6363
6464<!-- 这里可写通用的实现逻辑 -->
6565
66- 通过下面这段伪代码,不难理解除法本质上就是减法,但是一次循环只能做一次减法,效率太低会导致超时,所以再加上快速幂的思想优化即可
67- 68- ``` py
69- sign = - 1 if a * b < 0 else 1
70- a = abs (a)
71- b = abs (b)
72- cnt = 0
73- while a >= b:
74- a -= b
75- cnt += 1
76- return sign * cnt
77- ```
66+ ** 方法一:模拟 + 快速幂**
67+ 68+ 除法本质上就是减法,题目要求我们计算出两个数相除之后的取整结果,其实就是计算被除数是多少个除数加上一个小于除数的数构成的。但是一次循环只能做一次减法,效率太低会导致超时,可借助快速幂的思想进行优化。
69+ 70+ 需要注意的是,由于题目明确要求最大只能使用 32 位有符号整数,所以需要将除数和被除数同时转换为负数进行计算。因为转换正数可能会导致溢出,如当被除数为 ` INT32_MIN ` 时,转换为正数时会大于 ` INT32_MAX ` 。
71+ 72+ 假设被除数为 $a,ドル除数为 $b,ドル则时间复杂度为 $O(\log a \times \log b),ドル空间复杂度 $O(1)$。
7873
7974<!-- tabs:start -->
8075
@@ -85,19 +80,23 @@ return sign * cnt
8580``` python
8681class Solution :
8782 def divide (self a : int , b : int ) -> int :
88- INT_MAX = (1 << 31 ) - 1
89- INT_MIN = - (1 << 31 )
90- sign = - 1 if a * b < 0 else 1
91- a = abs (a)
92- b = abs (b)
93- tot = 0
94- while a >= b:
95- cnt = 0
96- while a >= (b << (cnt + 1 )):
97- cnt += 1
98- tot += 1 << cnt
99- a -= b << cnt
100- return sign * tot if INT_MIN <= sign * tot <= INT_MAX else INT_MAX
83+ if b == 1 :
84+ return a
85+ if a == - (2 ** 31 ) and b == - 1 :
86+ return 2 ** 31 - 1
87+ sign = (a > 0 and b > 0 ) or (a < 0 and b < 0 )
88+ a = - a if a > 0 else a
89+ b = - b if b > 0 else b
90+ ans = 0
91+ while a <= b:
92+ x = b
93+ cnt = 1
94+ while x >= (- (2 ** 30 )) and a <= (x << 1 ):
95+ x <<= 1
96+ cnt <<= 1
97+ a -= x
98+ ans += cnt
99+ return ans if sign else - ans
101100```
102101
103102### ** Java**
@@ -107,104 +106,161 @@ class Solution:
107106``` java
108107class Solution {
109108 public int divide (int a , int b ) {
110- int sign = 1 ;
111- if ((a < 0 ) != (b < 0 )) {
112- sign = - 1 ;
109+ if (b == 1 ) {
110+ return a;
113111 }
114- long x = abs(a);
115- long y = abs(b);
116- long tot = 0 ;
117- while (x >= y) {
118- int cnt = 0 ;
119- while (x >= (y << (cnt + 1 ))) {
120- cnt++ ;
121- }
122- tot += 1L << cnt;
123- x -= y << cnt;
112+ if (a == Integer . MIN_VALUE&& b == - 1 ) {
113+ return Integer . MAX_VALUE
124114 }
125- long ans = sign * tot;
126- if (ans >= Integer . MIN_VALUE&& ans <= Integer . MAX_VALUE
127- return (int ) ans;
115+ boolean sign = (a > 0 && b > 0 ) || (a < 0 && b < 0 );
116+ a = a > 0 ? - a : a;
117+ b = b > 0 ? - b : b;
118+ int ans = 0 ;
119+ while (a <= b) {
120+ int x = b;
121+ int cnt = 1 ;
122+ while (x >= (Integer . MIN_VALUE>> 1 ) && a <= (x << 1 )) {
123+ x << = 1 ;
124+ cnt << = 1 ;
125+ }
126+ ans += cnt;
127+ a -= x;
128128 }
129- return Integer . MAX_VALUE
129+ return sign ? ans : - ans ;
130130 }
131+ }
132+ ```
133+ 134+ ### ** C++**
131135
132- private long abs (long a ) {
133- if (a < 0 ) {
134- return - a;
136+ ``` cpp
137+ class Solution {
138+ public:
139+ int divide(int a, int b) {
140+ if (b == 1) {
141+ return a;
135142 }
136- return a;
143+ if (a == INT_MIN && b == -1) {
144+ return INT_MAX;
145+ }
146+ bool sign = (a > 0 && b > 0) || (a < 0 && b < 0);
147+ a = a > 0 ? -a : a;
148+ b = b > 0 ? -b : b;
149+ int ans = 0;
150+ while (a <= b) {
151+ int x = b;
152+ int cnt = 1;
