470 finish

Author: aQua

Algorithms/0470.implement-rand10-using-rand7/README.md

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+# [470. Implement Rand10() Using Rand7()](https://leetcode.com/problems/implement-rand10-using-rand7/)
+
+## 题目
+
+Given a function rand7 which generates a uniform random integer in the range 1 to 7, write a function rand10which generates a uniform random integer in the range 1 to 10.
+
+Do NOT use system's Math.random().
+
+Example 1:
+
+```text
+Input: 1
+Output: [7]
+```
+
+Example 2:
+
+```text
+Input: 2
+Output: [8,4]
+```
+
+Example 3:
+
+```text
+Input: 3
+Output: [8,1,10]
+```
+
+Note:
+
+1. rand7 is predefined.
+1. Each testcase has one argument:n, the number of times that rand10 is called.
+
+Follow up:
+
+1. What is the expected valuefor the number of calls torand7()function?
+1. Could you minimize the number of calls to rand7()?
+
+## 解题思路
+
+见程序注释

Algorithms/0470.implement-rand10-using-rand7/implement-rand10-using-rand7.go

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+package problem0470
+
+import "math/rand"
+
+func rand10() int {
+	t := 50
+	for t > 39 {
+		t = 7*(rand7()-1) + (rand7() - 1)
+		// t 的取值范围为 [0,48]，每个数字出现的概率都是为 1/49
+	}
+	// t 的范围是 [0,39]，t 出现在这个范围内的概率是 40/49
+	// 当 t 为 3, 13, 23 或 33 的时候， t%10+1 == 4
+	// 返回 4 的概率 = (4 * 1/49) / (40/49) == 1/10
+	// 同理可知，返回 [1,10] 中每个数字的概率都是 1/10
+	// 符合题意
+	return t%10 + 1
+}
+
+func rand7() int {
+	return rand.Intn(7) + 1
+}

Algorithms/0470.implement-rand10-using-rand7/implement-rand10-using-rand7_test.go

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+package problem0470
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/assert"
+)
+
+func Test_rand10(t *testing.T) {
+	ast := assert.New(t)
+	for i := 0; i < 100; i++ {
+		r := rand10()
+		ast.True(1 <= r && r <= 10)
+	}
+}
+
+func Benchmark_rand10(b *testing.B) {
+	for i := 0; i < b.N; i++ {
+		rand10()
+	}
+}