From 5093a177676af4604914729d5104f157b6fb55bf Mon Sep 17 00:00:00 2001
From: kr0st <kr0st@bioreactor.me>
Date: Sun, 9 Oct 2022 20:06:42 +0300
Subject: [PATCH] "837. New 21 Game" medium, trying to solve with probability
 manipulation

---
 837-new-21-game.go      | 85 +++++++++++++++++++++++++++++++++++++++--
 837-new-21-game_test.go |  2 +-
 2 files changed, 83 insertions(+), 4 deletions(-)

diff --git a/837-new-21-game.go b/837-new-21-game.go
index dd6305a..8f65ecf 100644
--- a/837-new-21-game.go
+++ b/837-new-21-game.go
@@ -3,6 +3,7 @@ package main
 import (
 	"math"
 	"math/rand"
+	"strconv"
 	"time"
 )
 
@@ -302,7 +303,7 @@ func new21GameExperimental(n int, k int, maxPts int, rngType RngType) float64 {
 	makeExperiment := func() float64 {
 
 		var sum uint64
-		for sum = 0; sum <= uintK; sum += getNextRandom() {
+		for sum = 0; sum < uintK; sum += getNextRandom() {
 		}
 
 		kOrMoreCount++
@@ -333,6 +334,84 @@ func new21GameExperimental(n int, k int, maxPts int, rngType RngType) float64 {
 	return probability
 }
 
-func New21Game(n int, k int, maxPts int) float64 {
-	return new21GameExperimental(n, k, maxPts, FastRng)
+func new21RecursiveBruteforceV2(n int, k int, p int, s int, str string) (int, int) {
+	moreThanK := 0
+	lessThanN := 0
+
+	if p <= 0 || n <= 0 || k <= 0 || s >= k {
+		return 0, 0
+	}
+
+	sum := s + p
+
+	if sum >= k {
+		str += strconv.Itoa(p) + "=" + strconv.Itoa(sum)
+		println(str)
+		moreThanK++
+		if sum <= n {
+			lessThanN++
+		}
+	} else {
+		str += strconv.Itoa(p) + "+"
+
+		for i := p; i > 0; i-- {
+			retMoreThanK, retLessThanN := new21RecursiveBruteforceV2(n, k, i, sum, str)
+			moreThanK += retMoreThanK
+			lessThanN += retLessThanN
+		}
+
+		return moreThanK, lessThanN
+	}
+
+	return moreThanK, lessThanN
+}
+
+func new21GameBruteforce(n int, k int, maxPts int) float64 {
+	moreThanK, lessThanN := 0, 0
+	for m := maxPts; m > 0; m-- {
+		retMoreThanK, retLessThanN := new21RecursiveBruteforceV2(n, k, m, 0, "")
+		moreThanK += retMoreThanK
+		lessThanN += retLessThanN
+	}
+
+	return float64(lessThanN) / float64(moreThanK)
+}
+
+func New21Game(n int, k int, maxPts int) float64 {
+	if k < 0 || n < 0 || maxPts < 0 {
+		return 0
+	}
+
+	if k == 0 {
+		return 1
+	}
+
+	if maxPts == 0 {
+		return 0
+	}
+
+	if n < k {
+		return 1
+	}
+
+	p := make([]float64, n+1)
+	m := float64(maxPts)
+
+	p[0] = 1
+	p[1] = p[0] / m
+
+	for i := 2; i <= k; i++ {
+		p[i] = p[i-1] + p[i-1]/m
+	}
+
+	for i := k + 1; i <= n; i++ {
+		p[i] = p[i-1] + p[i-1]/m - p[i-k]
+	}
+
+	sumP := float64(0)
+	for i := k; i <= n; i++ {
+		sumP += p[i]
+	}
+
+	return sumP
 }
diff --git a/837-new-21-game_test.go b/837-new-21-game_test.go
index 882f2dc..24e2da6 100644
--- a/837-new-21-game_test.go
+++ b/837-new-21-game_test.go
@@ -6,7 +6,7 @@ import (
 )
 
 func TestNew21Game(t *testing.T) {
-	//	assert.Equal(t, 1.0, New21Game(10, 1, 10))
+	assert.Equal(t, 1.0, New21Game(10, 1, 10))
 	assert.Equal(t, 0.6, New21Game(6, 1, 10))
 	assert.Equal(t, 0.73278, New21Game(21, 17, 10))
 }