Update 0045.跳跃游戏II.md

problems/0045.跳跃游戏II.md

@@ -205,66 +205,81 @@ class Solution {
 ```
 
 ### Python
-
+贪心（版本一）
 ```python
 class Solution:
-    def jump(self, nums: List[int]) -> int:
-        if len(nums) == 1: return 0
-        ans = 0
-        curDistance = 0
-        nextDistance = 0
-        for i in range(len(nums)):
-            nextDistance = max(i + nums[i], nextDistance)
-            if i == curDistance:
-                if curDistance != len(nums) - 1:
-                    ans += 1
-                    curDistance = nextDistance
-                    if nextDistance >= len(nums) - 1: break
-        return ans
-```
-
-```python
-# 贪心版本二
-class Solution:
-    def jump(self, nums: List[int]) -> int:
+    def jump(self, nums):
         if len(nums) == 1:
             return 0
-        curDistance, nextDistance = 0, 0
-        step = 0
-        for i in range(len(nums)-1):
-            nextDistance = max(nextDistance, nums[i]+i)
-            if i == curDistance:
-                curDistance = nextDistance
-                step += 1
-        return step
-```
-```python
-# 贪心版本三 - 类似‘55-跳跃游戏’写法
-class Solution:
-    def jump(self, nums) -> int:
-        if len(nums)==1: return 0
-        i = 0
-        count = 0
-        cover = 0
-        while i<=cover:
-            for i in range(i,cover+1):
-                cover = max(nums[i]+i,cover)
-                if cover>=len(nums)-1: return count+1
-            count+=1
         
+        cur_distance = 0  # 当前覆盖最远距离下标
+        ans = 0  # 记录走的最大步数
+        next_distance = 0  # 下一步覆盖最远距离下标
+        
+        for i in range(len(nums)):
+            next_distance = max(nums[i] + i, next_distance)  # 更新下一步覆盖最远距离下标
+            if i == cur_distance:  # 遇到当前覆盖最远距离下标
+                ans += 1  # 需要走下一步
+                cur_distance = next_distance  # 更新当前覆盖最远距离下标（相当于加油了）
+                if next_distance >= len(nums) - 1:  # 当前覆盖最远距离达到数组末尾，不用再做ans++操作，直接结束
+                    break
+        
+        return ans
+
 ```
+贪心（版本二）
 
 ```python
-# 动态规划做法
+class Solution:
+    def jump(self, nums):
+        cur_distance = 0  # 当前覆盖的最远距离下标
+        ans = 0  # 记录走的最大步数
+        next_distance = 0  # 下一步覆盖的最远距离下标
+        
+        for i in range(len(nums) - 1):  # 注意这里是小于len(nums) - 1，这是关键所在
+            next_distance = max(nums[i] + i, next_distance)  # 更新下一步覆盖的最远距离下标
+            if i == cur_distance:  # 遇到当前覆盖的最远距离下标
+                cur_distance = next_distance  # 更新当前覆盖的最远距离下标
+                ans += 1
+        
+        return ans
+
+```
+贪心（版本三） 类似‘55-跳跃游戏’写法
+
+```python
+class Solution:
+    def jump(self, nums) -> int:
+        if len(nums)==1:  # 如果数组只有一个元素，不需要跳跃，步数为0
+            return 0
+        
+        i = 0  # 当前位置
+        count = 0  # 步数计数器
+        cover = 0  # 当前能够覆盖的最远距离
+        
+        while i <= cover:  # 当前位置小于等于当前能够覆盖的最远距离时循环
+            for i in range(i, cover+1):  # 遍历从当前位置到当前能够覆盖的最远距离之间的所有位置
+                cover = max(nums[i]+i, cover)  # 更新当前能够覆盖的最远距离
+                if cover >= len(nums)-1:  # 如果当前能够覆盖的最远距离达到或超过数组的最后一个位置，直接返回步数+1
+                    return count+1
+            count += 1  # 每一轮遍历结束后，步数+1
+
+        
+```
+动态规划
+```python
 class Solution:
     def jump(self, nums: List[int]) -> int:
-        result = [10**4+1]*len(nums)
-        result[0]=0
-        for i in range(len(nums)):
-            for j in range(nums[i]+1):
-                if i+j<len(nums): result[i+j]=min(result[i+j],result[i]+1)
-        #print(result) #打印数组
-        return result[-1]
+        result = [10**4+1] * len(nums)  # 初始化结果数组，初始值为一个较大的数
+        result[0] = 0  # 起始位置的步数为0
+
+        for i in range(len(nums)):  # 遍历数组
+            for j in range(nums[i] + 1):  # 在当前位置能够跳跃的范围内遍历
+                if i + j < len(nums):  # 确保下一跳的位置不超过数组范围
+                    result[i + j] = min(result[i + j], result[i] + 1)  # 更新到达下一跳位置的最小步数
+
+        return result[-1]  # 返回到达最后一个位置的最小步数
+
 
 ```