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‎Problemset/1862-Sum of Floored Pairs/README.md

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# 1862. Sum of Floored Pairs
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Given an integer array `nums`, return the sum of `floor(nums[i] / nums[j])` for all pairs of indices `0 <= i, j < nums.length` in the array. Since the answer may be too large, return it **modulo** <code>10<sup>9</sup> + 7</code>.
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The `floor()` function returns the integer part of the division.
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#### Example 1:
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<pre>
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<strong>Input:</strong> nums = [2,5,9]
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<strong>Output:</strong> 10
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<strong>Explanation:</strong>
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floor(2 / 5) = floor(2 / 9) = floor(5 / 9) = 0
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floor(2 / 2) = floor(5 / 5) = floor(9 / 9) = 1
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floor(5 / 2) = 2
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floor(9 / 2) = 4
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floor(9 / 5) = 1
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We calculate the floor of the division for every pair of indices in the array then sum them up.
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</pre>
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#### Example 2:
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<pre>
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<strong>Input:</strong> nums = [7,7,7,7,7,7,7]
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<strong>Output:</strong> 49
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</pre>
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#### Constraints:
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* <code>1 <= nums.length <= 10<sup>5</sup></code>
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* <code>1 <= nums[i] <= 10<sup>5</sup></code>
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## Solutions (Python)
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### 1. Solution
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```Python
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class Solution:
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def sumOfFlooredPairs(self, nums: List[int]) -> int:
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prevsum = 0
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ret = 0
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nums.sort()
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for j in range(len(nums)):
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if j > 0 and nums[j] == nums[j - 1]:
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ret = (ret + prevsum) % 1000000007
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continue
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i = bisect.bisect(nums, nums[j] - 1)
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prevsum = 0
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for x in range(1, nums[-1] // nums[j] + 1):
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k = bisect.bisect(nums, nums[j] * (x + 1) - 1, lo=i)
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prevsum = (prevsum + x * (k - i)) % 1000000007
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i = k
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ret = (ret + prevsum) % 1000000007
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return ret
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```

‎Problemset/1862-Sum of Floored Pairs/README_CN.md

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# 1862. 向下取整数对和
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给你一个整数数组 `nums` ，请你返回所有下标对 `0 <= i, j < nums.length` 的 `floor(nums[i] / nums[j])` 结果之和。由于答案可能会很大，请你返回答案对<code>10<sup>9</sup> + 7</code> **取余** 的结果。
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函数 `floor()` 返回输入数字的整数部分。
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#### 示例 1:
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<pre>
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<strong>输入:</strong> nums = [2,5,9]
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<strong>输出:</strong> 10
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<strong>解释:</strong>
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floor(2 / 5) = floor(2 / 9) = floor(5 / 9) = 0
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floor(2 / 2) = floor(5 / 5) = floor(9 / 9) = 1
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floor(5 / 2) = 2
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floor(9 / 2) = 4
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floor(9 / 5) = 1
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我们计算每一个数对商向下取整的结果并求和得到 10 。
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</pre>
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#### 示例 2:
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<pre>
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<strong>输入:</strong> nums = [7,7,7,7,7,7,7]
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<strong>输出:</strong> 49
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</pre>
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#### 提示:
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* <code>1 <= nums.length <= 10<sup>5</sup></code>
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* <code>1 <= nums[i] <= 10<sup>5</sup></code>
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## 题解 (Python)
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### 1. 题解
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```Python
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class Solution:
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def sumOfFlooredPairs(self, nums: List[int]) -> int:
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prevsum = 0
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ret = 0
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nums.sort()
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for j in range(len(nums)):
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if j > 0 and nums[j] == nums[j - 1]:
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ret = (ret + prevsum) % 1000000007
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continue
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i = bisect.bisect(nums, nums[j] - 1)
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prevsum = 0
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for x in range(1, nums[-1] // nums[j] + 1):
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k = bisect.bisect(nums, nums[j] * (x + 1) - 1, lo=i)
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prevsum = (prevsum + x * (k - i)) % 1000000007
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i = k
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ret = (ret + prevsum) % 1000000007
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return ret
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```

‎Problemset/1862-Sum of Floored Pairs/Solution.py

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class Solution:
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def sumOfFlooredPairs(self, nums: List[int]) -> int:
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prevsum = 0
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ret = 0
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nums.sort()
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for j in range(len(nums)):
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if j > 0 and nums[j] == nums[j - 1]:
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ret = (ret + prevsum) % 1000000007
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continue
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i = bisect.bisect(nums, nums[j] - 1)
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prevsum = 0
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for x in range(1, nums[-1] // nums[j] + 1):
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k = bisect.bisect(nums, nums[j] * (x + 1) - 1, lo=i)
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prevsum = (prevsum + x * (k - i)) % 1000000007
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i = k
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ret = (ret + prevsum) % 1000000007
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return ret

