From f326444b31b576619a36548f2d3581cf2086b5d1 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:06 +0800 Subject: [PATCH] =?UTF-8?q?Update=2059.=20=E6=BB=91=E5=8A=A8=E7=AA=97?= =?UTF-8?q?=E5=8F=A3=E7=9A=84=E6=9C=80=E5=A4=A7=E5=80=BC.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 更新大顶堆解法的时间复杂度分析,补充单调队列解法及对应的原理配图与实现代码。 --- notes/59. 滑动窗口的最大值.md | 35 ++++++++++++++++++++++++- notes/pics/offer59-monotonic-deque.png | Bin 0 -> 149923 bytes 2 files changed, 34 insertions(+), 1 deletion(-) create mode 100644 notes/pics/offer59-monotonic-deque.png diff --git a/notes/59. 滑动窗口的最大值.md b/notes/59. 滑动窗口的最大值.md index 95b03876..3161e28e 100644 --- a/notes/59. 滑动窗口的最大值.md +++ b/notes/59. 滑动窗口的最大值.md @@ -14,9 +14,11 @@ ## 解题思路 +### 大顶堆 + 维护一个大小为窗口大小的大顶堆,堆顶元素即为当前窗口的最大值。 -假设窗口的大小为 M,数组的长度为 N。在窗口向右移动时,需要先在堆中删除离开窗口的元素,并将新到达的元素添加到堆中,这两个操作的时间复杂度都为 log2M,因此算法的时间复杂度为 O(Nlog2M),空间复杂度为 O(M)。 +假设窗口的大小为 M,数组的长度为 N。在窗口向右移动时,需要先在堆中删除离开窗口的元素,并将新到达的元素添加到堆中。添加的时间复杂度为 O(logM),但 PriorityQueue.remove(Object) 要先线性查找这个元素,时间复杂度为 O(M),因此算法的时间复杂度为 O(NM),空间复杂度为 O(M),N 和 M 都很大时会超时。 ```java public int[] maxAltitude(int[] heights, int limit) { @@ -38,3 +40,34 @@ public int[] maxAltitude(int[] heights, int limit) { return ret; } ``` + +### 单调队列 + +用双端队列保存窗口中有可能成为最大值的元素的下标,并让它们对应的值从队头到队尾递减,队头就是当前窗口的最大值: + +- 新元素入队前,从队尾删除所有不大于它的元素:它们比新元素先离开窗口,值又不比它大,以后不可能成为最大值; +- 队头的下标离开窗口时,从队头删除。 + +每个下标最多入队、出队各一次,时间复杂度为 O(N),空间复杂度为 O(M)。以 {2, 3, 4, 2, 6, 2, 5, 1}、窗口大小 3 为例: + +

+ +```java +public int[] maxAltitude(int[] heights, int limit) { + if (heights == null || heights.length == 0 || limit <= 0) { + return new int[0]; + } + int[] ret = new int[heights.length - limit + 1]; + Deque deque = new ArrayDeque<>(); /* 保存下标,对应的值从队头到队尾递减 */ + for (int i = 0; i < heights.length; i++) { + while (!deque.isEmpty() && heights[deque.peekLast()] <= heights[i]) + deque.pollLast(); + deque.addLast(i); + if (deque.peekFirst() <= i - limit) /* 队头已经离开窗口 [i - limit + 1, i] */ + deque.pollFirst(); + if (i >= limit - 1) + ret[i - limit + 1] = heights[deque.peekFirst()]; + } + return