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Description: Algorithm for Interview and Operating Examination. Contribute to timerring/algorithms-notes development by creating an account on GitHub.

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GPL-3.0 license	https://github.com/timerring/algorithms-notes
	https://github.com/timerring/algorithms-notes#algorithms-notes
	https://github.com/timerring/algorithms-notes#overview
快速排序	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/quick_sort.md#%E5%BF%AB%E9%80%9F%E6%8E%92%E5%BA%8F
算法详解	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/quick_sort.md#%E7%AE%97%E6%B3%95%E8%AF%A6%E8%A7%A3
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例题：快速排序	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/quick_sort.md#%E4%BE%8B%E9%A2%98%E5%BF%AB%E9%80%9F%E6%8E%92%E5%BA%8F
练习：排序数组	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/quick_sort.md#%E7%BB%83%E4%B9%A0%E6%8E%92%E5%BA%8F%E6%95%B0%E7%BB%84
归并排序	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/merge_sort.md#%E5%BD%92%E5%B9%B6%E6%8E%92%E5%BA%8F
算法详解	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/merge_sort.md#%E7%AE%97%E6%B3%95%E8%AF%A6%E8%A7%A3
算法模板	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/merge_sort.md#%E7%AE%97%E6%B3%95%E6%A8%A1%E6%9D%BF
例题：归并排序	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/merge_sort.md#%E4%BE%8B%E9%A2%98%E5%BD%92%E5%B9%B6%E6%8E%92%E5%BA%8F
练习：逆序对	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/merge_sort.md#%E7%BB%83%E4%B9%A0%E9%80%86%E5%BA%8F%E5%AF%B9
练习：剑指 Offer 51. 数组中的逆序对	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/merge_sort.md#%E7%BB%83%E4%B9%A0%E5%89%91%E6%8C%87-offer-51-%E6%95%B0%E7%BB%84%E4%B8%AD%E7%9A%84%E9%80%86%E5%BA%8F%E5%AF%B9
二分查找	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E4%BA%8C%E5%88%86%E6%9F%A5%E6%89%BE
整数二分	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E6%95%B4%E6%95%B0%E4%BA%8C%E5%88%86
二分步骤	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E4%BA%8C%E5%88%86%E6%AD%A5%E9%AA%A4
浮点数二分	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E6%B5%AE%E7%82%B9%E6%95%B0%E4%BA%8C%E5%88%86
二分模板整理	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E4%BA%8C%E5%88%86%E6%A8%A1%E6%9D%BF%E6%95%B4%E7%90%86
例题：数的范围	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E4%BE%8B%E9%A2%98%E6%95%B0%E7%9A%84%E8%8C%83%E5%9B%B4
例题：开平方	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E4%BE%8B%E9%A2%98%E5%BC%80%E5%B9%B3%E6%96%B9
练习：数的三次方根	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E7%BB%83%E4%B9%A0%E6%95%B0%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9%E6%A0%B9
练习：剑指 Offer II 072. 求平方根	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/binary_search.md#%E7%BB%83%E4%B9%A0%E5%89%91%E6%8C%87-offer-ii-072-%E6%B1%82%E5%B9%B3%E6%96%B9%E6%A0%B9
高精度算法详解	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E9%AB%98%E7%B2%BE%E5%BA%A6%E7%AE%97%E6%B3%95%E8%AF%A6%E8%A7%A3
高精度加法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E9%AB%98%E7%B2%BE%E5%BA%A6%E5%8A%A0%E6%B3%95
高精度减法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E9%AB%98%E7%B2%BE%E5%BA%A6%E5%87%8F%E6%B3%95
