From f08a4fabd00057d181e189cb98c77376cd7dfbee Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Wed, 28 Oct 2026 22:51:15 +0800 Subject: [PATCH] =?UTF-8?q?Update=2016.=20=E6=95=B0=E5=80=BC=E7=9A=84?= =?UTF-8?q?=E6=95=B4=E6=95=B0=E6=AC=A1=E6=96=B9.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 重新绘制配图,删除注释中的公式图片,用词校对。 --- notes/16. 数值的整数次方.md | 8 +++----- notes/pics/pow-divide.png | Bin 0 -> 112294 bytes 2 files changed, 3 insertions(+), 5 deletions(-) create mode 100644 notes/pics/pow-divide.png diff --git a/notes/16. 数值的整数次方.md b/notes/16. 数值的整数次方.md index b617a4f8..7760cb09 100644 --- a/notes/16. 数值的整数次方.md +++ b/notes/16. 数值的整数次方.md @@ -6,19 +6,17 @@ ## 题目描述 -给定一个 double 类型的浮点数 x和 int 类型的整数 n,求 x 的 n 次方。 +给定一个 double 类型的浮点数 x 和 int 类型的整数 n,求 x 的 n 次方。 ## 解题思路 - - 最直观的解法是将 x 重复乘 n 次,x\*x\*x...\*x,那么时间复杂度为 O(N)。因为乘法是可交换的,所以可以将上述操作拆开成两半 (x\*x..\*x)\* (x\*x..\*x),两半的计算是一样的,因此只需要计算一次。而且对于新拆开的计算,又可以继续拆开。这就是分治思想,将原问题的规模拆成多个规模较小的子问题,最后子问题的解合并起来。 -本题中子问题是 xn/2,在将子问题合并时将子问题的解乘于自身相乘即可。但如果 n 不为偶数,那么拆成两半还会剩下一个 x,在将子问题合并时还需要需要多乘于一个 x。 +本题中子问题是 xn/2,在将子问题合并时将子问题的解与自身相乘即可。但如果 n 不为偶数,那么拆成两半还会剩下一个 x,在将子问题合并时还需要多乘一个 x。 -

+

因为 (x\*x)n/2 可以通过递归求解,并且每次递归 n 都减小一半,因此整个算法的时间复杂度为 O(logN)。 diff --git a/notes/pics/pow-divide.png b/notes/pics/pow-divide.png new file mode 100644 index 0000000000000000000000000000000000000000..389eb3507dae84e7a77997331d68fc2e59d154e7 GIT binary patch literal 112294 zcmXVYbzD^I_w^{C2uOz_If8T}-3(F^BP}H$rF1tapoD;gph!7%h|(!sNoffM1f)ah z2B~+?_xJk8y&v&<=A85Fz4lsbuep)hn#$J+XbBJq#C25_)B^+pcMO5JoP>WFeqxkC zeg*zT=AmThVPN55?dE9V_7tJ$t0>4XAQt<^Bo}cBflx)s>-zj!OZWAm)ce_?#bf%T z&*pWQsT?&L*P05~h!U+$>5aBA(N<=3^_aX$Pfr<+w$PTRq@g6WP8viT;XX#2L~vVB zw5g1ZBCZ(^nVR+-b_yJF6-lJq5Kg5Z9$wYTZy3tq5%v5=FQ7h!+-@8H5Ca?&PS-+b|bJu1&WLur_wsMFQwqp(KeKH;bLjW6al za*=E^qaC54FP}S36cuqsA$!ViFrLbxDSOJfdmd1>f0>@+I;Lk)Eq8qXG6}!@k>)Cma5{WE$Ph{v%L4@#M$AJObIV0UsfcrMCz(h6Sgdl zWZ%9&EKH>Mc&pr)lK?er65*DV7CbH`V`vd|l+WGMNJ2rgHM2!`L1@}-aOLtPB6@@z zId7sv(9Gf7JV*4dgHpI{Z>XWhu*1YsT`b$ZNkjMys&{t6-SM0vI*)Q^MlWN&wVU@X zYwDBd@)}wU8%0DVb8dLt^}0b$9gn=zf3YLC{dl>Yqr%Q0gq#C`V0|i9DXi?HpP#^@ zls%}z(h`&BL$<%{?P4Ld!3Njf0n09gTwYyW@BwP}K 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