mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-10 18:48:13 +08:00
181 lines
19 KiB
JSON
181 lines
19 KiB
JSON
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"title": "魔术排列",
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"content": "English description is not available for the problem. Please switch to Chinese.",
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"translatedTitle": "魔术排列",
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"translatedContent": "秋日市集上，魔术师邀请小扣与他互动。魔术师的道具为分别写有数字 `1~N` 的 `N` 张卡牌，然后请小扣思考一个 `N` 张卡牌的排列 `target`。\n\n魔术师的目标是找到一个数字 k（k >= 1），使得初始排列顺序为 `1~N` 的卡牌经过特殊的洗牌方式最终变成小扣所想的排列 `target`，特殊的洗牌方式为：\n- 第一步，魔术师将当前位于 **偶数位置** 的卡牌（下标自 1 开始），保持 **当前排列顺序** 放在位于 **奇数位置** 的卡牌之前。例如：将当前排列 [1,2,3,4,5] 位于偶数位置的 [2,4] 置于奇数位置的 [1,3,5] 前，排列变为 [2,4,1,3,5]；\n- 第二步，若当前卡牌数量小于等于 `k`，则魔术师按排列顺序取走全部卡牌；若当前卡牌数量大于 `k`，则取走前 `k` 张卡牌，剩余卡牌继续重复这两个步骤，直至所有卡牌全部被取走；\n\n卡牌按照魔术师取走顺序构成的新排列为「魔术取数排列」，请返回是否存在这个数字 k 使得「魔术取数排列」恰好就是 `target`，从而让小扣感到大吃一惊。\n\n**示例 1：**\n>输入：`target = [2,4,3,1,5]`\n>\n>输出：`true`\n>\n>解释：排列 target 长度为 5，初始排列为：1,2,3,4,5。我们选择 k = 2：\n>第一次：将当前排列 [1,2,3,4,5] 位于偶数位置的 [2,4] 置于奇数位置的 [1,3,5] 前，排列变为 [2,4,1,3,5]。取走前 2 张卡牌 2,4，剩余 [1,3,5]；\n>第二次：将当前排列 [1,3,5] 位于偶数位置的 [3] 置于奇数位置的 [1,5] 前，排列变为 [3,1,5]。取走前 2 张 3,1，剩余 [5]；\n>第三次：当前排列为 [5]，全部取出。\n>最后，数字按照取出顺序构成的「魔术取数排列」2,4,3,1,5 恰好为 target。\n\n**示例 2：**\n>输入：`target = [5,4,3,2,1]`\n>\n>输出：`false`\n>\n>解释：无法找到一个数字 k 可以使「魔术取数排列」恰好为 target。\n\n\n**提示：**\n- `1 <= target.length = N <= 5000`\n- 题目保证 `target` 是 `1~N` 的一个排列。",
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