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feat: add solutions to lc problem: No.2180
No.2180.Count Integers With Even Digit Sum
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‎solution/2100-2199/2180.Count Integers With Even Digit Sum/README.md

+119-31
Original file line numberDiff line numberDiff line change
@@ -43,6 +43,26 @@
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<!-- 这里可写通用的实现逻辑 -->
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**方法一：枚举**
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一种最简单直接的方法是枚举 $[1,..num]$ 的所有整数 $x$，判断 $x$ 各位数字之和是否为偶数，是则答案加一。
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时间复杂度 $O(n \times \log n)$，空间复杂度 $O(1)$。其中 $n$ 为 $num$ 的值。
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**方法二：数学**
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我们观察发现，在 $[0,..x]$ 的所有数中，每 $10$ 个数中，就有 $5$ 个数的各位数字之和为偶数。例如，$[0,..9]$ 中，每 $10$ 个数中，就有 $5$ 个数的各位数字之和为偶数，分别是 $0,2,4,6,8$。
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因此，我们可以先算出 $num$ 中有多少个 $10$ 的倍数，然后乘以 $5$ 再减去 $1$（排除 $0$ 这个偶数），可以得到初始答案 $ans=\left\lfloor \frac{num}{10} \right\rfloor \times 5 - 1$。
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接下来，我们还需要考虑剩下的 $num \% 10 + 1$ 个数字中，有多少个数的各位数字之和为偶数。这些数字是否是偶数，跟数字的前面数字之和有关，因此，我们可以算出 $num$ 的前面数字之和 $s$，那么剩余的数字中，还有 $\left\lfloor \frac{num \% 10 + 2 - (s \& 1)}{2} \right\rfloor$ 个数的各位数字之和为偶数。累加到答案 $ans$ 中即可。
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我们不妨举个例子，假设 $num$ 为 $123$，那么前面 $[0,..119]$ 中一共有 $12$ 个 $10$ 的倍数，每个 $10$ 的倍数中有 $5$ 个数的各位数字之和为偶数，因此，初始答案为 $ans=12 \times 5 - 1=59$。
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剩下的数字分别是 $120,121,122,123$，每个数字的前两位数字之和为 $s = 1+2=3$，是奇数，因此，剩下的数字中，只有 $2$ 个数的各位数字之和为偶数，累加到答案 $ans$ 中，最终答案为 $ans+2=61$。
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时间复杂度 $O(\log n)$，空间复杂度 $O(1)$。其中 $n$ 为 $num$ 的值。
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<!-- tabs:start -->
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### **Python3**
@@ -53,13 +73,24 @@
5373
class Solution:
5474
def countEven(self, num: int) -> int:
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ans = 0
56-
for i in range(1, num + 1):
57-
t = 0
58-
while i:
59-
t += i % 10
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i //= 10
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if t % 2 == 0:
62-
ans += 1
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for x in range(1, num + 1):
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s = 0
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while x:
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s += x % 10
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x //= 10
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ans += s % 2 == 0
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return ans
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```
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```python
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class Solution:
87+
def countEven(self, num: int) -> int:
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ans = num // 10 * 5 - 1
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x, s = num // 10, 0
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while x:
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s += x % 10
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x //= 10
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ans += (num % 10 + 2 - (s & 1)) >> 1
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return ans
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```
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@@ -72,12 +103,11 @@ class Solution {
72103
public int countEven(int num) {
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int ans = 0;
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for (int i = 1; i <= num; ++i) {
75-
int j = i, t = 0;
76-
while (j > 0) {
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t += j % 10;
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j /= 10;
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int s = 0;
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for (int x = i; x > 0; x /= 10) {
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s += x % 10;
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}
80-
if (t % 2 == 0) {
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if (s % 2 == 0) {
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++ans;
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}
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}
@@ -86,17 +116,17 @@ class Solution {
86116
}
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```
88118

