diff --git a/solution/0300-0399/0360.Sort Transformed Array/README.md b/solution/0300-0399/0360.Sort Transformed Array/README.md index 85361f93c7cf3..0b96fba068495 100644 --- a/solution/0300-0399/0360.Sort Transformed Array/README.md +++ b/solution/0300-0399/0360.Sort Transformed Array/README.md @@ -57,7 +57,13 @@ tags: -### 方法一 +### 方法一：数学 + 双指针 + +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。 + +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。 + +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。 @@ -68,31 +74,29 @@ class Solution: def sortTransformedArray( self, nums: List[int], a: int, b: int, c: int ) -> List[int]: - def f(x): + def f(x: int) -> int: return a * x * x + b * x + c n = len(nums) - i, j, k = 0, n - 1, 0 if a < 0 else n - 1 - res = [0] * n - while i <= j: - v1, v2 = f(nums[i]), f(nums[j]) - if a < 0: - if v1 <= v2: - res[k] = v1 + i, j = 0, n - 1 + ans = [0] * n + for k in range(n): + y1, y2 = f(nums[i]), f(nums[j]) + if a > 0: + if y1 > y2: + ans[n - k - 1] = y1 i += 1 else: - res[k] = v2 + ans[n - k - 1] = y2 j -= 1 - k += 1 else: - if v1 >= v2: - res[k] = v1 - i += 1 - else: - res[k] = v2 + if y1 > y2: + ans[k] = y2 j -= 1 - k -= 1 - return res + else: + ans[k] = y1 + i += 1 + return ans ``` #### Java @@ -101,35 +105,33 @@ class Solution: class Solution { public int[] sortTransformedArray(int[] nums, int a, int b, int c) { int n = nums.length; - int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1; - int[] res = new int[n]; - while (i <= j) { - int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]); - if (a < 0) { - if (v1 <= v2) { - res[k] = v1; - ++i; + int[] ans = new int[n]; + int i = 0, j = n - 1; + + IntUnaryOperator f = x -> a * x * x + b * x + c; + + for (int k = 0; k < n; k++) { + int y1 = f.applyAsInt(nums[i]); + int y2 = f.applyAsInt(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + i++; } else { - res[k] = v2; - --j; + ans[n - k - 1] = y2; + j--; } - ++k; } else { - if (v1 >= v2) { - res[k] = v1; - ++i; + if (y1 > y2) { + ans[k] = y2; + j--; } else { - res[k] = v2; - --j; + ans[k] = y1; + i++; } - --k; } } - return res; - } - - private int f(int a, int b, int c, int x) { - return a * x * x + b * x + c; + return ans; } } ``` @@ -141,35 +143,35 @@ class Solution { public: vector sortTransformedArray(vector& nums, int a, int b, int c) { int n = nums.size(); - int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1; - vector res(n); - while (i <= j) { - int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]); - if (a < 0) { - if (v1 <= v2) { - res[k] = v1; - ++i; + vector ans(n); + int i = 0, j = n - 1; + + auto f = [&](int x) { + return a * x * x + b * x + c; + }; + + for (int k = 0; k < n; k++) { + int y1 = f(nums[i]); + int y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + i++; } else { - res[k] = v2; - --j; + ans[n - k - 1] = y2; + j--; } - ++k; } else { - if (v1 >= v2) { - res[k] = v1; - ++i; + if (y1 > y2) { + ans[k] = y2; + j--; } else { - res[k] = v2; - --j; + ans[k] = y1; + i++; } - --k; } } - return res; - } - - int f(int a, int b, int c, int x) { - return a * x * x + b * x + c; + return ans; } }; ``` @@ -178,42 +180,111 @@ public: ```go func sortTransformedArray(nums []int, a int, b int, c int) []int { - n := len(nums) - i, j, k := 0, n-1, 0 - if a >= 0 { - k = n - 1 + f := func(x int) int { + return a*x*x + b*x + c } - res := make([]int, n) - for i <= j { - v1, v2 := f(a, b, c, nums[i]), f(a, b, c, nums[j]) - if a < 0 { - if v1 <= v2 { - res[k] = v1 + + n := len(nums) + ans := make([]int, n) + i, j := 0, n-1 + + for k := 0; k < n; k++ { + y1, y2 := f(nums[i]), f(nums[j]) + if a > 0 { + if y1 > y2 { + ans[n-k-1] = y1 i++ } else { - res[k] = v2 + ans[n-k-1] = y2 j-- } - k++ } else { - if v1 >= v2 { - res[k] = v1 - i++ - } else { - res[k] = v2 + if y1 > y2 { + ans[k] = y2 j-- + } else { + ans[k] = y1 + i++ } - k-- } } - return res + return ans } +``` -func f(a, b, c, x int) int { - return a*x*x + b*x + c +#### TypeScript + +```ts +function sortTransformedArray(nums: number[], a: number, b: number, c: number): number[] { + const f = (x: number): number => a * x * x + b * x + c; + const n = nums.length; + let [i, j] = [0, n - 1]; + const ans: number[] = Array(n); + for (let k = 0; k < n; ++k) { + const y1 = f(nums[i]); + const y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + ++i; + } else { + ans[n - k - 1] = y2; + --j; + } + } else { + if (y1 > y2) { + ans[k] = y2; + --j; + } else { + ans[k] = y1; + ++i; + } + } + } + return ans; } ``` +#### JavaScript + +```js +/** + * @param {number[]} nums + * @param {number} a + * @param {number} b + * @param {number} c + * @return {number[]} + */ +var sortTransformedArray = function (nums, a, b, c) { + const f = x => a * x * x + b * x + c; + const n = nums.length; + let [i, j] = [0, n - 1]; + const ans = Array(n); + for (let k = 0; k < n; ++k) { + const y1 = f(nums[i]); + const y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + ++i; + } else { + ans[n - k - 1] = y2; + --j; + } + } else { + if (y1 > y2) { + ans[k] = y2; + --j; + } else { + ans[k] = y1; + ++i; + } + } + } + return ans; +}; +``` + diff --git a/solution/0300-0399/0360.Sort Transformed Array/README_EN.md b/solution/0300-0399/0360.Sort Transformed Array/README_EN.md index 9f4d054ccf088..d780500ea5341 100644 --- a/solution/0300-0399/0360.Sort Transformed Array/README_EN.md +++ b/solution/0300-0399/0360.Sort Transformed Array/README_EN.md @@ -47,7 +47,13 @@ tags: -### Solution 1 +### Solution 1: Math + Two Pointers + +By mathematical knowledge, the graph of a quadratic function is a parabola. When $a \gt 0$, the parabola opens upwards and its vertex is the minimum value; when $a \lt 0$, the parabola opens downwards and its vertex is the maximum value. + +Since the array $\textit{nums}$ is already sorted, we can use two pointers at both ends of the array. Depending on the sign of $a$, we decide whether to fill the result array from the beginning or the end with the larger (or smaller) values. + +The time complexity is $O(n)$, and the space complexity is $O(n)$, where $n$ is the length of the array $\textit{nums}$. @@ -58,31 +64,29 @@ class Solution: def sortTransformedArray( self, nums: List[int], a: int, b: int, c: int ) -> List[int]: - def f(x): + def f(x: int) -> int: return a * x * x + b * x + c n = len(nums) - i, j, k = 0, n - 1, 0 if a < 0 else n - 1 - res = [0] * n - while i <= j: - v1, v2 = f(nums[i]), f(nums[j]) - if a < 0: - if v1 <= v2: - res[k] = v1 + i, j = 0, n - 1 + ans = [0] * n + for k in range(n): + y1, y2 = f(nums[i]), f(nums[j]) + if a > 0: + if y1 > y2: + ans[n - k - 1] = y1 i += 1 else: - res[k] = v2 + ans[n - k - 1] = y2 j -= 1 - k += 1 else: - if v1 >= v2: - res[k] = v1 - i += 1 - else: - res[k] = v2 + if y1 > y2: + ans[k] = y2 j -= 1 - k -= 1 - return res + else: + ans[k] = y1 + i += 1 + return ans ``` #### Java @@ -91,35 +95,33 @@ class Solution: class Solution { public int[] sortTransformedArray(int[] nums, int a, int b, int c) { int n = nums.length; - int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1; - int[] res = new int[n]; - while (i <= j) { - int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]); - if (a < 0) { - if (v1 <= v2) { - res[k] = v1; - ++i; + int[] ans = new int[n]; + int i = 0, j = n - 1; + + IntUnaryOperator f = x -> a * x * x + b * x + c; + + for (int k = 0; k < n; k++) { + int y1 = f.applyAsInt(nums[i]); + int y2 = f.applyAsInt(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + i++; } else { - res[k] = v2; - --j; + ans[n - k - 1] = y2; + j--; } - ++k; } else { - if (v1 >= v2) { - res[k] = v1; - ++i; + if (y1 > y2) { + ans[k] = y2; + j--; } else { - res[k] = v2; - --j; + ans[k] = y1; + i++; } - --k; } } - return res; - } - - private int f(int a, int b, int c, int x) { - return a * x * x + b * x + c; + return ans; } } ``` @@ -131,35 +133,35 @@ class Solution { public: vector sortTransformedArray(vector& nums, int a, int b, int c) { int n = nums.size(); - int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1; - vector res(n); - while (i <= j) { - int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]); - if (a < 0) { - if (v1 <= v2) { - res[k] = v1; - ++i; + vector ans(n); + int i = 0, j = n - 1; + + auto f = [&](int x) { + return a * x * x + b * x + c; + }; + + for (int k = 0; k < n; k++) { + int y1 = f(nums[i]); + int y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + i++; } else { - res[k] = v2; - --j; + ans[n - k - 1] = y2; + j--; } - ++k; } else { - if (v1 >= v2) { - res[k] = v1; - ++i; + if (y1 > y2) { + ans[k] = y2; + j--; } else { - res[k] = v2; - --j; + ans[k] = y1; + i++; } - --k; } } - return res; - } - - int f(int a, int b, int c, int x) { - return a * x * x + b * x + c; + return ans; } }; ``` @@ -168,42 +170,111 @@ public: ```go func sortTransformedArray(nums []int, a int, b int, c int) []int { - n := len(nums) - i, j, k := 0, n-1, 0 - if a >= 0 { - k = n - 1 + f := func(x int) int { + return a*x*x + b*x + c } - res := make([]int, n) - for i <= j { - v1, v2 := f(a, b, c, nums[i]), f(a, b, c, nums[j]) - if a < 0 { - if v1 <= v2 { - res[k] = v1 + + n := len(nums) + ans := make([]int, n) + i, j := 0, n-1 + + for k := 0; k < n; k++ { + y1, y2 := f(nums[i]), f(nums[j]) + if a > 0 { + if y1 > y2 { + ans[n-k-1] = y1 i++ } else { - res[k] = v2 + ans[n-k-1] = y2 j-- } - k++ } else { - if v1 >= v2 { - res[k] = v1 - i++ - } else { - res[k] = v2 + if y1 > y2 { + ans[k] = y2 j-- + } else { + ans[k] = y1 + i++ } - k-- } } - return res + return ans } +``` -func f(a, b, c, x int) int { - return a*x*x + b*x + c +#### TypeScript + +```ts +function sortTransformedArray(nums: number[], a: number, b: number, c: number): number[] { + const f = (x: number): number => a * x * x + b * x + c; + const n = nums.length; + let [i, j] = [0, n - 1]; + const ans: number[] = Array(n); + for (let k = 0; k < n; ++k) { + const y1 = f(nums[i]); + const y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + ++i; + } else { + ans[n - k - 1] = y2; + --j; + } + } else { + if (y1 > y2) { + ans[k] = y2; + --j; + } else { + ans[k] = y1; + ++i; + } + } + } + return ans; } ``` +#### JavaScript + +```js +/** + * @param {number[]} nums + * @param {number} a + * @param {number} b + * @param {number} c + * @return {number[]} + */ +var sortTransformedArray = function (nums, a, b, c) { + const f = x => a * x * x + b * x + c; + const n = nums.length; + let [i, j] = [0, n - 1]; + const ans = Array(n); + for (let k = 0; k < n; ++k) { + const y1 = f(nums[i]); + const y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + ++i; + } else { + ans[n - k - 1] = y2; + --j; + } + } else { + if (y1 > y2) { + ans[k] = y2; + --j; + } else { + ans[k] = y1; + ++i; + } + } + } + return ans; +}; +``` + diff --git a/solution/0300-0399/0360.Sort Transformed Array/Solution.cpp b/solution/0300-0399/0360.Sort Transformed Array/Solution.cpp index 1c407f215929c..1d5e36bd848f2 100644 --- a/solution/0300-0399/0360.Sort Transformed Array/Solution.cpp +++ b/solution/0300-0399/0360.Sort Transformed Array/Solution.cpp @@ -2,34 +2,34 @@ class Solution { public: vector sortTransformedArray(vector& nums, int a, int b, int c) { int n = nums.size(); - int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1; - vector res(n); - while (i <= j) { - int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]); - if (a < 0) { - if (v1 <= v2) { - res[k] = v1; - ++i; + vector ans(n); + int i = 0, j = n - 1; + + auto f = [&](int x) { + return a * x * x + b * x + c; + }; + + for (int k = 0; k < n; k++) { + int y1 = f(nums[i]); + int y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + i++; } else { - res[k] = v2; - --j; + ans[n - k - 1] = y2; + j--; } - ++k; } else { - if (v1 >= v2) { - res[k] = v1; - ++i; + if (y1 > y2) { + ans[k] = y2; + j--; } else { - res[k] = v2; - --j; + ans[k] = y1; + i++; } - --k; } } - return res; - } - - int f(int a, int b, int c, int x) { - return a * x * x + b * x + c; + return ans; } -}; \ No newline at end of file +}; diff --git a/solution/0300-0399/0360.Sort Transformed Array/Solution.go b/solution/0300-0399/0360.Sort Transformed Array/Solution.go index b209afcf651f7..990cdc55985c5 100644 --- a/solution/0300-0399/0360.Sort Transformed Array/Solution.go +++ b/solution/0300-0399/0360.Sort Transformed Array/Solution.go @@ -1,35 +1,31 @@ func sortTransformedArray(nums []int, a int, b int, c int) []int { - n := len(nums) - i, j, k := 0, n-1, 0 - if a >= 0 { - k = n - 1 + f := func(x int) int { + return a*x*x + b*x + c } - res := make([]int, n) - for i <= j { - v1, v2 := f(a, b, c, nums[i]), f(a, b, c, nums[j]) - if a < 0 { - if v1 <= v2 { - res[k] = v1 + + n := len(nums) + ans := make([]int, n) + i, j := 0, n-1 + + for k := 0; k < n; k++ { + y1, y2 := f(nums[i]), f(nums[j]) + if a > 0 { + if y1 > y2 { + ans[n-k-1] = y1 i++ } else { - res[k] = v2 + ans[n-k-1] = y2 j-- } - k++ } else { - if v1 >= v2 { - res[k] = v1 - i++ - } else { - res[k] = v2 + if y1 > y2 { + ans[k] = y2 j-- + } else { + ans[k] = y1 + i++ } - k-- } } - return res + return ans } - -func f(a, b, c, x int) int { - return a*x*x + b*x + c -} \ No newline at end of file diff --git a/solution/0300-0399/0360.Sort Transformed Array/Solution.java b/solution/0300-0399/0360.Sort Transformed Array/Solution.java index ad4aa386489bc..8982463e2d31a 100644 --- a/solution/0300-0399/0360.Sort Transformed Array/Solution.java +++ b/solution/0300-0399/0360.Sort Transformed Array/Solution.java @@ -1,34 +1,32 @@ class Solution { public int[] sortTransformedArray(int[] nums, int a, int b, int c) { int n = nums.length; - int i = 0, j = n - 1, k = a < 0 ? 