New Problem "Arithmetic Slices"

README.md

@@ -9,6 +9,8 @@ LeetCode
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
 |415|[Add Strings](https://leetcode.com/problems/add-strings/) | [C++](./algorithms/cpp/addStrings/AddStrings.cpp)|Easy|
+|414|[Third Maximum Number](https://leetcode.com/problems/third-maximum-number/) | [C++](./algorithms/cpp/thirdMaximumNumber/ThirdMaximumNumber.cpp)|Easy|
+|413|[Arithmetic Slices](https://leetcode.com/problems/arithmetic-slices/) | [C++](./algorithms/cpp/arithmeticSlices/ArithmeticSlices.cpp)|Medium|
 |406|[Queue Reconstruction by Height](https://leetcode.com/problems/queue-reconstruction-by-height/) | [C++](./algorithms/cpp/queueReconstructionByHeight/QueueReconstructionByHeight.cpp)|Medium|
 |405|[Convert a Number to Hexadecimal](https://leetcode.com/problems/convert-a-number-to-hexadecimal/) | [C++](./algorithms/cpp/convertANumberToHexadecimal/ConvertANumberToHexadecimal.cpp)|Easy|
 |404|[Sum of Left Leaves](https://leetcode.com/problems/sum-of-left-leaves/) | [C++](./algorithms/cpp/sumOfLeftLeaves/SumOfLeftLeaves.cpp)|Easy|

algorithms/cpp/arithmeticSlices/ArithmeticSlices.cpp

@@ -0,0 +1,72 @@
+// Source : https://leetcode.com/problems/arithmetic-slices/
+// Author : Hao Chen
+// Date : 2016-11-13
+
+/*************************************************************************************** 
+ *
+ * A sequence of number is called arithmetic if it consists of at least three elements 
+ * and if the difference between any two consecutive elements is the same.
+ * 
+ * For example, these are arithmetic sequence:
+ * 1, 3, 5, 7, 9
+ * 7, 7, 7, 7
+ * 3, -1, -5, -9
+ * 
+ * The following sequence is not arithmetic. 1, 1, 2, 5, 7 
+ * 
+ * A zero-indexed array A consisting of N numbers is given. A slice of that array is 
+ * any pair of integers (P, Q) such that 0 
+ * 
+ * A slice (P, Q) of array A is called arithmetic if the sequence:
+ * A[P], A[p + 1], ..., A[Q - 1], A[Q] is arithmetic. In particular, this means 
+ * that P + 1 
+ * 
+ * The function should return the number of arithmetic slices in the array A. 
+ * 
+ * Example:
+ * 
+ * A = [1, 2, 3, 4]
+ * 
+ * return: 3, for 3 arithmetic slices in A: [1, 2, 3], [2, 3, 4] and [1, 2, 3, 4] 
+ * itself.
+ ***************************************************************************************/
+
+class Solution {
+public:
+ //
+ // It's easy to find out how many 3-length slices in an arithmetic array with N length.
+ //
+ // len = 3, then 1 slices, sum(1)
+ // len = 4, then 3 slices, sum(1,2) - TWO 3-length slices + ONE 4-length slice
+ // len = 5, then 6 slices, sum(1,2,3) - THREE 3-length slices + TWO 4-length slices + ONE 5-length slice
+ // len = 6, then 10 slices, sum(1,2,3,4) - ...
+ // len = 7, then 15 slices, sum(1,2,3,4,5) - ..
+ //
+ // So, with N length arithmetic array, there are Sum[1, N-3+1] 3-length slices
+ //
+ // And, we know the formula sum from 1 to n is:
+ //
+ // n * ( n + 1 )
+ // sum [1, n] = ---------------
+ // 2
+ // Then, we could have the solution - O(n) Time with O(1) Space
+ //
+
+ int sum1toN(int n) {
+ return n * (n+1) / 2;
+ }
+
+ int numberOfArithmeticSlices(vector<int>& A) {
+ int result = 0;
+ int len = 0; // the current length of arithmetic
+ for (int i=2; i<A.size(); i++) {
+ if (A[i] - A[i-1] == A[i-1] - A[i-2]) {
+ len++;
+ }else{
+ result += sum1toN(len);
+ len=0;
+ }
+ }
+ return len==0 ? result : result + sum1toN(len);
+ }
+};

algorithms/cpp/thirdMaximumNumber/ThirdMaximumNumber.cpp

@@ -0,0 +1,51 @@
+// Source : https://leetcode.com/problems/third-maximum-number/
+// Author : Hao Chen
+// Date : 2016-11-12
+
+/*************************************************************************************** 
+ *
+ * Given a non-empty array of integers, return the third maximum number in this array. 
+ * If it does not exist, return the maximum number. The time complexity must be in O(n).
+ * 
+ * Example 1:
+ * 
+ * Input: [3, 2, 1]
+ * 
+ * Output: 1
+ * 
+ * Explanation: The third maximum is 1.
+ * 
+ * Example 2:
+ * 
+ * Input: [1, 2]
+ * 
+ * Output: 2
+ * 
+ * Explanation: The third maximum does not exist, so the maximum (2) is returned 
+ * instead.
+ * 
+ * Example 3:
+ * 
+ * Input: [2, 2, 3, 1]
+ * 
+ * Output: 1
+ * 
+ * Explanation: Note that the third maximum here means the third maximum distinct 
+ * number.
+ * Both numbers with value 2 are both considered as second maximum.
+ ***************************************************************************************/
+
+class Solution {
+public:
+ int nMax(vector<int>& nums, int n) {
+ set<int> topN;
+ for(auto num : nums) {
+ topN.insert(num);
+ if (topN.size() > n) topN.erase(topN.begin());
+ }
+ return (topN.size() >= n) ? *(topN.begin()) : *(topN.rbegin());
+ }
+ int thirdMax(vector<int>& nums) {
+ return nMax(nums, 3);
+ }
+};