89-
### **TypeScript**
90-
91-
```ts
92-
function countEven(num: number): number {
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let ans = 0;
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for (let i = 2; i <= num; i++) {
95-
if ([...String(i)].reduce((a, c) => a + Number(c), 0) % 2 == 0) {
96-
ans++;
119+
```java
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class Solution {
121+
public int countEven(int num) {
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int ans = num / 10 * 5 - 1;
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int s = 0;
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for (int x = num / 10; x > 0; x /= 10) {
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s += x % 10;
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}
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ans += (num % 10 + 2 - (s & 1)) >> 1;
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return ans;
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}
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return ans;
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}
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```
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@@ -108,30 +138,88 @@ public:
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int countEven(int num) {
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int ans = 0;
110140
for (int i = 1; i <= num; ++i) {
111-
int t = 0;
112-
for (int j = i; j; j /= 10) t += j % 10;
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if (t % 2 == 0) ++ans;
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int s = 0;
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for (int x = i; x; x /= 10) {
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s += x % 10;
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}
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ans += s % 2 == 0;
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}
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return ans;
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}
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};
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```
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```cpp
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class Solution {
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public:
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int countEven(int num) {
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int ans = num / 10 * 5 - 1;
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int s = 0;
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for (int x = num / 10; x > 0; x /= 10) {
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s += x % 10;
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}
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ans += (num % 10 + 2 - (s & 1)) >> 1;
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return ans;
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}
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};
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```
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120167
### **Go**
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```go
123-
func countEven(num int) int {
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ans := 0
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func countEven(num int) (ans int) {
125171
for i := 1; i <= num; i++ {
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t := 0
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for j := i; j > 0; j /= 10 {
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t += j % 10
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s := 0
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for x := i; x > 0; x /= 10 {
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s += x % 10
129175
}
130-
if t%2 == 0 {
176+
if s%2 == 0 {
131177
ans++
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}
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}
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return ans
180+
return
181+
}
182+
```
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```go
185+
func countEven(num int) (ans int) {
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ans = num/10*5 - 1
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s := 0
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for x := num / 10; x > 0; x /= 10 {
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s += x % 10
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}
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ans += (num%10 + 2 - (s & 1)) >> 1
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return
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}
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```
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### **TypeScript**
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```ts
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function countEven(num: number): number {
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let ans = 0;
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for (let i = 1; i <= num; ++i) {
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let s = 0;
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for (let x = i; x; x = Math.floor(x / 10)) {
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s += x % 10;
205+
}
206+
if (s % 2 == 0) {
207+
++ans;
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}
209+
}
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return ans;
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}
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```
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```ts
215+
function countEven(num: number): number {
216+
let ans = Math.floor(num / 10) * 5 - 1;
217+
let s = 0;
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for (let x = Math.floor(num / 10); x; x = Math.floor(x / 10)) {
219+
s += x % 10;
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}
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ans += ((num % 10) + 2 - (s & 1)) >> 1;
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return ans;
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}
136224
```
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‎solution/2100-2199/2180.Count Integers With Even Digit Sum/README_EN.md