高精度乘法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E9%AB%98%E7%B2%BE%E5%BA%A6%E4%B9%98%E6%B3%95
高精度除法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E9%AB%98%E7%B2%BE%E5%BA%A6%E9%99%A4%E6%B3%95
例题：高精度加法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E4%BE%8B%E9%A2%98%E9%AB%98%E7%B2%BE%E5%BA%A6%E5%8A%A0%E6%B3%95
例题：高精度减法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E4%BE%8B%E9%A2%98%E9%AB%98%E7%B2%BE%E5%BA%A6%E5%87%8F%E6%B3%95
例题：高精度乘法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E4%BE%8B%E9%A2%98%E9%AB%98%E7%B2%BE%E5%BA%A6%E4%B9%98%E6%B3%95
例题：高精度除法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/high_accuracy_algorithm.md#%E4%BE%8B%E9%A2%98%E9%AB%98%E7%B2%BE%E5%BA%A6%E9%99%A4%E6%B3%95
前缀和算法及模板详解	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/prefix_sum.md#%E5%89%8D%E7%BC%80%E5%92%8C%E7%AE%97%E6%B3%95%E5%8F%8A%E6%A8%A1%E6%9D%BF%E8%AF%A6%E8%A7%A3
一维前缀和	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/prefix_sum.md#%E4%B8%80%E7%BB%B4%E5%89%8D%E7%BC%80%E5%92%8C
二维前缀和	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/prefix_sum.md#%E4%BA%8C%E7%BB%B4%E5%89%8D%E7%BC%80%E5%92%8C
例题：前缀和	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/prefix_sum.md#%E4%BE%8B%E9%A2%98%E5%89%8D%E7%BC%80%E5%92%8C
例题：子矩阵的和	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/prefix_sum.md#%E4%BE%8B%E9%A2%98%E5%AD%90%E7%9F%A9%E9%98%B5%E7%9A%84%E5%92%8C
差分算法及模板应用	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/difference_algorithm.md#%E5%B7%AE%E5%88%86%E7%AE%97%E6%B3%95%E5%8F%8A%E6%A8%A1%E6%9D%BF%E5%BA%94%E7%94%A8
一维差分	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/difference_algorithm.md#%E4%B8%80%E7%BB%B4%E5%B7%AE%E5%88%86
二维差分	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/difference_algorithm.md#%E4%BA%8C%E7%BB%B4%E5%B7%AE%E5%88%86
例题：差分	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/difference_algorithm.md#%E4%BE%8B%E9%A2%98%E5%B7%AE%E5%88%86
例题：差分矩阵	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/difference_algorithm.md#%E4%BE%8B%E9%A2%98%E5%B7%AE%E5%88%86%E7%9F%A9%E9%98%B5
双指针算法	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/double_pointer.md#%E5%8F%8C%E6%8C%87%E9%92%88%E7%AE%97%E6%B3%95
基本思路	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/double_pointer.md#%E5%9F%BA%E6%9C%AC%E6%80%9D%E8%B7%AF%E9%87%87%E7%94%A8%E5%8F%8C%E6%8C%87%E9%92%88%E7%AE%97%E6%B3%95
模板应用	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/double_pointer.md#%E6%A8%A1%E6%9D%BF%E5%BA%94%E7%94%A8
最长连续不重复子序列	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/double_pointer.md#%E6%9C%80%E9%95%BF%E8%BF%9E%E7%BB%AD%E4%B8%8D%E9%87%8D%E5%A4%8D%E5%AD%90%E5%BA%8F%E5%88%97
数组元素的目标和	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/double_pointer.md#%E6%95%B0%E7%BB%84%E5%85%83%E7%B4%A0%E7%9A%84%E7%9B%AE%E6%A0%87%E5%92%8C
判断子序列	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/double_pointer.md#%E5%88%A4%E6%96%AD%E5%AD%90%E5%BA%8F%E5%88%97
位运算	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/bitwise_operation.md#%E4%BD%8D%E8%BF%90%E7%AE%97
lowbit(x)	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/bitwise_operation.md#lowbitx%E8%BF%94%E5%9B%9Ex%E7%9A%84%E6%9C%80%E5%90%8E%E4%B8%80%E4%BD%8D1