153+ while (x >= (INT_MIN >> 1) && a <= (x << 1)) {
154+ x <<= 1;
155+ cnt <<= 1;
156+ }
157+ ans += cnt;
158+ a -= x;
159+ }
160+ return sign ? ans : -ans;
137161 }
138- }
162+ };
139163```
140164
141165### **Go**
142166
143167```go
144168func divide(a int, b int) int {
145- sign := 1
146- if a*b < 0 {
147- sign = -1
169+ if b == 1 {
170+ return a
171+ }
172+ if a == math.MinInt32 && b == -1 {
173+ return math.MaxInt32
148174 }
149175
150- a = abs (a)
151- b = abs (b)
152- 153- tot := 0
154- for a >= b {
155- cnt := 0
156- for a >= (b << (cnt + 1 )) {
157- cnt++
176+ sign := (a > 0 && b > 0) || (a < 0 && b < 0)
177+ if a > 0 {
178+ a = -a
179+ }
180+ if b > 0 {
181+ b = -b
182+ }
183+ ans := 0
184+
185+ for a <= b {
186+ x := b
187+ cnt := 1
188+ for x >= (math.MinInt32>>1) && a <= (x<<1) {
189+ x <<= 1
190+ cnt <<= 1
158191 }
159- tot +=1 << cnt
160- a -= b << cnt
192+ ans += cnt
193+ a -= x
161194 }
162195
163- ans := sign * tot
164- if ans >= math.MinInt32 && ans <= math.MaxInt32 {
196+ if sign {
165197 return ans
166198 }
167- return math. MaxInt32
199+ return -ans
168200}
201+ ```
169202
170- func abs (a int ) int {
171- if a < 0 {
172- return -a
173- }
174- return a
203+ ### ** TypeScript**
204+ 205+ ``` ts
206+ function divide(a : number , b : number ): number {
207+ if (b === 1 ) {
208+ return a ;
209+ }
210+ if (a === - (2 ** 31 ) && b === - 1 ) {
211+ return 2 ** 31 - 1 ;
212+ }
213+ 214+ const : boolean = (a > 0 && b > 0 ) || (a < 0 && b < 0 );
215+ a = a > 0 ? - a : a ;
216+ b = b > 0 ? - b : b ;
217+ let ans: number = 0 ;
218+ 219+ while (a <= b ) {
220+ let x: number = b ;
221+ let cnt: number = 1 ;
222+ 223+ while (x >= - (2 ** 30 ) && a <= x << 1 ) {
224+ x <<= 1 ;
225+ cnt <<= 1 ;
226+ }
227+ 228+ ans += cnt ;
229+ a -= x ;
230+ }
231+ 232+ return sign ? ans : - ans ;
175233}
176234```
177235
178- ### ** C++ **
236+ ### ** C# **
179237
180- ``` cpp
181- class Solution {
182- public:
183- int divide(int a, int b) {
184- int sign = 1;
185- if (a < 0 ^ b < 0) {
186- sign = -1;
238+ ``` cs
239+ public class Solution {
240+ public int Divide (int a , int b ) {
241+ if (b == 1 ) {
242+ return a ;
187243 }
188- 189- auto x = abs(static_cast<long long>(a));
190- auto y = abs(static_cast<long long>(b));
191- auto tot = 0ll;
192- while (x >= y) {
193- int cnt = 0;
194- while (x >= (y << (cnt + 1))) {
195- ++cnt;
196- }
197- tot += 1ll << cnt;
198- x -= y << cnt;
244+ if (a == int .MinValue && b == - 1 ) {
245+ return int .MaxValue ;
199246 }
200- 201- auto ans = sign * tot;
202- if (ans >= INT32_MIN && ans <= INT32_MAX) {
203- return static_cast<int>(ans);
247+ bool sign = (a > 0 && b > 0 ) || (a < 0 && b < 0 );
248+ a = a > 0 ? - a : a ;
249+ b = b > 0 ? - b : b ;
250+ int ans = 0 ;
251+ while (a <= b ) {
252+ int x = b ;
253+ int cnt = 1 ;
254+ while (x >= (int .MinValue >> 1 ) && a <= (x << 1 )) {
255+ x <<= 1 ;
256+ cnt <<= 1 ;
257+ }
258+ ans += cnt ;
259+ a -= x ;
204260 }
205- return INT32_MAX ;
261+ return sign ? ans : - ans ;
206262 }
207- };
263+ }
208264```
209265
210266### ** ...**
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