From c3a9c3a38bedf5bc202d8a0891c36eab108779a3 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:04 +0800 Subject: [PATCH] =?UTF-8?q?Update=2043.=20=E4=BB=8E=201=20=E5=88=B0=20n=20?= =?UTF-8?q?=E6=95=B4=E6=95=B0=E4=B8=AD=201=20=E5=87=BA=E7=8E=B0=E7=9A=84?= =?UTF-8?q?=E6=AC=A1=E6=95=B0.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 补充逐位统计思路与代码逻辑说明,新增计算示例配图,调整参考资料排版格式。 --- notes/43. 从 1 到 n 整数中 1 出现的次数.md | 16 +++++++++++++++- notes/pics/offer43-digit-one.png | Bin 0 -> 106626 bytes 2 files changed, 15 insertions(+), 1 deletion(-) create mode 100644 notes/pics/offer43-digit-one.png diff --git a/notes/43. 从 1 到 n 整数中 1 出现的次数.md b/notes/43. 从 1 到 n 整数中 1 出现的次数.md index 2a947e23..4bd61f34 100644 --- a/notes/43. 从 1 到 n 整数中 1 出现的次数.md +++ b/notes/43. 从 1 到 n 整数中 1 出现的次数.md @@ -4,6 +4,18 @@ ## 解题思路 +逐位统计:分别算出个位、十位、百位……上出现 1 的数有多少个,再相加。设当前位的权重为 m(个位 m = 1,十位 m = 10),把 n 分成三段:高位 high = n / (10m),当前位 cur = n / m % 10,低位 low = n % m。在 0~n 中,这一位为 1 的数的个数为: + +- cur = 0 时为 high × m:高位取 0~high - 1,低位任取 m 种; +- cur = 1 时为 high × m + low + 1:比上一种多出高位等于 high、低位取 0~low 的 low + 1 个; +- cur ≥ 2 时为 (high + 1) × m:高位取 0~high 都可以,低位任取。 + +以 n = 3104 为例: + +

+ +代码中 a = n / m 是高位和当前位,b = n % m 是低位。(a + 8) / 10 在 cur ≥ 2 时等于 high + 1,否则等于 high,正好合并了第一种和第三种情况;cur = 1 时再加上 b + 1。 + ```java public int digitOneInNumber(int num) { int cnt = 0; @@ -15,4 +27,6 @@ public int digitOneInNumber(int num) { } ``` -> [Leetcode : 233. Number of Digit One](https://leetcode.com/problems/number-of-digit-one/discuss/64381/4+-lines-O(log-n)-C++JavaPython) +## 参考资料 + +- [Leetcode : 233. Number of Digit One](https://leetcode.com/problems/number-of-digit-one/discuss/64381/4+-lines-O(log-n)-C++JavaPython) diff --git a/notes/pics/offer43-digit-one.png b/notes/pics/offer43-digit-one.png new file mode 100644 index 0000000000000000000000000000000000000000..596974c4d3f1fe464c63e5861de00d980ff72389 GIT binary patch literal 106626 zcmXV21z46_v;9bEkdg*zmF`YK2?^=$4nb)UkyKhxq*DbcX^;?Ul5`VZ^PT_t z@EniC8+*^5S+mv}UTdg5z{jD&K_C$LN)PWpMj+735C~KrEL8XmB@>1p{B_eqLEl5q z!o%jNi^WqXguJgj9}llc>^tL+2owZD>AtMC&-7M?uQBP-b=TapEv|?H28LI)K3N|= z8>FT@NVQ2d{A7?~OZU-sMaMB!_s<(W2gjt3DW8(gj>a3w;u@cHkjTn%-So2awhesI zxN<;kN3KugcI)?mbO1+N@YdE=fYg_heZOagg{ZR2L`7pi4;rVOF%b>3Ts;-<-@os( z)zTSr7CMml;{UB}p=@S5n4zFBb?O;bFar*qf+n+)rErz=8=I*Gw}Qfrl@$fMxWU}Q z!dX{6(y%2F9i2z4i40gChFHOFFYL9{teel@*cfP%x@-k4i704J5_h}PAhLfa+Dx6Q zxM^yWDiEP_b8|lqL6@z=rs-P1@9WqrV8HVEVs#=D{JnbEwz8azsN;6WFYMqwtovdZ z_sM(Gyd+7`Un&e@$iky}HOyM`S+J8L?rT~P-(+EwNT>7QMW_>@YsLr1&klN=ut&S? 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