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feat: add solutions to lc problem: No.0360 (#4737)
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‎solution/0300-0399/0360.Sort Transformed Array/README.md‎

Lines changed: 154 additions & 83 deletions
Original file line numberDiff line numberDiff line change
@@ -57,7 +57,13 @@ tags:
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<!-- solution:start -->
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60-
### 方法一
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### 方法一：数学 + 双指针
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根据数学知识可知，二次函数的图像是一条抛物线，当 $a \gt 0$ 时，抛物线开口向上，顶点为最小值；当 $a \lt 0$ 时，抛物线开口向下，顶点为最大值。
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由于数组 $\textit{nums}$ 已经排好序，我们可以使用双指针分别指向数组的两端，根据 $a$ 的正负决定从结果数组的头部还是尾部开始填充较大（或较小）的值。
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时间复杂度 $O(n)$，空间复杂度 $O(n)$。其中 $n$ 是数组 $\textit{nums}$ 的长度。
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<!-- tabs:start -->
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@@ -68,31 +74,29 @@ class Solution:
6874
def sortTransformedArray(
6975
self, nums: List[int], a: int, b: int, c: int
7076
) -> List[int]:
71-
def f(x):
77+
def f(x: int) -> int:
7278
return a * x * x + b * x + c
7379

7480
n = len(nums)
75-
i, j, k = 0, n - 1, 0 if a < 0 else n - 1
76-
res = [0] * n
77-
while i <= j:
78-
v1, v2 = f(nums[i]), f(nums[j])
79-
if a < 0:
80-
if v1 <= v2:
81-
res[k] = v1
81+
i, j = 0, n - 1
82+
ans = [0] * n
83+
for k in range(n):
84+
y1, y2 = f(nums[i]), f(nums[j])
85+
if a > 0:
86+
if y1 > y2:
87+
ans[n - k - 1] = y1
8288
i += 1
8389
else:
84-
res[k] = v2
90+
ans[n - k - 1] = y2
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j -= 1
86-
k += 1
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else:
88-
if v1 >= v2:
89-
res[k] = v1
90-
i += 1
91-
else:
92-
res[k] = v2
93+
if y1 > y2:
94+
ans[k] = y2
9395
j -= 1
94-
k -= 1
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return res
96+
else:
97+
ans[k] = y1
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i += 1
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return ans
96100
```
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98102
#### Java
@@ -101,35 +105,33 @@ class Solution:
101105
class Solution {
102106
public int[] sortTransformedArray(int[] nums, int a, int b, int c) {
103107
int n = nums.length;
104-
int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1;
105-
int[] res = new int[n];
106-
while (i <= j) {
107-
int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]);
108-
if (a < 0) {
109-
if (v1 <= v2) {
110-
res[k] = v1;
111-
++i;
108+
int[] ans = new int[n];
109+
int i = 0, j = n - 1;
110+
111+
IntUnaryOperator f = x -> a * x * x + b * x + c;
112+
113+
for (int k = 0; k < n; k++) {
114+
int y1 = f.applyAsInt(nums[i]);
115+
int y2 = f.applyAsInt(nums[j]);
116+
if (a > 0) {
117+
if (y1 > y2) {
118+
ans[n - k - 1] = y1;
119+
i++;
112120
} else {
113-
res[k] = v2;
114-
--j;
121+
ans[n - k - 1] = y2;
122+
j--;
115123
}
116-
++k;
117124
} else {
118-
if (v1 >= v2) {
119-
res[k] = v1;
120-
++i;
125+
if (y1 > y2) {
126+
ans[k] = y2;
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j--;
121128
} else {
122-
res[k] = v2;
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--j;
129+
ans[k] = y1;
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i++;
124131
}
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--k;
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}
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}
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return res;
129-
}
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131-
private int f(int a, int b, int c, int x) {
132-
return a * x * x + b * x + c;
134+
return ans;
133135
}
134136
}
135137
```
@@ -141,35 +143,35 @@ class Solution {
