New Problem Solution - "1823. Find the Winner of the Circular Game"

README.md

@@ -9,6 +9,7 @@ LeetCode
 
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
+|1823|[Find the Winner of the Circular Game](https://leetcode.com/problems/find-the-winner-of-the-circular-game/) | [C++](./algorithms/cpp/findTheWinnerOfTheCircularGame/FindTheWinnerOfTheCircularGame.cpp)|Medium|
 |1822|[Sign of the Product of an Array](https://leetcode.com/problems/sign-of-the-product-of-an-array/) | [C++](./algorithms/cpp/signOfTheProductOfAnArray/SignOfTheProductOfAnArray.cpp)|Easy|
 |1819|[Number of Different Subsequences GCDs](https://leetcode.com/problems/number-of-different-subsequences-gcds/) | [C++](./algorithms/cpp/numberOfDifferentSubsequencesGcds/NumberOfDifferentSubsequencesGcds.cpp)|Hard|
 |1818|[Minimum Absolute Sum Difference](https://leetcode.com/problems/minimum-absolute-sum-difference/) | [C++](./algorithms/cpp/minimumAbsoluteSumDifference/MinimumAbsoluteSumDifference.cpp)|Medium|

algorithms/cpp/findTheWinnerOfTheCircularGame/FindTheWinnerOfTheCircularGame.cpp

@@ -0,0 +1,63 @@
+// Source : https://leetcode.com/problems/find-the-winner-of-the-circular-game/
+// Author : Hao Chen
+// Date   : 2021-04-11
+
+/***************************************************************************************************** 
+ *
+ * There are n friends that are playing a game. The friends are sitting in a circle and are numbered 
+ * from 1 to n in clockwise order. More formally, moving clockwise from the i^th friend brings you to 
+ * the (i+1)^th friend for 1 <= i < n, and moving clockwise from the n^th friend brings you to the 
+ * 1^st friend.
+ * 
+ * The rules of the game are as follows:
+ * 
+ * 	Start at the 1^st friend.
+ * 	Count the next k friends in the clockwise direction including the friend you started at. 
+ * The counting wraps around the circle and may count some friends more than once.
+ * 	The last friend you counted leaves the circle and loses the game.
+ * 	If there is still more than one friend in the circle, go back to step 2 starting from the 
+ * friend immediately clockwise of the friend who just lost and repeat.
+ * 	Else, the last friend in the circle wins the game.
+ * 
+ * Given the number of friends, n, and an integer k, return the winner of the game.
+ * 
+ * Example 1:
+ * 
+ * Input: n = 5, k = 2
+ * Output: 3
+ * Explanation: Here are the steps of the game:
+ * 1) Start at friend 1.
+ * 2) Count 2 friends clockwise, which are friends 1 and 2.
+ * 3) Friend 2 leaves the circle. Next start is friend 3.
+ * 4) Count 2 friends clockwise, which are friends 3 and 4.
+ * 5) Friend 4 leaves the circle. Next start is friend 5.
+ * 6) Count 2 friends clockwise, which are friends 5 and 1.
+ * 7) Friend 1 leaves the circle. Next start is friend 3.
+ * 8) Count 2 friends clockwise, which are friends 3 and 5.
+ * 9) Friend 5 leaves the circle. Only friend 3 is left, so they are the winner.
+ * 
+ * Example 2:
+ * 
+ * Input: n = 6, k = 5
+ * Output: 1
+ * Explanation: The friends leave in this order: 5, 4, 6, 2, 3. The winner is friend 1.
+ * 
+ * Constraints:
+ * 
+ * 	1 <= k <= n <= 500
+ ******************************************************************************************************/
+
+class Solution {
+public:
+    int findTheWinner(int n, int k) {
+        vector<int> persons(n);
+        for(int i=0; i<n; i++) persons[i] = i + 1;
+
+        for(int start=0; n>1; n--){
+            start = (start + k -1) % n;
+            persons.erase(persons.begin() + start);
+            start = start %(n-1);
+        }
+        return persons[0];
+    }
+};