From d83a78fadee357d802ebb8ba5caf67f9eb1b1e54 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:03 +0800 Subject: [PATCH] =?UTF-8?q?Update=2041.1=20=E6=95=B0=E6=8D=AE=E6=B5=81?= =?UTF-8?q?=E4=B8=AD=E7=9A=84=E4=B8=AD=E4=BD=8D=E6=95=B0.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 补充双堆维护中位数的思路说明与插入流程配图,文字校对代码注释。 --- notes/41.1 数据流中的中位数.md | 10 ++++++++-- notes/pics/offer41-median-heaps.png | Bin 0 -> 100618 bytes 2 files changed, 8 insertions(+), 2 deletions(-) create mode 100644 notes/pics/offer41-median-heaps.png diff --git a/notes/41.1 数据流中的中位数.md b/notes/41.1 数据流中的中位数.md index 1ed76391..0e8f956c 100644 --- a/notes/41.1 数据流中的中位数.md +++ b/notes/41.1 数据流中的中位数.md @@ -10,6 +10,12 @@ ## 解题思路 +用两个堆把数据分成较小的一半和较大的一半:left 是大顶堆,存较小的一半,堆顶是这一半的最大值;right 是小顶堆,存较大的一半,堆顶是这一半的最小值。让 right 的元素个数等于 left 或比 left 多一个,中位数就只和两个堆顶有关:总数为奇数时是 right 的堆顶,为偶数时是两个堆顶的平均值。插入的时间复杂度为 O(logN),查找中位数为 O(1)。 + +新元素不能直接放进要变多的那个堆,因为它可能比另一个堆的堆顶更大或更小。做法是先放进另一个堆,再把那个堆的堆顶移过来。例如 left = {1, 2}、right = {5, 8} 时: + +

+ ```java class MedianFinder { @@ -25,10 +31,10 @@ class MedianFinder { } public void addNum(int num) { - /* 插入要保证两个堆存于平衡状态 */ + /* 插入要保证两个堆处于平衡状态 */ if (N % 2 == 0) { /* N 为偶数的情况下插入到右半边。 - * 因为右半边元素都要大于左半边,但是新插入的元素不一定比左半边元素来的大, + * 因为右半边元素都要大于左半边,但是新插入的元素不一定比左半边元素来得大, * 因此需要先将元素插入左半边,然后利用左半边为大顶堆的特点,取出堆顶元素即为最大元素,此时插入右半边 */ left.add(num); right.add(left.poll()); diff --git a/notes/pics/offer41-median-heaps.png b/notes/pics/offer41-median-heaps.png new file mode 100644 index 0000000000000000000000000000000000000000..68323d0dc2da556c2d9286e5c962cad7b5855fc7 GIT binary patch literal 100618 zcmXV22RPO3|33DyLS{loSy|a3BeTfNo*^?UGn?#9l9eqZdxSDdcJ|85P6%aZ`+v^+ z`**$9^}2G#^L?JrxIg!OKSijiJRl~ZB|sn$#0n2(A0rUhl?VhT1rihfCWJv+AO1(? zDyQqJW9n+*Y;Wppi;(e@;p5>Ij(ua8kHA166lA3|J*GD^tV}2@CPD`jGiE79P>f8j zNcwd-(sdLPGk5ZOq?!MgNk{1Co`2KV3AAN#2$4nMno{w`??SFHGQQle9{qA7Oiaa6 z=-X9A_q(enwNpu(o93CT5-SqvHfi@sErtb@wX~9ZnIp|`RQZ)Pk}NV;l}81Lun^c% zq;juTJw-#|2ib0uw1QkV1S&GOz$Vlb8Mxs5NjSDfe3XYsFG(cUrEzxrfm6at>18IJafQyP 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