141143
public:
142144
vector<int> sortTransformedArray(vector<int>& nums, int a, int b, int c) {
143145
int n = nums.size();
144-
int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1;
145-
vector<int> res(n);
146-
while (i <= j) {
147-
int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]);
148-
if (a < 0) {
149-
if (v1 <= v2) {
150-
res[k] = v1;
151-
++i;
146+
vector<int> ans(n);
147+
int i = 0, j = n - 1;
148+
149+
auto f = [&](int x) {
150+
return a * x * x + b * x + c;
151+
};
152+
153+
for (int k = 0; k < n; k++) {
154+
int y1 = f(nums[i]);
155+
int y2 = f(nums[j]);
156+
if (a > 0) {
157+
if (y1 > y2) {
158+
ans[n - k - 1] = y1;
159+
i++;
152160
} else {
153-
res[k] = v2;
154-
--j;
161+
ans[n - k - 1] = y2;
162+
j--;
155163
}
156-
++k;
157164
} else {
158-
if (v1 >= v2) {
159-
res[k] = v1;
160-
++i;
165+
if (y1 > y2) {
166+
ans[k] = y2;
167+
j--;
161168
} else {
162-
res[k] = v2;
163-
--j;
169+
ans[k] = y1;
170+
i++;
164171
}
165-
--k;
166172
}
167173
}
168-
return res;
169-
}
170-
171-
int f(int a, int b, int c, int x) {
172-
return a * x * x + b * x + c;
174+
return ans;
173175
}
174176
};
175177
```
@@ -178,42 +180,111 @@ public:
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179181
```go
180182
func sortTransformedArray(nums []int, a int, b int, c int) []int {
181-
n := len(nums)
182-
i, j, k := 0, n-1, 0
183-
if a >= 0 {
184-
k = n - 1
183+
f := func(x int) int {
184+
return a*x*x + b*x + c
185185
}
186-
res := make([]int, n)
187-
for i <= j {
188-
v1, v2 := f(a, b, c, nums[i]), f(a, b, c, nums[j])
189-
if a < 0 {
190-
if v1 <= v2 {
191-
res[k] = v1
186+
187+
n := len(nums)
188+
ans := make([]int, n)
189+
i, j := 0, n-1
190+
191+
for k := 0; k < n; k++ {
192+
y1, y2 := f(nums[i]), f(nums[j])
193+
if a > 0 {
194+
if y1 > y2 {
195+
ans[n-k-1] = y1
192196
i++
193197
} else {
194-
res[k] = v2
198+
ans[n-k-1] = y2
195199
j--
196200
}
197-
k++
198201
} else {
199-
if v1 >= v2 {
200-
res[k] = v1
201-
i++
202-
} else {
203-
res[k] = v2
202+
if y1 > y2 {
203+
ans[k] = y2
204204
j--
205+
} else {
206+
ans[k] = y1
207+
i++
205208
}
206-
k--
207209
}
208210
}
209-
return res
211+
return ans
210212
}
213+
```
211214

212-
func f(a, b, c, x int) int {
213-
return a*x*x + b*x + c
215+
#### TypeScript
216+
217+
```ts
218+
function sortTransformedArray(nums: number[], a: number, b: number, c: number): number[] {
219+
const f = (x: number): number => a * x * x + b * x + c;
220+
const n = nums.length;
221+
let [i, j] = [0, n - 1];
222+
const ans: number[] = Array(n);
223+
for (let k = 0; k < n; ++k) {
224+
const y1 = f(nums[i]);
225+
const y2 = f(nums[j]);
226+
if (a > 0) {
227+
if (y1 > y2) {
228+
ans[n - k - 1] = y1;
229+
++i;
230+
} else {
231+
ans[n - k - 1] = y2;
232+
--j;
233+
}
234+
} else {
235+
if (y1 > y2) {
236+
ans[k] = y2;
237+
--j;
238+
} else {
239+
ans[k] = y1;
240+
++i;
241+
}
242+
}
243+
}
244+
return ans;
214245
}
215246
```
216247

248+
#### JavaScript
249+
250+
```js
251+
/**
252+
* @param {number[]} nums
253+
* @param {number} a
254+
* @param {number} b
255+
* @param {number} c
256+
* @return {number[]}
257+
*/
258+
var sortTransformedArray = function (nums, a, b, c) {
259+
const f = x => a * x * x + b * x + c;
260+
const n = nums.length;
261+
let [i, j] = [0, n - 1];
262+
const ans = Array(n);
263+
for (let k = 0; k < n; ++k) {
264+
const y1 = f(nums[i]);
265+
const y2 = f(nums[j]);
266+
if (a > 0) {
267+
if (y1 > y2) {
268+
ans[n - k - 1] = y1;
269+
++i;
270+
} else {
271+
ans[n - k - 1] = y2;
272+
--j;
273+
}
274+
} else {
275+
if (y1 > y2) {
276+
ans[k] = y2;
277+
--j;
278+
} else {
279+
ans[k] = y1;
280+
++i;
281+
}
282+
}
283+
}
284+
return ans;
285+
};
286+
```
287+
217288
<!-- tabs:end -->
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219290
<!-- solution:end -->

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