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50 lines
1.4 KiB
Markdown
50 lines
1.4 KiB
Markdown
# [923. 3Sum With Multiplicity](https://leetcode.com/problems/3sum-with-multiplicity/)
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## 题目
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Given an integer array A, and an integer target, return the number of tuples i, j, k such that i < j < k and A[i] + A[j] + A[k] == target.
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As the answer can be very large, return it modulo 10^9 + 7.
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Example 1:
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```c
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Input: A = [1,1,2,2,3,3,4,4,5,5], target = 8
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Output: 20
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Explanation:
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Enumerating by the values (A[i], A[j], A[k]):
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(1, 2, 5) occurs 8 times;
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(1, 3, 4) occurs 8 times;
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(2, 2, 4) occurs 2 times;
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(2, 3, 3) occurs 2 times.
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```
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Example 2:
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```c
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Input: A = [1,1,2,2,2,2], target = 5
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Output: 12
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Explanation:
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A[i] = 1, A[j] = A[k] = 2 occurs 12 times:
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We choose one 1 from [1,1] in 2 ways,
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and two 2s from [2,2,2,2] in 6 ways.
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```
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Note:
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- 3 <= A.length <= 3000
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- 0 <= A[i] <= 100
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- 0 <= target <= 300
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## 题目大意
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这道题是第 15 题的升级版。给出一个数组，要求找到 3 个数相加的和等于 target 的解组合的个数，并且要求 i < j < k。解的组合个数不需要去重，相同数值不同下标算不同解(这里也是和第 15 题的区别)
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## 解题思路
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这一题大体解法和第 15 题一样的，只不过算所有解组合的时候需要一点排列组合的知识，如果取 3 个一样的数，需要计算 C n 3，去 2 个相同的数字的时候，计算 C n 2，取一个数字就正常计算。最后所有解的个数都加起来就可以了。
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