ret; +} +``` diff --git a/notes/pics/offer59-monotonic-deque.png b/notes/pics/offer59-monotonic-deque.png new file mode 100644 index 0000000000000000000000000000000000000000..49d9e7dfa573d972c4a4351498aa92d8c1c9b4be GIT binary patch literal 149923 zcmX_I2RPOJ`##Fvo2-y=%&hDYq3oHEy+fjGqHtuZ>^(~M9*LB_cVuT3A-nAHf6n{6 zuK&5Nx7Wq-J>T!=^L(D?e(w8zgllWwCBmn}M<5VHD)$t15eUpl1mY?#?iKh>g2qq; z{Ey6C$5O;j;2nh&^$0V5KAutdK6-9Y{@994oUjCHhhlfK48uvKy zxJd8eHieie+ly=od#p4mgOOp=OQ}^sh zSzY6j@O0p_<8H{mCS}K6x~yUERm;$PRgA=O;*$QhHL8)PyDP1g_61YEUPLudx71*H zFje^-nWIi*N2>_8RDm|~UJ$vqzdK|8y|jVO{m)a*2HXj`M8rYN_rl2At?@erZqaFk z6L6&s*wq@NMiBa$&YF2W3Cy?!nrp_*BDI;HKf0 zr#wSDtOU~rjwnaYS#Zg7G360z*PiaFr^_1|6$S_C1~KD4P|VR@_`%SrBu~mqwK-*( zOfZyxs@xomrzo1HQEDJORj6AS5=$XZ%BF~S1xZ2_oV(C|!M}B~T(@;8>#e_~K&qHv za=&1_b&*WZGjBOxGyffe2IHVk`2A@7-c!7w5TraQ3GaKuw|wH2U!6qg+>Am$5X46- zlPXd%F{#B9z30I#9`D`%jO30vt#iN(BQ|un8Ec!X%ftKM3Sdgh8r?A{rux=TiH~JW zogjX*s{2KETQD^Sf#TD>gs!(s;Az+g&_IwdQK@XI=CHc>FBEn z^0m^B6)klwS@|7xX202fA&3uCgT;_uabJSqaUbj#@MmR;C zE*ksci_rrj^bWnaGlNB$I7vrIk~(0=8}Jgx6j5o5gg~{(D%R&VGDX_{B*%R1#4mq4 zfydl!_C8kJ6IdAKySsPqMWPo+(d}7rx4K!5cJ?Zt@k(p(uWZBPp6N_ChF8}<9qFm} z!h00rnTv?UKPD7#>qHifJE~K#Qo-%XlWIy*31<1A6fA3v^Ufa#AR#_`Y=r2d`#oR& zx28HBr$Leui;qO;N}g0sIgfQkp+lnLiKrbR-m1Y^dMkp)kT1A5UV+6ch(KlkR$!yd>yPQ)n(cLz7c@$W zPWfHlmzpIZ%t(QWK}p7r`ye)q`lEaw@2P6PI4iEDmNBgUl&xKLN+v}Rb5Rk#?ZA*> z1F0`%WtEobN1>_kE~W5$1rJ7I%! zR`6O6Y#|U2EaEMcNip?1qD(SZQ4%$dwbM32l?_y)A9D?Dzab?rRc74uE*}RWBErZq zr30ouO~zxXnG8qb&ZI8#^62OE@5a_S<2CjPC8*|2YLW1@mevigV;vlb|Gpr_Tx>AprB=sMxMYd!&`r-G4OO{rXj?RXM6cazm5EE7>~8(P zD_!O*sio6#1&1LJCYs@y)RejPiftW<4&zD@@yxic1M6P#@dezBgtms6%&8)RS|No- zdAfz))_!;XFQjmC&H8p zzvJhu5E)PJ96Rn6*anCq#Hv*e?P@#C&O+x`NaAbmlQoFv%&?LT@{$f%ilmqrd;Bu4 z98|bG_fWOjNGqkU5nG)9W#=Gf)l!84JK;`IqXNCuh3JPDCG;5I>8o8a;55~1nw8x% z3u@EV{qSJGu6o2l@lviK8uP!R74+ii%C9SkgU1gF^$p34tqgDfU4}!zZVW$0R52o26GVEa-ZLT12JKJJ)z!