0 : n - 1; - int[] res = new int[n]; - while (i <= j) { - int v1 = f(a, b, c, nums[i]), v2 = f(a, b, c, nums[j]); - if (a < 0) { - if (v1 <= v2) { - res[k] = v1; - ++i; + int[] ans = new int[n]; + int i = 0, j = n - 1; + + IntUnaryOperator f = x -> a * x * x + b * x + c; + + for (int k = 0; k < n; k++) { + int y1 = f.applyAsInt(nums[i]); + int y2 = f.applyAsInt(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + i++; } else { - res[k] = v2; - --j; + ans[n - k - 1] = y2; + j--; } - ++k; } else { - if (v1 >= v2) { - res[k] = v1; - ++i; + if (y1 > y2) { + ans[k] = y2; + j--; } else { - res[k] = v2; - --j; + ans[k] = y1; + i++; } - --k; } } - return res; - } - - private int f(int a, int b, int c, int x) { - return a * x * x + b * x + c; + return ans; } -} \ No newline at end of file +} diff --git a/solution/0300-0399/0360.Sort Transformed Array/Solution.js b/solution/0300-0399/0360.Sort Transformed Array/Solution.js new file mode 100644 index 0000000000000..10dc059ff1a2b --- /dev/null +++ b/solution/0300-0399/0360.Sort Transformed Array/Solution.js @@ -0,0 +1,35 @@ +/** + * @param {number[]} nums + * @param {number} a + * @param {number} b + * @param {number} c + * @return {number[]} + */ +var sortTransformedArray = function (nums, a, b, c) { + const f = x => a * x * x + b * x + c; + const n = nums.length; + let [i, j] = [0, n - 1]; + const ans = Array(n); + for (let k = 0; k < n; ++k) { + const y1 = f(nums[i]); + const y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + ++i; + } else { + ans[n - k - 1] = y2; + --j; + } + } else { + if (y1 > y2) { + ans[k] = y2; + --j; + } else { + ans[k] = y1; + ++i; + } + } + } + return ans; +}; diff --git a/solution/0300-0399/0360.Sort Transformed Array/Solution.py b/solution/0300-0399/0360.Sort Transformed Array/Solution.py index f080f3cc0793d..7f7529ff4b371 100644 --- a/solution/0300-0399/0360.Sort Transformed Array/Solution.py +++ b/solution/0300-0399/0360.Sort Transformed Array/Solution.py @@ -2,28 +2,26 @@ class Solution: def sortTransformedArray( self, nums: List[int], a: int, b: int, c: int ) -> List[int]: - def f(x): + def f(x: int) -> int: return a * x * x + b * x + c n = len(nums) - i, j, k = 0, n - 1, 0 if a < 0 else n - 1 - res = [0] * n - while i <= j: - v1, v2 = f(nums[i]), f(nums[j]) - if a < 0: - if v1 <= v2: - res[k] = v1 + i, j = 0, n - 1 + ans = [0] * n + for k in range(n): + y1, y2 = f(nums[i]), f(nums[j]) + if a > 0: + if y1 > y2: + ans[n - k - 1] = y1 i += 1 else: - res[k] = v2 + ans[n - k - 1] = y2 j -= 1 - k += 1 else: - if v1 >= v2: - res[k] = v1 - i += 1 - else: - res[k] = v2 + if y1 > y2: + ans[k] = y2 j -= 1 - k -= 1 - return res + else: + ans[k] = y1 + i += 1 + return ans diff --git a/solution/0300-0399/0360.Sort Transformed Array/Solution.ts b/solution/0300-0399/0360.Sort Transformed Array/Solution.ts new file mode 100644 index 0000000000000..990ebf0754dd1 --- /dev/null +++ b/solution/0300-0399/0360.Sort Transformed Array/Solution.ts @@ -0,0 +1,28 @@ +function sortTransformedArray(nums: number[], a: number, b: number, c: number): number[] { + const f = (x: number): number => a * x * x + b * x + c; + const n = nums.length; + let [i, j] = [0, n - 1]; + const ans: number[] = Array(n); + for (let k = 0; k < n; ++k) { + const y1 = f(nums[i]); + const y2 = f(nums[j]); + if (a > 0) { + if (y1 > y2) { + ans[n - k - 1] = y1; + ++i; + } else { + ans[n - k - 1] = y2; + --j; + } + } else { + if (y1 > y2) { + ans[k] = y2; + --j; + } else { + ans[k] = y1; + ++i; + } + } + } + return ans; +}