位运算模板	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/bitwise_operation.md#%E4%BD%8D%E8%BF%90%E7%AE%97%E6%A8%A1%E6%9D%BF
例题：二进制中1的个数	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/bitwise_operation.md#%E4%BE%8B%E9%A2%98%E4%BA%8C%E8%BF%9B%E5%88%B6%E4%B8%AD1%E7%9A%84%E4%B8%AA%E6%95%B0
离散化及模板详解	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/discretization.md#%E7%A6%BB%E6%95%A3%E5%8C%96%E5%8F%8A%E6%A8%A1%E6%9D%BF%E8%AF%A6%E8%A7%A3
基本思想	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/discretization.md#%E5%9F%BA%E6%9C%AC%E6%80%9D%E6%83%B3
算法思路	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/discretization.md#%E7%AE%97%E6%B3%95%E6%80%9D%E8%B7%AF
模板	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/discretization.md#%E6%A8%A1%E6%9D%BF
例题：区间和	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/discretization.md#%E4%BE%8B%E9%A2%98%E5%8C%BA%E9%97%B4%E5%92%8C
区间合并算法及模板应用	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/interval_merge.md#%E5%8C%BA%E9%97%B4%E5%90%88%E5%B9%B6%E7%AE%97%E6%B3%95%E5%8F%8A%E6%A8%A1%E6%9D%BF%E5%BA%94%E7%94%A8
基本思想	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/interval_merge.md#%E5%9F%BA%E6%9C%AC%E6%80%9D%E6%83%B3
算法思路	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/interval_merge.md#%E7%AE%97%E6%B3%95%E6%80%9D%E8%B7%AF
例题：区间合并	https://github.com/timerring/algorithms-notes/blob/main/basic/basic_algorithms/interval_merge.md#%E4%BE%8B%E9%A2%98%E5%8C%BA%E9%97%B4%E5%90%88%E5%B9%B6
单链表图解及模板总结	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/singly_linked_list.md#%E5%8D%95%E9%93%BE%E8%A1%A8%E5%9B%BE%E8%A7%A3%E5%8F%8A%E6%A8%A1%E6%9D%BF%E6%80%BB%E7%BB%93
静态链表	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/singly_linked_list.md#%E9%9D%99%E6%80%81%E9%93%BE%E8%A1%A8
链表与邻接表	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/singly_linked_list.md#%E9%93%BE%E8%A1%A8%E4%B8%8E%E9%82%BB%E6%8E%A5%E8%A1%A8
用数组模拟单链表	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/singly_linked_list.md#%E7%94%A8%E6%95%B0%E7%BB%84%E6%A8%A1%E6%8B%9F%E5%8D%95%E9%93%BE%E8%A1%A8
单链表模板总结	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/singly_linked_list.md#%E5%8D%95%E9%93%BE%E8%A1%A8%E6%A8%A1%E6%9D%BF%E6%80%BB%E7%BB%93
例题：单链表	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/singly_linked_list.md#%E4%BE%8B%E9%A2%98%E5%8D%95%E9%93%BE%E8%A1%A8
双链表图解及模板总结	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E5%8F%8C%E9%93%BE%E8%A1%A8%E5%9B%BE%E8%A7%A3%E5%8F%8A%E6%A8%A1%E6%9D%BF%E6%80%BB%E7%BB%93
双链表的参数	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E5%8F%8C%E9%93%BE%E8%A1%A8%E7%9A%84%E5%8F%82%E6%95%B0
双链表的初始化	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E5%8F%8C%E9%93%BE%E8%A1%A8%E7%9A%84%E5%88%9D%E5%A7%8B%E5%8C%96
节点k的右边插入一个数x	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E8%8A%82%E7%82%B9k%E7%9A%84%E5%8F%B3%E8%BE%B9%E6%8F%92%E5%85%A5%E4%B8%80%E4%B8%AA%E6%95%B0x
在k的左边插入一个数	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E5%9C%A8k%E7%9A%84%E5%B7%A6%E8%BE%B9%E6%8F%92%E5%85%A5%E4%B8%80%E4%B8%AA%E6%95%B0
删除节点k	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9k
模板总结	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E6%A8%A1%E6%9D%BF%E6%80%BB%E7%BB%93