_38n|4aU-PoLah;r%am^+)QS zoE~mp9mXjT>%TMRgf4UVCv{M^1=%?fmxYoJ1$ouA8{{;A%>B_#80GJF3+A|^6A z+O)x)E73RL@5o(QS=mu<4s4}L2_}ky;s@nsH4bETBr>iGh_Z0|q0IAEf}8GJvs1eX zCZC@Ex;Q`0kn|vDyvfTO?;Ak*skYk_OBAhO>%@c@E9+8Tl9}U7UFq+T&6$rw8B!DQU0&Wl#pPf2{{8dV z6Py1U_|^H*By91}P&uL8Q47xXGguSEaL%1qN|DqFo1t(kwts(*+_)RVAo0}Z-o3ED zAxB3?g4Ugg+uq(s=@QTAM4gYc?^Yz4`L6XQ@E`=9{_Otv!?)N`+JodDV@=;cn%Lpy z%q#SbU#Fv6|0zn;P*vG!=kSq(@u7H3TQ_IW%i*Pf%?K)lUheA_Hf9< z?-26(@}7Stcj1nfH*S7CdwTF^Dwo2_%F4C0?%ArQoSa;jf(Q$XWorl?cJN|L&YN(1Juj}eyMv{4e z1Rvk#?5AgXAJnhO1^BzUjqI-uef>MCh7fQZD|qzn174EDRUG2}-rlEsU-$n_m`A$& znQQc7yxS13YHMTjUi+@ZWeD_38Xl#~eD4^ECt zbj2{XQK)moef%gUo)J0>_aJG`{~=GQ)~Gn_phNyg1zsyga8t zzz2@kJo>iS_9~begCsZ)v9Pfr6>#R=MX)hp9>{oq10n#f)Z{!>CF!w#Tf%tsB}KSd zF4ncv7V-&6hOUHzB6MhNeCI>p5)e4ee`#`;|DcWRw-Y|`3}a((8pt&$MyY&Gj`91| zOOg6h9-T5=NQhrL6``>RuTv(1`(M{)i^;2%j! zN=_fwtUu)zS-mrVVE?x&G&xFndHd^SOgX)%v-jWMI%^5-ot;$^aPpMcZ=QXFeJ*)T z`#@E-7oIq}oKqvUT^9HLLZP4ccJ@9!dve#yHKvY)_T_9&UX|waThy172UQA>Qs2C> ztTgoZ_g9qQP=L(Ash(WnfBY12v|e1^;I+*}NvXJh>%R=0tD2)*xB~J0^yfW&d5E(o z6J?Bgv2f6BYTtd!*Rr3g(^jwl)42V`Z?kq{=Yg%Qtwy@I+ppe)ogGG@KkK^D%6f}| zPJM}dmuLGVh`(ENjSvB>k@uiX>lRj!y!>5mUGk!IbGYnIp?;NQgY5GYZ*T9kRI-=F-_+^pUeedy%QcJ4s(v^|YVQU8!8_C(UBs>K4iYcuk_ zttA*oQ2D_iW6IK%ZBDJsb{ZMKgLq>G0;LCOqK|tICj8(imlz4#v&rxe+e1uRsnxU!-mW>MG9&Q6oxVHH)VE1A#f!6rnNP_(_+H0iZ# zpX>%w*S_U1uS@grIE}tnA)w*6;dGv?U}0uPAn*wYAO<7)k|1wdxjfd@B|ok8OdDxB zn0890|LnHh36GDs{q2K>Qio|tc8wy7ag(oy!BTQo))2lb4hhq2&K(?Y0dMxlYT3|f zPPqXP9(ae;L!Z{;DAZol{s`??D4dS+mhn- z>(^5op@}Rw_r!t@I+3)NzN_A6f2GQ{@6QEp-$;kYGq*=iE-o%2X>JC1IhD;j>*^ih}5)Q{lhmk9KB@`4C=Fk6)_fkrnpZud>OqUD1I6L0o^?No}Hc5*NX$iA}u}4NW)&B--xeNI2SzX zn$p;K8iYk)*Prb6v-?etqJtlEI-GYe?M*YX~Z`!^=Vc?VD|K|%&;-wr# z%OXijPQJ9Z=Cixh0q6M7bZun#&s$F4vo-q$2F?MT5Mf{awus&%_|My0Jhgn?T@puB zAKvT!MKx~KhvQ$)Un+Nm>ry*j<2GY_{3PB%Q0{^WIahp}g~1UEU)vKX-dAx)Ro(jT z_)bF!+NGFo^7Crs)W=oN4G9gE)O0Qr(lR}smv?RT>2~S4JkAj-lkXb*6f>YCZyy!kGs;;iCsPkkqensHfZWlnxNbgT2=_&!gxpN)-;|G)7ExxxKKmGu@SxON4?7R`u9Ig}extDi}!_=wDXeo-yz0@qjT zGIvrtVHQ_5>DrfNTeaBSt$@iKwpEqvi2Cg0m63i%m0KL2~RXKGUB-zGs(>1Zw2sI?8%SM92%(=k^~~GLTLjG zT{-e(l-7^g`+u2L+i5^r&O!2hLdQLah80)igEEsh2E>p^@F*(aWb5hajf7_~hjr

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