Create 11New21Game.cpp

Flipkart/11New21Game.cpp

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+// 837. New 21 Game
+// Alice plays the following game, loosely based on the card game "21".
+// Alice starts with 0 points and draws numbers while she has less than k points. During each draw, she gains an integer number of points randomly from the range [1, maxPts], where maxPts is an integer. Each draw is independent and the outcomes have equal probabilities.
+
+// Alice stops drawing numbers when she gets k or more points.
+
+// Return the probability that Alice has n or fewer points.
+
+// Answers within 10-5 of the actual answer are considered accepted.
+// Example 1:
+
+// Input: n = 10, k = 1, maxPts = 10
+// Output: 1.00000
+// Explanation: Alice gets a single card, then stops.
+// Example 2:
+
+// Input: n = 6, k = 1, maxPts = 10
+// Output: 0.60000
+// Explanation: Alice gets a single card, then stops.
+// In 6 out of 10 possibilities, she is at or below 6 points.
+
+class Solution {
+public:
+    double new21Game(int N, int K, int W) {
+
+        if (K == 0 || N >= K + W) return 1.0;
+        vector<double> dp(N + 1);
+        dp[0] = 1.0;
+        double Wsum = 1.0, res = 0.0;
+        for (int i = 1; i <= N; ++i) {
+            dp[i] = Wsum / W;
+            if (i < K) Wsum += dp[i]; else res += dp[i];
+            if (i - W >= 0) Wsum -= dp[i - W];
+        }
+        return res;
+
+    }
+};