feat: add solutions to lc problem: No.1228

No.1228.Missing Number In Arithmetic Progression

Author: yanglbme

solution/1200-1299/1228.Missing Number In Arithmetic Progression/README.md

@@ -43,12 +43,28 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
+**方法一：等差数列求和公式**
+
+等差数列求和公式为 $\frac{n(a_1 + a_n)}{2}$，其中 $n$ 为等差数列的项数，$a_1$ 为等差数列的首项，$a_n$ 为等差数列的末项。
+
+因为题目中给出的数组是一个等差数列，且缺失了一个数，所以数组的项数为 $n + 1$，首项为 $a_1$，末项为 $a_n$，则数组的和为 $\frac{n + 1}{2}(a_1 + a_n)$。
+
+因此，缺失的数为 $\frac{n + 1}{2}(a_1 + a_n) - \sum_{i = 0}^n a_i$。
+
+时间复杂度 $O(n)$，空间复杂度 $O(1)$。其中 $n$ 为数组的长度。
+
 <!-- tabs:start -->
 
 ### **Python3**
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+```python
+class Solution:
+    def missingNumber(self, arr: List[int]) -> int:
+        return (arr[0] + arr[-1]) * (len(arr) + 1) // 2 - sum(arr)
+```
+
 ```python
 class Solution:
     def missingNumber(self, arr: List[int]) -> int:
@@ -64,6 +80,17 @@ class Solution:
 
 <!-- 这里可写当前语言的特殊实现逻辑 -->
 
+```java
+class Solution {
+    public int missingNumber(int[] arr) {
+        int n = arr.length;
+        int x = (arr[0] + arr[n - 1]) * (n + 1) / 2;
+        int y = Arrays.stream(arr).sum();
+        return x - y;
+    }
+}
+```
+
 ```java
 class Solution {
     public int missingNumber(int[] arr) {
@@ -81,6 +108,18 @@ class Solution {
 
 ### **C++**
 
+```cpp
+class Solution {
+public:
+    int missingNumber(vector<int>& arr) {
+        int n = arr.size();
+        int x = (arr[0] + arr[n - 1]) * (n + 1) / 2;
+        int y = accumulate(arr.begin(), arr.end(), 0);
+        return x - y;
+    }
+};
+```
+
 ```cpp
 class Solution {
 public:

solution/1200-1299/1228.Missing Number In Arithmetic Progression/README_EN.md

@@ -41,6 +41,12 @@
 
 ### **Python3**
 
+```python
+class Solution:
+    def missingNumber(self, arr: List[int]) -> int:
+        return (arr[0] + arr[-1]) * (len(arr) + 1) // 2 - sum(arr)
+```
+
 ```python
 class Solution:
     def missingNumber(self, arr: List[int]) -> int:
@@ -54,6 +60,17 @@ class Solution:
 
 ### **Java**
 
+```java
+class Solution {
+    public int missingNumber(int[] arr) {
+        int n = arr.length;
+        int x = (arr[0] + arr[n - 1]) * (n + 1) / 2;
+        int y = Arrays.stream(arr).sum();
+        return x - y;
+    }
+}
+```
+
 ```java
 class Solution {
     public int missingNumber(int[] arr) {
@@ -71,6 +88,18 @@ class Solution {
 
 ### **C++**
 
+```cpp
+class Solution {
+public:
+    int missingNumber(vector<int>& arr) {
+        int n = arr.size();
+        int x = (arr[0] + arr[n - 1]) * (n + 1) / 2;
+        int y = accumulate(arr.begin(), arr.end(), 0);
+        return x - y;
+    }
+};
+```
+
 ```cpp
 class Solution {
 public:
@@ -86,6 +115,18 @@ public:
 
 ### **Go**
 
+```go
+func missingNumber(arr []int) int {
+	n := len(arr)
+	x := (arr[0] + arr[n-1]) * (n + 1) / 2
+	y := 0
+	for _, v := range arr {
+		y += v
+	}
+	return x - y
+}
+```
+
 ```go
 func missingNumber(arr []int) int {
 	n := len(arr)

solution/1200-1299/1228.Missing Number In Arithmetic Progression/Solution.cpp

@@ -2,9 +2,8 @@ class Solution {
 public:
     int missingNumber(vector<int>& arr) {
         int n = arr.size();
-        int d = (arr[n - 1] - arr[0]) / n;
-        for (int i = 1; i < n; ++i)
-            if (arr[i] != arr[i - 1] + d) return arr[i - 1] + d;
-        return arr[0];
+        int x = (arr[0] + arr[n - 1]) * (n + 1) / 2;
+        int y = accumulate(arr.begin(), arr.end(), 0);
+        return x - y;
     }
 };

solution/1200-1299/1228.Missing Number In Arithmetic Progression/Solution.go

@@ -1,10 +1,9 @@
 func missingNumber(arr []int) int {
 	n := len(arr)
-	d := (arr[n-1] - arr[0]) / n
-	for i := 1; i < n; i++ {
-		if arr[i] != arr[i-1]+d {
-			return arr[i-1] + d
-		}
+	x := (arr[0] + arr[n-1]) * (n + 1) / 2
+	y := 0
+	for _, v := range arr {
+		y += v
 	}
-	return arr[0]
+	return x - y
 }

solution/1200-1299/1228.Missing Number In Arithmetic Progression/Solution.java

@@ -1,12 +1,8 @@
 class Solution {
     public int missingNumber(int[] arr) {
         int n = arr.length;
-        int d = (arr[n - 1] - arr[0]) / n;
-        for (int i = 1; i < n; ++i) {
-            if (arr[i] != arr[i - 1] + d) {
-                return arr[i - 1] + d;
-            }
-        }
-        return arr[0];
+        int x = (arr[0] + arr[n - 1]) * (n + 1) / 2;
+        int y = Arrays.stream(arr).sum();
+        return x - y;
     }
 }

solution/1200-1299/1228.Missing Number In Arithmetic Progression/Solution.py

@@ -1,8 +1,3 @@
 class Solution:
     def missingNumber(self, arr: List[int]) -> int:
-        n = len(arr)
-        d = (arr[-1] - arr[0]) // n
-        for i in range(1, n):
-            if arr[i] != arr[i - 1] + d:
-                return arr[i - 1] + d
-        return arr[0]
+        return (arr[0] + arr[-1]) * (len(arr) + 1) // 2 - sum(arr)