"837. New 21 Game" medium, accepted solution.

837-new-21-game.go

@@ -394,18 +394,25 @@ func New21Game(n int, k int, maxPts int) float64 {
 		return 1
 	}
 
-	p := make([]float64, n+1)
+	if n >= k+maxPts {
+		return 1
+	}
+
+	p := make([]float64, k+maxPts)
 	m := float64(maxPts)
 
 	p[0] = 1
-	p[1] = p[0] / m
+	sum := 1.0
 
-	for i := 2; i <= k; i++ {
+	for i := 1; i <= n; i++ {
-		p[i] = p[i-1] + p[i-1]/m
+		p[i] = sum / m
+		sum += p[i]
+		if i-maxPts >= 0 {
+			sum -= p[i-maxPts]
+		}
+		if i >= k {
+			sum -= p[i]
 		}
-
-	for i := k + 1; i <= n; i++ {
-		p[i] = p[i-1] + p[i-1]/m - p[i-k]
 	}
 
 	sumP := float64(0)