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53 lines
1.9 KiB
Markdown
Executable File
53 lines
1.9 KiB
Markdown
Executable File
# [668. Kth Smallest Number in Multiplication Table](https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/)
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## 题目
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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?
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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.
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**Example 1:**
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Input: m = 3, n = 3, k = 5
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Output:
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Explanation:
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The Multiplication Table:
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1 2 3
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2 4 6
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3 6 9
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The 5-th smallest number is 3 (1, 2, 2, 3, 3).
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**Example 2:**
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Input: m = 2, n = 3, k = 6
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Output:
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Explanation:
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The Multiplication Table:
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1 2 3
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2 4 6
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The 6-th smallest number is 6 (1, 2, 2, 3, 4, 6).
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**Note:**
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1. The `m` and `n` will be in the range [1, 30000].
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2. The `k` will be in the range [1, m * n]
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## 题目大意
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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。
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注意：
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- m 和 n 的范围在 [1, 30000] 之间。
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- k 的范围在 [1, m * n] 之间。
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## 解题思路
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- 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。
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- 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。
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