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Commit 0d13b1e

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feat: add solutions to lc problem: No.2436
No.2436.Minimum Split Into Subarrays With GCD Greater Than One
1 parent 297edde commit 0d13b1e

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7 files changed

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-60
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7 files changed

+116
-60
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‎solution/2400-2499/2436.Minimum Split Into Subarrays With GCD Greater Than One/README.md‎

Lines changed: 45 additions & 20 deletions
Original file line numberDiff line numberDiff line change
@@ -60,6 +60,16 @@
6060

6161
<!-- 这里可写通用的实现逻辑 -->
6262

63+
**方法一:贪心 + 数学**
64+
65+
对于数组中的每个元素,如果它与前面的元素的最大公约数为 1ドル,ドル那么它需要作为一个新的子数组的第一个元素。否则,它可以与前面的元素放在同一个子数组中。
66+
67+
因此,我们先初始化一个变量 $g,ドル表示当前子数组的最大公约数。初始时 $g=0,ドル答案变量 $ans=1$。
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69+
接下来,我们从前往后遍历数组,维护当前子数组的最大公约数 $g$。如果当前元素 $x$ 与 $g$ 的最大公约数为 1ドル,ドル那么我们需要将当前元素作为一个新的子数组的第一个元素,因此,答案加 1ドル,ドル并将 $g$ 更新为 $x$。否则,当前元素可以与前面的元素放在同一个子数组中。继续遍历数组,直到遍历结束。
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时间复杂度 $O(n \times \log m),ドル空间复杂度 $O(1)$。其中 $n$ 和 $m$ 分别是数组的长度和数组中元素的最大值。
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<!-- tabs:start -->
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### **Python3**
@@ -69,12 +79,12 @@
6979
```python
7080
class Solution:
7181
def minimumSplits(self, nums: List[int]) -> int:
72-
ans, x = 1, nums[0]
73-
for v in nums:
74-
x = gcd(x, v)
75-
if x == 1:
76-
x = v
82+
ans, g = 1, 0
83+
for x in nums:
84+
g = gcd(g, x)
85+
if g == 1:
7786
ans += 1
87+
g = x
7888
return ans
7989
```
8090

@@ -85,12 +95,12 @@ class Solution:
8595
```java
8696
class Solution {
8797
public int minimumSplits(int[] nums) {
88-
int ans = 1, x = nums[0];
89-
for (int v : nums) {
90-
x = gcd(x, v);
91-
if (x == 1) {
92-
x = v;
98+
int ans = 1, g = 0;
99+
for (int x : nums) {
100+
g = gcd(g, x);
101+
if (g == 1) {
93102
++ans;
103+
g = x;
94104
}
95105
}
96106
return ans;
@@ -108,12 +118,12 @@ class Solution {
108118
class Solution {
109119
public:
110120
int minimumSplits(vector<int>& nums) {
111-
int ans = 1, x = nums[0];
112-
for (int v : nums) {
113-
x = gcd(x, v);
114-
if (x == 1) {
115-
x = v;
121+
int ans = 1, g = 0;
122+
for (int x : nums) {
123+
g = gcd(g, x);
124+
if (g == 1) {
116125
++ans;
126+
g = x;
117127
}
118128
}
119129
return ans;
@@ -125,12 +135,12 @@ public:
125135
126136
```go
127137
func minimumSplits(nums []int) int {
128-
ans, x := 1, nums[0]
129-
for _, v := range nums {
130-
x = gcd(x, v)
131-
if x == 1 {
132-
x = v
138+
ans, g := 1, 0
139+
for _, x := range nums {
140+
g = gcd(g, x)
141+
if g == 1 {
133142
ans++
143+
g = x
134144
}
135145
}
136146
return ans
@@ -147,7 +157,22 @@ func gcd(a, b int) int {
147157
### **TypeScript**
148158

149159
```ts
160+
function minimumSplits(nums: number[]): number {
161+
let ans = 1;
162+
let g = 0;
163+
for (const x of nums) {
164+
g = gcd(g, x);
165+
if (g == 1) {
166+
++ans;
167+
g = x;
168+
}
169+
}
170+
return ans;
171+
}
150172

173+
function gcd(a: number, b: number): number {
174+
return b ? gcd(b, a % b) : a;
175+
}
151176
```
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153178
### **...**

‎solution/2400-2499/2436.Minimum Split Into Subarrays With GCD Greater Than One/README_EN.md‎