‎README.md

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[1859][1859l]|[Sorting the Sentence][1859] |![py]
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[1860][1860l]|[Incremental Memory Leak][1860] |![rs]
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[1861][1861l]|[Rotating the Box][1861] |![rs]
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[1862][1862l]|[Sum of Floored Pairs][1862] |![py]
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[1863][1863l]|[Sum of All Subset XOR Totals][1863] |![py]
12241225
[1864][1864l]|[Minimum Number of Swaps to Make the Binary String Alternating][1864] |![rs]
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[1865][1865l]|[Finding Pairs With a Certain Sum][1865] |![rs]
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[1859]:Problemset/1859-Sorting%20the%20Sentence/README.md#1859-sorting-the-sentence
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[1860]:Problemset/1860-Incremental%20Memory%20Leak/README.md#1860-incremental-memory-leak
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[1861]:Problemset/1861-Rotating%20the%20Box/README.md#1861-rotating-the-box
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[1862]:Problemset/1862-Sum%20of%20Floored%20Pairs/README.md#1862-sum-of-floored-pairs
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[1863]:Problemset/1863-Sum%20of%20All%20Subset%20XOR%20Totals/README.md#1863-sum-of-all-subset-xor-totals
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[1864]:Problemset/1864-Minimum%20Number%20of%20Swaps%20to%20Make%20the%20Binary%20String%20Alternating/README.md#1864-minimum-number-of-swaps-to-make-the-binary-string-alternating
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[1865]:Problemset/1865-Finding%20Pairs%20With%20a%20Certain%20Sum/README.md#1865-finding-pairs-with-a-certain-sum
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[1859l]:https://leetcode.com/problems/sorting-the-sentence/
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[1860l]:https://leetcode.com/problems/incremental-memory-leak/
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[1861l]:https://leetcode.com/problems/rotating-the-box/
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[1862l]:https://leetcode.com/problems/sum-of-floored-pairs/
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[1863l]:https://leetcode.com/problems/sum-of-all-subset-xor-totals/
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[1864l]:https://leetcode.com/problems/minimum-number-of-swaps-to-make-the-binary-string-alternating/
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[1865l]:https://leetcode.com/problems/finding-pairs-with-a-certain-sum/

‎README_CN.md

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[1859][1859l]|[将句子排序][1859] |![py]
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[1860][1860l]|[增长的内存泄露][1860] |![rs]
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[1861][1861l]|[旋转盒子][1861] |![rs]
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[1862][1862l]|[向下取整数对和][1862] |![py]
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[1863][1863l]|[找出所有子集的异或总和再求和][1863] |![py]
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[1864][1864l]|[构成交替字符串需要的最小交换次数][1864] |![rs]
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[1865][1865l]|[找出和为指定值的下标对][1865] |![rs]
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[1859]:Problemset/1859-Sorting%20the%20Sentence/README_CN.md#1859-将句子排序
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[1860]:Problemset/1860-Incremental%20Memory%20Leak/README_CN.md#1860-增长的内存泄露
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[1861]:Problemset/1861-Rotating%20the%20Box/README_CN.md#1861-旋转盒子
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[1862]:Problemset/1862-Sum%20of%20Floored%20Pairs/README_CN.md#1862-向下取整数对和
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[1863]:Problemset/1863-Sum%20of%20All%20Subset%20XOR%20Totals/README_CN.md#1863-找出所有子集的异或总和再求和
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[1864]:Problemset/1864-Minimum%20Number%20of%20Swaps%20to%20Make%20the%20Binary%20String%20Alternating/README_CN.md#1864-构成交替字符串需要的最小交换次数
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[1865]:Problemset/1865-Finding%20Pairs%20With%20a%20Certain%20Sum/README_CN.md#1865-找出和为指定值的下标对
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[1859l]:https://leetcode.cn/problems/sorting-the-sentence/
45874589
[1860l]:https://leetcode.cn/problems/incremental-memory-leak/
45884590
[1861l]:https://leetcode.cn/problems/rotating-the-box/
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[1862l]:https://leetcode.cn/problems/sum-of-floored-pairs/
45894592
[1863l]:https://leetcode.cn/problems/sum-of-all-subset-xor-totals/
45904593
[1864l]:https://leetcode.cn/problems/minimum-number-of-swaps-to-make-the-binary-string-alternating/
45914594
[1865l]:https://leetcode.cn/problems/finding-pairs-with-a-certain-sum/

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