例题：双链表	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/double_linked_list.md#%E4%BE%8B%E9%A2%98%E5%8F%8C%E9%93%BE%E8%A1%A8
单调栈模板	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/monotonic_stack.md#%E5%8D%95%E8%B0%83%E6%A0%88%E6%A8%A1%E6%9D%BF
栈算法模板	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/monotonic_stack.md#%E6%A0%88%E7%AE%97%E6%B3%95%E6%A8%A1%E6%9D%BF
例题：单调栈	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/monotonic_stack.md#%E4%BE%8B%E9%A2%98%E5%8D%95%E8%B0%83%E6%A0%88
队列算法模板	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/monotonic_queue.md#%E9%98%9F%E5%88%97%E7%AE%97%E6%B3%95%E6%A8%A1%E6%9D%BF
队列算法模板	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/monotonic_queue.md#%E9%98%9F%E5%88%97%E7%AE%97%E6%B3%95%E6%A8%A1%E6%9D%BF
例题：滑动窗口	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/monotonic_queue.md#%E4%BE%8B%E9%A2%98%E6%BB%91%E5%8A%A8%E7%AA%97%E5%8F%A3
KMP	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/KMP.md#kmp
最朴素的做法(暴力做法)	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/KMP.md#%E6%9C%80%E6%9C%B4%E7%B4%A0%E7%9A%84%E5%81%9A%E6%B3%95%E6%9A%B4%E5%8A%9B%E5%81%9A%E6%B3%95
KMP算法	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/KMP.md#kmp%E7%AE%97%E6%B3%95
KMP	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/KMP.md#kmp
Trie树（字典树）	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/trie_tree.md#trie%E6%A0%91%E5%AD%97%E5%85%B8%E6%A0%91
基本思想	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/trie_tree.md#%E5%9F%BA%E6%9C%AC%E6%80%9D%E6%83%B3
模板总结	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/trie_tree.md#%E6%A8%A1%E6%9D%BF%E6%80%BB%E7%BB%93
关于idx的理解	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/trie_tree.md#%E5%85%B3%E4%BA%8Eidx%E7%9A%84%E7%90%86%E8%A7%A3
例题 Trie字符串统计	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/trie_tree.md#%E4%BE%8B%E9%A2%98-trie%E5%AD%97%E7%AC%A6%E4%B8%B2%E7%BB%9F%E8%AE%A1
应用最大异或对	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/trie_tree.md#%E5%BA%94%E7%94%A8-%E6%9C%80%E5%A4%A7%E5%BC%82%E6%88%96%E5%AF%B9
并查集	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/union_find_disjoint_sets.md#%E5%B9%B6%E6%9F%A5%E9%9B%86
优化方法	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/union_find_disjoint_sets.md#%E4%BC%98%E5%8C%96%E6%96%B9%E6%B3%95
模板总结	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/union_find_disjoint_sets.md#%E6%A8%A1%E6%9D%BF%E6%80%BB%E7%BB%93
例题：合并集合	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/union_find_disjoint_sets.md#%E4%BE%8B%E9%A2%98%E5%90%88%E5%B9%B6%E9%9B%86%E5%90%88
例题：连通块中点的数量	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/union_find_disjoint_sets.md#%E4%BE%8B%E9%A2%98%E8%BF%9E%E9%80%9A%E5%9D%97%E4%B8%AD%E7%82%B9%E7%9A%84%E6%95%B0%E9%87%8F
例题：食物链	https://github.com/timerring/algorithms-notes/blob/main/basic/data_structure/union_find_disjoint_sets.md#%E4%BE%8B%E9%A2%98%E9%A3%9F%E7%89%A9%E9%93%BE
	https://github.com/timerring/algorithms-notes#参考书籍
李煜东. 算法竞赛进阶指南[M]. 河南：电子音像出版社, 2018.	https://github.com/timerring/algorithms-notes/blob/main/reference/algorithm_competition_guidelines.pdf
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