From 319a2cc242bc18aa19c8ea3135f5914434cfe718 Mon Sep 17 00:00:00 2001
From: YDZ <ydz627@gmail.com>
Date: Thu, 7 Nov 2019 12:06:01 +0800
Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=20problem=20668?=
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---
 ...Smallest Number in Multiplication Table.go | 24 +++++++
 ...est Number in Multiplication Table_test.go | 64 +++++++++++++++++++
 .../README.md                                 | 52 +++++++++++++++
 3 files changed, 140 insertions(+)
 create mode 100644 Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table.go
 create mode 100644 Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table_test.go
 create mode 100755 Algorithms/0668. Kth Smallest Number in Multiplication Table/README.md

diff --git a/Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table.go b/Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table.go
new file mode 100644
index 00000000..c6c63d70
--- /dev/null
+++ b/Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table.go	
@@ -0,0 +1,24 @@
+package leetcode
+
+import "math"
+
+func findKthNumber(m int, n int, k int) int {
+	low, high := 1, m*n
+	for low < high {
+		mid := low + (high-low)>>1
+		if counterKthNum(m, n, mid) >= k {
+			high = mid
+		} else {
+			low = mid + 1
+		}
+	}
+	return low
+}
+
+func counterKthNum(m, n, mid int) int {
+	count := 0
+	for i := 1; i <= m; i++ {
+		count += int(math.Min(math.Floor(float64(mid)/float64(i)), float64(n)))
+	}
+	return count
+}
diff --git a/Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table_test.go b/Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table_test.go
new file mode 100644
index 00000000..8285b611
--- /dev/null
+++ b/Algorithms/0668. Kth Smallest Number in Multiplication Table/668. Kth Smallest Number in Multiplication Table_test.go	
@@ -0,0 +1,64 @@
+package leetcode
+
+import (
+	"fmt"
+	"testing"
+)
+
+type question668 struct {
+	para668
+	ans668
+}
+
+// para 是参数
+// one 代表第一个参数
+type para668 struct {
+	m int
+	n int
+	k int
+}
+
+// ans 是答案
+// one 代表第一个答案
+type ans668 struct {
+	one int
+}
+
+func Test_Problem668(t *testing.T) {
+
+	qs := []question668{
+
+		question668{
+			para668{3, 3, 5},
+			ans668{3},
+		},
+
+		question668{
+			para668{2, 3, 6},
+			ans668{6},
+		},
+
+		question668{
+			para668{1, 3, 2},
+			ans668{2},
+		},
+
+		question668{
+			para668{42, 34, 401},
+			ans668{126},
+		},
+
+		question668{
+			para668{7341, 13535, 12330027},
+			ans668{2673783},
+		},
+	}
+
+	fmt.Printf("------------------------Leetcode Problem 668------------------------\n")
+
+	for _, q := range qs {
+		_, p := q.ans668, q.para668
+		fmt.Printf("【input】:%v       【output】:%v\n", p, findKthNumber(p.m, p.n, p.k))
+	}
+	fmt.Printf("\n\n\n")
+}
diff --git a/Algorithms/0668. Kth Smallest Number in Multiplication Table/README.md b/Algorithms/0668. Kth Smallest Number in Multiplication Table/README.md
new file mode 100755
index 00000000..2d1f3526
--- /dev/null
+++ b/Algorithms/0668. Kth Smallest Number in Multiplication Table/README.md	
@@ -0,0 +1,52 @@
+# [668. Kth Smallest Number in Multiplication Table](https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/)
+
+
+## 题目:
+
+Nearly every one have used the [Multiplication Table](https://en.wikipedia.org/wiki/Multiplication_table). But could you find out the `k-th` smallest number quickly from the multiplication table?
+
+Given the height `m` and the length `n` of a `m * n` Multiplication Table, and a positive integer `k`, you need to return the `k-th` smallest number in this table.
+
+**Example 1:**
+
+    Input: m = 3, n = 3, k = 5
+    Output: 
+    Explanation: 
+    The Multiplication Table:
+    1	2	3
+    2	4	6
+    3	6	9
+    
+    The 5-th smallest number is 3 (1, 2, 2, 3, 3).
+
+**Example 2:**
+
+    Input: m = 2, n = 3, k = 6
+    Output: 
+    Explanation: 
+    The Multiplication Table:
+    1	2	3
+    2	4	6
+    
+    The 6-th smallest number is 6 (1, 2, 2, 3, 4, 6).
+
+**Note:**
+
+1. The `m` and `n` will be in the range [1, 30000].
+2. The `k` will be in the range [1, m * n]
+
+
+## 题目大意
+
+几乎每一个人都用乘法表。但是你能在乘法表中快速找到第 k 小的数字吗？给定高度 m 、宽度 n 的一张 m * n 的乘法表，以及正整数 k，你需要返回表中第 k 小的数字。
+
+
+注意：
+
+- m 和 n 的范围在 [1, 30000] 之间。
+- k 的范围在 [1, m * n] 之间。
+
+## 解题思路
+
+- 给出 3 个数字，m，n，k。m  和 n 分别代表乘法口诀表的行和列。要求在这个乘法口诀表中找第 k 小的数字。
+- 这一题是第 378 题变种题。利用二分搜索，在 `[1,m*n]` 的区间内搜索第 `k` 小的数。每次二分统计 `≤ mid` 数字的个数。由于是在两数乘法构成的矩阵中计数，知道乘数，被乘数也就知道了，所以计数只需要一层循环。整体代码和第 378 题完全一致，只是计数的部分不同罢了。可以对比第 378 题一起练习。