Add solution 390

website/content/ChapterFour/0300~0399/0390.Elimination-Game.md

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+# [390. Elimination Game](https://leetcode.com/problems/elimination-game/)
+
+
+## 题目
+
+You have a list `arr` of all integers in the range `[1, n]` sorted in a strictly increasing order. Apply the following algorithm on `arr`:
+
+- Starting from left to right, remove the first number and every other number afterward until you reach the end of the list.
+- Repeat the previous step again, but this time from right to left, remove the rightmost number and every other number from the remaining numbers.
+- Keep repeating the steps again, alternating left to right and right to left, until a single number remains.
+
+Given the integer `n`, return *the last number that remains in* `arr`.
+
+**Example 1:**
+
+```
+Input: n = 9
+Output: 6
+Explanation:
+arr = [1, 2,3, 4,5, 6,7, 8,9]
+arr = [2,4, 6,8]
+arr = [2, 6]
+arr = [6]
+
+```
+
+**Example 2:**
+
+```
+Input: n = 1
+Output: 1
+
+```
+
+**Constraints:**
+
+- `1 <= n <= 109`
+
+## 题目大意
+
+列表 arr 由在范围 [1, n] 中的所有整数组成，并按严格递增排序。请你对 arr 应用下述算法：
+
+- 从左到右，删除第一个数字，然后每隔一个数字删除一个，直到到达列表末尾。
+- 重复上面的步骤，但这次是从右到左。也就是，删除最右侧的数字，然后剩下的数字每隔一个删除一个。
+- 不断重复这两步，从左到右和从右到左交替进行，直到只剩下一个数字。
+
+给你整数 n ，返回 arr 最后剩下的数字。
+
+## 解题思路
+
+- 模拟题。按照题意，第一轮从左往右删除数字，第二轮从右往左删除数字。题目要求最后剩下的数字，模拟过程中不需要真的删除元素。只需要标记起始元素，该轮步长和方向即可。最后总元素只剩下一个即为所求。
+
+## 代码
+
+```go
+package leetcode
+
+func lastRemaining(n int) int {
+	start, dir, step := 1, true, 1
+	for n > 1 {
+		if dir { // 正向
+			start += step
+		} else { // 反向
+			if n%2 == 1 {
+				start += step
+			}
+		}
+		dir = !dir
+		n >>= 1
+		step <<= 1
+	}
+	return start
+}
+```
+
+
+----------------------------------------------
+<div style="display: flex;justify-content: space-between;align-items: center;">
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