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Original file line numberDiff line numberDiff line change
@@ -45,13 +45,24 @@ The 14 integers less than or equal to 30 whose digit sums are even are
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class Solution:
4646
def countEven(self, num: int) -> int:
4747
ans = 0
48-
for i in range(1, num + 1):
49-
t = 0
50-
while i:
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t += i % 10
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i //= 10
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if t % 2 == 0:
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ans += 1
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for x in range(1, num + 1):
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s = 0
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while x:
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s += x % 10
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x //= 10
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ans += s % 2 == 0
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return ans
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```
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```python
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class Solution:
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def countEven(self, num: int) -> int:
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ans = num // 10 * 5 - 1
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x, s = num // 10, 0
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while x:
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s += x % 10
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x //= 10
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ans += (num % 10 + 2 - (s & 1)) >> 1
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return ans
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```
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@@ -62,12 +73,11 @@ class Solution {
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public int countEven(int num) {
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int ans = 0;
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for (int i = 1; i <= num; ++i) {
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int j = i, t = 0;
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while (j > 0) {
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t += j % 10;
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j /= 10;
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int s = 0;
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for (int x = i; x > 0; x /= 10) {
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s += x % 10;
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}
70-
if (t % 2 == 0) {
80+
if (s % 2 == 0) {
7181
++ans;
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}
7383
}
@@ -76,17 +86,17 @@ class Solution {
7686
}
7787
```
7888

79-
### **TypeScript**
80-
81-
```ts
82-
function countEven(num: number): number {
83-
let ans = 0;
84-
for (let i = 2; i <= num; i++) {
85-
if ([...String(i)].reduce((a, c) => a + Number(c), 0) % 2 == 0) {
86-
ans++;
89+
```java
90+
class Solution {
91+
public int countEven(int num) {
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int ans = num / 10 * 5 - 1;
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int s = 0;
94+
for (int x = num / 10; x > 0; x /= 10) {
95+
s += x % 10;
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}
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ans += (num % 10 + 2 - (s & 1)) >> 1;
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return ans;
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}
89-
return ans;
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}
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```
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@@ -98,30 +108,88 @@ public:
98108
int countEven(int num) {
99109
int ans = 0;
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for (int i = 1; i <= num; ++i) {
101-
int t = 0;
102-
for (int j = i; j; j /= 10) t += j % 10;
103-
if (t % 2 == 0) ++ans;
111+
int s = 0;
112+
for (int x = i; x; x /= 10) {
113+
s += x % 10;
114+
}
115+
ans += s % 2 == 0;
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}
105117
return ans;
106118
}
107119
};
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```
109121
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```cpp
123+
class Solution {
124+
public:
125+
int countEven(int num) {
126+
int ans = num / 10 * 5 - 1;
127+
int s = 0;
128+
for (int x = num / 10; x > 0; x /= 10) {
129+
s += x % 10;
130+
}
131+
ans += (num % 10 + 2 - (s & 1)) >> 1;
132+
return ans;
133+
}
134+
};
135+
```
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110137
### **Go**
111138

112139
```go
113-
func countEven(num int) int {
114-
ans := 0
140+
func countEven(num int) (ans int) {
115141
for i := 1; i <= num; i++ {
116-
t := 0
117-
for j := i; j > 0; j /= 10 {
118-
t += j % 10
142+
s := 0
143+
for x := i; x > 0; x /= 10 {
144+
s += x % 10
119145
}
120-
if t%2 == 0 {
146+
if s%2 == 0 {
121147
ans++
122148
}
123149
}
124-
return ans
150+
return
151+
}
152+
```
153+
154+
```go
155+
func countEven(num int) (ans int) {
156+
ans = num/10*5 - 1
157+
s := 0
158+
for x := num / 10; x > 0; x /= 10 {
159+
s += x % 10
160+
}
161+
ans += (num%10 + 2 - (s & 1)) >> 1
162+
return
163+
}
164+
```
165+
166+
### **TypeScript**
167+
168+
```ts
169+
function countEven(num: number): number {
170+
let ans = 0;
171+
for (let i = 1; i <= num; ++i) {
172+
let s = 0;
173+
for (let x = i; x; x = Math.floor(x / 10)) {
174+
s += x % 10;
175+
}
176+
if (s % 2 == 0) {
177+
++ans;
178+
}
179+
}
180+
return ans;
181+
}
182+
```
183+
184+
```ts
185+
function countEven(num: number): number {
186+
let ans = Math.floor(num / 10) * 5 - 1;
187+
let s = 0;
188+
for (let x = Math.floor(num / 10); x; x = Math.floor(x / 10)) {
189+
s += x % 10;
190+
}
191+
ans += ((num % 10) + 2 - (s & 1)) >> 1;
192+
return ans;
125193
}
126194
```
127195

‎solution/2100-2199/2180.Count Integers With Even Digit Sum/Solution.cpp

+5-5
Original file line numberDiff line numberDiff line change
@@ -1,12 +1,12 @@
11
class Solution {
22
public:
33
int countEven(int num) {
4-
int ans = 0;
5-
for (int i = 1; i <= num; ++i) {
6-
int t = 0;
7-
for (int j = i; j; j /= 10) t += j % 10;
8-
if (t % 2 == 0) ++ans;
4+
int ans = num / 10 * 5 - 1;
5+
int s = 0;
6+
for (int x = num / 10; x > 0; x /= 10) {
7+
s += x % 10;
98
}
9+
ans += (num % 10 + 2 - (s & 1)) >> 1;
1010
return ans;
1111
}
1212
};

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