Lines changed: 35 additions & 20 deletions
Original file line numberDiff line numberDiff line change
@@ -59,12 +59,12 @@ It can be shown that splitting the array into one subarray will make the GCD = 1
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```python
6060
class Solution:
6161
def minimumSplits(self, nums: List[int]) -> int:
62-
ans, x = 1, nums[0]
63-
for v in nums:
64-
x = gcd(x, v)
65-
if x == 1:
66-
x = v
62+
ans, g = 1, 0
63+
for x in nums:
64+
g = gcd(g, x)
65+
if g == 1:
6766
ans += 1
67+
g = x
6868
return ans
6969
```
7070

@@ -73,12 +73,12 @@ class Solution:
7373
```java
7474
class Solution {
7575
public int minimumSplits(int[] nums) {
76-
int ans = 1, x = nums[0];
77-
for (int v : nums) {
78-
x = gcd(x, v);
79-
if (x == 1) {
80-
x = v;
76+
int ans = 1, g = 0;
77+
for (int x : nums) {
78+
g = gcd(g, x);
79+
if (g == 1) {
8180
++ans;
81+
g = x;
8282
}
8383
}
8484
return ans;
@@ -96,12 +96,12 @@ class Solution {
9696
class Solution {
9797
public:
9898
int minimumSplits(vector<int>& nums) {
99-
int ans = 1, x = nums[0];
100-
for (int v : nums) {
101-
x = gcd(x, v);
102-
if (x == 1) {
103-
x = v;
99+
int ans = 1, g = 0;
100+
for (int x : nums) {
101+
g = gcd(g, x);
102+
if (g == 1) {
104103
++ans;
104+
g = x;
105105
}
106106
}
107107
return ans;
@@ -113,12 +113,12 @@ public:
113113
114114
```go
115115
func minimumSplits(nums []int) int {
116-
ans, x := 1, nums[0]
117-
for _, v := range nums {
118-
x = gcd(x, v)
119-
if x == 1 {
120-
x = v
116+
ans, g := 1, 0
117+
for _, x := range nums {
118+
g = gcd(g, x)
119+
if g == 1 {
121120
ans++
121+
g = x
122122
}
123123
}
124124
return ans
@@ -135,7 +135,22 @@ func gcd(a, b int) int {
135135
### **TypeScript**
136136

137137
```ts
138+
function minimumSplits(nums: number[]): number {
139+
let ans = 1;
140+
let g = 0;
141+
for (const x of nums) {
142+
g = gcd(g, x);
143+
if (g == 1) {
144+
++ans;
145+
g = x;
146+
}
147+
}
148+
return ans;
149+
}
138150

151+
function gcd(a: number, b: number): number {
152+
return b ? gcd(b, a % b) : a;
153+
}
139154
```
140155

141156
### **...**

‎solution/2400-2499/2436.Minimum Split Into Subarrays With GCD Greater Than One/Solution.cpp‎

Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -1,12 +1,12 @@
11
class Solution {
22
public:
33
int minimumSplits(vector<int>& nums) {
4-
int ans = 1, x = nums[0];
5-
for (int v : nums) {
6-
x = gcd(x, v);
7-
if (x == 1) {
8-
x = v;
4+
int ans = 1, g = 0;
5+
for (int x : nums) {
6+
g = gcd(g, x);
7+
if (g == 1) {
98
++ans;
9+
g = x;
1010
}
1111
}
1212
return ans;

‎solution/2400-2499/2436.Minimum Split Into Subarrays With GCD Greater Than One/Solution.go‎

Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -1,10 +1,10 @@
11
func minimumSplits(nums []int) int {
2-
ans, x := 1, nums[0]
3-
for _, v := range nums {
4-
x = gcd(x, v)
5-
if x == 1 {
6-
x = v
2+
ans, g := 1, 0
3+
for _, x := range nums {
4+
g = gcd(g, x)
5+
if g == 1 {
76
ans++
7+
g = x
88
}
99
}
1010
return ans

‎solution/2400-2499/2436.Minimum Split Into Subarrays With GCD Greater Than One/Solution.java‎

Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -1,11 +1,11 @@
11
class Solution {
22
public int minimumSplits(int[] nums) {
3-
int ans = 1, x = nums[0];
4-
for (int v : nums) {
5-
x = gcd(x, v);
6-
if (x == 1) {
7-
x = v;
3+
int ans = 1, g = 0;
4+
for (int x : nums) {
5+
g = gcd(g, x);
6+
if (g == 1) {
87
++ans;
8+
g = x;
99
}
1010
}
1111
return ans;
Lines changed: 5 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -1,9 +1,9 @@
11
class Solution:
22
def minimumSplits(self, nums: List[int]) -> int:
3-
ans, x = 1, nums[0]
4-
for v in nums:
5-
x = gcd(x, v)
6-
if x == 1:
7-
x = v
3+
ans, g = 1, 0
4+
for x in nums:
5+
g = gcd(g, x)
6+
if g == 1:
87
ans += 1
8+
g = x
99
return ans
Lines changed: 16 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -0,0 +1,16 @@
1+
function minimumSplits(nums: number[]): number {
2+
let ans = 1;
3+
let g = 0;
4+
for (const x of nums) {
5+
g = gcd(g, x);
6+
if (g == 1) {
7+
++ans;
8+
g = x;
9+
}
10+
}
11+
return ans;
12+
}
13+
14+
function gcd(a: number, b: number): number {
15+
return b ? gcd(b, a % b) : a;
16+
}

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