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feat: add solutions to lc problem: No.0668
No.0668.Kth Smallest Number in Multiplication Table
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‎solution/0600-0699/0668.Kth Smallest Number in Multiplication Table/README.md

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<!-- 这里可写通用的实现逻辑 -->
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**方法一：二分查找**
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题目可以转换为，求有多少个数不超过 x。对于每一行 i，所有数都是 i 的倍数，不超过 x 的个数有 `x / i` 个。
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二分枚举 x，累加每一行不超过 x 的个数，得到 cnt。找到 `cnt >= k` 的最小 x。
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<!-- tabs:start -->
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### **Python3**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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class Solution:
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def findKthNumber(self, m: int, n: int, k: int) -> int:
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left, right = 1, m * n
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while left < right:
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mid = (left + right) >> 1
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cnt = 0
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for i in range(1, m + 1):
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cnt += min(mid // i, n)
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if cnt >= k:
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right = mid
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else:
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left = mid + 1
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return left
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```
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### **Java**
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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```java
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class Solution {
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public int findKthNumber(int m, int n, int k) {
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int left = 1, right = m * n;
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while (left < right) {
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int mid = (left + right) >>> 1;
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int cnt = 0;
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for (int i = 1; i <= m; ++i) {
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cnt += Math.min(mid / i, n);
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}
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if (cnt >= k) {
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right = mid;
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} else {
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left = mid + 1;
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}
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}
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return left;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int findKthNumber(int m, int n, int k) {
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int left = 1, right = m * n;
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while (left < right)
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{
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int mid = (left + right) >> 1;
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int cnt = 0;
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for (int i = 1; i <= m; ++i) cnt += min(mid / i, n);
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if (cnt >= k) right = mid;
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else left = mid + 1;
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}
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return left;
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}
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};
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```
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### **Go**
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```go
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func findKthNumber(m int, n int, k int) int {
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left, right := 1, m*n
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for left < right {
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mid := (left + right) >> 1
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cnt := 0
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for i := 1; i <= m; i++ {
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cnt += min(mid/i, n)
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}
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if cnt >= k {
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right = mid
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} else {
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left = mid + 1
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}
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}
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return left
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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```
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### **...**

‎solution/0600-0699/0668.Kth Smallest Number in Multiplication Table/README_EN.md

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## Solutions
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Binary search.
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<!-- tabs:start -->
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### **Python3**
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```python
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class Solution:
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def findKthNumber(self, m: int, n: int, k: int) -> int:
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left, right = 1, m * n
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while left < right:
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mid = (left + right) >> 1
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cnt = 0
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for i in range(1, m + 1):
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cnt += min(mid // i, n)
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if cnt >= k:
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right = mid
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else:
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left = mid + 1
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return left
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```
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### **Java**
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```java
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class Solution {
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public int findKthNumber(int m, int n, int k) {
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int left = 1, right = m * n;
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while (left < right) {
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int mid = (left + right) >>> 1;
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int cnt = 0;
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for (int i = 1; i <= m; ++i) {
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cnt += Math.min(mid / i, n);
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}
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if (cnt >= k) {
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right = mid;
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} else {
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left = mid + 1;
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}
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}
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return left;
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}
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}
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```
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### **C++**
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```cpp
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class Solution {
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public:
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int findKthNumber(int m, int n, int k) {
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int left = 1, right = m * n;
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while (left < right)
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{
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int mid = (left + right) >> 1;
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int cnt = 0;
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for (int i = 1; i <= m; ++i) cnt += min(mid / i, n);
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if (cnt >= k) right = mid;
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else left = mid + 1;
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}
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return left;
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}
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};
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```
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### **Go**
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```go
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func findKthNumber(m int, n int, k int) int {
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left, right := 1, m*n
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for left < right {
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mid := (left + right) >> 1
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cnt := 0
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for i := 1; i <= m; i++ {
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cnt += min(mid/i, n)
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}
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if cnt >= k {
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right = mid
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} else {
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left = mid + 1
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}
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}
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return left
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}
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```
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### **...**

‎solution/0600-0699/0668.Kth Smallest Number in Multiplication Table/Solution.cpp

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class Solution {
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public:
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int findKthNumber(int m, int n, int k) {
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int left = 1, right = m * n;
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while (left < right)
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{
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int mid = (left + right) >> 1;
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int cnt = 0;
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for (int i = 1; i <= m; ++i) cnt += min(mid / i, n);
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if (cnt >= k) right = mid;
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else left = mid + 1;
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}
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return left;
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}
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};

‎solution/0600-0699/0668.Kth Smallest Number in Multiplication Table/Solution.go

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func findKthNumber(m int, n int, k int) int {
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left, right := 1, m*n
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for left < right {
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mid := (left + right) >> 1
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cnt := 0
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for i := 1; i <= m; i++ {
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cnt += min(mid/i, n)
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}
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if cnt >= k {
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right = mid
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} else {
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left = mid + 1
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}
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}
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return left
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}
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func min(a, b int) int {
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if a < b {
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return a
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}
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return b
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}

‎solution/0600-0699/0668.Kth Smallest Number in Multiplication Table/Solution.java

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class Solution {
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public int findKthNumber(int m, int n, int k) {
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int left = 1, right = m * n;
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while (left < right) {
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int mid = (left + right) >>> 1;
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int cnt = 0;
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for (int i = 1; i <= m; ++i) {
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cnt += Math.min(mid / i, n);
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}
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if (cnt >= k) {
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right = mid;
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} else {
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left = mid + 1;
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}
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}
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return left;
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}
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}

‎solution/0600-0699/0668.Kth Smallest Number in Multiplication Table/Solution.py

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class Solution:
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def findKthNumber(self, m: int, n: int, k: int) -> int:
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left, right = 1, m * n
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while left < right:
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mid = (left + right) >> 1
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cnt = 0
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for i in range(1, m + 1):
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cnt += min(mid // i, n)
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if cnt >= k:
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right = mid
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else:
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left = mid + 1
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return left

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