跳到了结尾处 
            if (i == arr.length - 1) 
                return jump; 
  
            // 更新  maxReach 
            maxReach = Math.max(maxReach, i+arr[i]); 
  
            // 我们使用 step 来获得当前的 index  
            step--; 
  
            // 如果没有步数了 step==0
            if (step == 0) 
            { 
                jump++; 
                   
                if(i>=maxReach) 
                   return -1; 
  
                step = maxReach - i; 
            } 
        } 
  
        return -1; 
    } 
	
	public boolean canJump(int[] A) {
    
        if(A.length <= 1)
			return true;
		if(A[0] >= (A.length - 1))
			return true;
		int maxlength = A[0];
		if(maxlength == 0)
		    return false;
		for(int i = 1; i < A.length - 1; i++)
		{
			if(maxlength >= i && (i + A[i]) >= A.length - 1)
				return true;
			if(maxlength <= i && A[i] == 0)
				return false;
			if((i + A[i]) > maxlength)
				maxlength = i + A[i];
		}
		return false;
    }

	public static void main(String[] args) {

		JumpGame55_4 jump = new JumpGame55_4();

		//int[] array = { 2, 3, 1, 1, 4 };
		int[] array = {5,6,4,4,6,9,4,4,7,4,4,8,2,6,8,1,5,9,6,5,2,7,9,7,9,6,9,4,1,6,8,8,4,4,2,0,3,8,5};
		// int[] array = { 3, 2, 1, 0, 4 };

		// int[] array= {9, 4, 2, 1, 0, 2, 0};
		
		//int[] array = { 5,4,0,0,0,0,0 };
		boolean flag = jump.canJump(array);
		if (flag) {
			System.out.println("Jump Game is successed.");
		} else {
			System.out.println("Jump Game is failed.");
		}
		
		int minStep=jump.minStepJump(array);
		System.out.println("min step is: "+minStep);
		
	}

}

程序运行结果：

Jump Game is successed.
min step is: 5

（完）