LeetCode

题目：

Given an array of non-negative integers, you are initially positioned at the first index of the array.

Each element in the array represents your maximum jump length at that position.

Your goal is to reach the last index in the minimum number of jumps.

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.)

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思路：

1）用一个dp数组来记录到达当前位置的最小步数

package dp;

public class JumpGameII {

    public int jump(int[] nums) {        
        int len = nums.length;
        int[] dp = new int[len];
        for (int i = 0; i < len; ++i)
            dp[i] = Integer.MAX_VALUE;
        dp[0] = 0;
        // In order to save time, we don't visit the elements which already been visited.
        int start = 1;
        for (int i = 0; i < len - 1; ++i) {
            start = go(i, nums[i], start, dp);
        }
        
        return dp[len-1];
    }
    
    // Get next start position.
    private int go(int current, int step, int start, int[] dp) {
        int i = start;
        for (; i <= current + step && i < dp.length; ++i) {
            if (dp[i] > dp[current] + 1)
                dp[i] = dp[current] + 1;
        }
        
        return i;
    }
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[] nums = { 2,3,1,1,4 };
        JumpGameII j = new JumpGameII();
        System.out.println(j.jump(nums));
    }

}

2）不用数组，就直接往前移动，第一次扫走一步能到的地方，第二次扫走二步能到的地方，在这个过程中，只要碰到了最后一个位置，就终止，证明是最小步数。

package dp;

public class JumpGameII {

    public int jump(int[] nums) {
        int len; 
        if ((len = nums.length) == 1) return 0;
        int count = 0;
        int start = 0;
        int end = 0;
        while (end < len) {
            int mostRight = 0;
            ++count;
            for (int j = start; j <= end; ++j) {
                if (j + nums[j] >= len - 1)
                    return count;
                if (j + nums[j] > mostRight)
                    mostRight = j + nums[j];
            }
            
            start  = end + 1;
            end = mostRight;
        }
        
        return count;
    }
    
    public static void main(String[] args) {
        // TODO Auto-generated method stub
        int[] nums = { 2,3,1,1,4 };
        JumpGameII j = new JumpGameII();
        System.out.println(j.jump(nums));
    }

}