From 698c2e7fe5b17e10989154a9364ac1ba157a7bba Mon Sep 17 00:00:00 2001 From: krahets Date: Mon, 5 Jun 2023 01:03:39 +0800 Subject: [PATCH] Fix some codes and a figure. --- .../chapter_searching/binary_search_edge.js | 38 +++++++++--------- codes/javascript/chapter_sorting/heap_sort.js | 12 +++--- .../chapter_sorting/selection_sort.js | 8 ++-- .../chapter_searching/binary_search_edge.ts | 8 ++-- codes/typescript/chapter_sorting/heap_sort.ts | 14 +++---- .../chapter_sorting/selection_sort.ts | 10 ++--- .../time_complexity.md | 4 +- .../1s_2s_complement.png | Bin 64536 -> 62416 bytes 8 files changed, 48 insertions(+), 46 deletions(-) diff --git a/codes/javascript/chapter_searching/binary_search_edge.js b/codes/javascript/chapter_searching/binary_search_edge.js index d82d60469..179543235 100644 --- a/codes/javascript/chapter_searching/binary_search_edge.js +++ b/codes/javascript/chapter_searching/binary_search_edge.js @@ -5,39 +5,41 @@ */ /* 二分查找最左一个元素 */ -function binary_search_left_edge(nums, target) { - let i = 0, j = nums.length - 1; // 初始化双闭区间 [0, n-1] +function binarySearchLeftEdge(nums, target) { + let i = 0, + j = nums.length - 1; // 初始化双闭区间 [0, n-1] while (i <= j) { - let m = Math.floor((i + j) / 2); // 计算中点索引 m + let m = Math.floor((i + j) / 2); // 计算中点索引 m if (nums[m] < target) { - i = m + 1; // target 在区间 [m+1, j] 中 + i = m + 1; // target 在区间 [m+1, j] 中 } else if (nums[m] > target) { - j = m - 1; // target 在区间 [i, m-1] 中 + j = m - 1; // target 在区间 [i, m-1] 中 } else { - j = m - 1; // 首个小于 target 的元素在区间 [i, m-1] 中 + j = m - 1; // 首个小于 target 的元素在区间 [i, m-1] 中 } } if (i == nums.length || nums[i] != target) { - return -1; // 未找到目标元素,返回 -1 + return -1; // 未找到目标元素,返回 -1 } return i; } /* 二分查找最右一个元素 */ -function binary_search_right_edge(nums, target) { - let i = 0, j = nums.length - 1; // 初始化双闭区间 [0, n-1] +function binarySearchRightEdge(nums, target) { + let i = 0, + j = nums.length - 1; // 初始化双闭区间 [0, n-1] while (i <= j) { - let m = Math.floor((i + j) / 2); // 计算中点索引 m + let m = Math.floor((i + j) / 2); // 计算中点索引 m if (nums[m] < target) { - i = m + 1; // target 在区间 [m+1, j] 中 + i = m + 1; // target 在区间 [m+1, j] 中 } else if (nums[m] > target) { - j = m - 1; // target 在区间 [i, m-1] 中 + j = m - 1; // target 在区间 [i, m-1] 中 } else { - i = m + 1; // 首个大于 target 的元素在区间 [m+1, j] 中 + i = m + 1; // 首个大于 target 的元素在区间 [m+1, j] 中 } } if (j == nums.length || nums[j] != target) { - return -1; // 未找到目标元素,返回 -1 + return -1; // 未找到目标元素,返回 -1 } return j; } @@ -47,9 +49,9 @@ let target = 6; const nums = [1, 3, 6, 6, 6, 6, 6, 10, 12, 15]; // 二分查找最左一个元素 -let index_left = binary_search_left_edge(nums, target); -console.log("数组中最左一个元素 6 的索引 = ", index_left); +let index_left = binarySearchLeftEdge(nums, target); +console.log('数组中最左一个元素 6 的索引 = ', index_left); // 二分查找最右一个元素 -let index_right = binary_search_right_edge(nums, target); -console.log("数组中最右一个元素 6 的索引 = ", index_right); +let index_right = binarySearchRightEdge(nums, target); +console.log('数组中最右一个元素 6 的索引 = ', index_right); diff --git a/codes/javascript/chapter_sorting/heap_sort.js b/codes/javascript/chapter_sorting/heap_sort.js index 2b83c3e73..ce7ab482c 100644 --- a/codes/javascript/chapter_sorting/heap_sort.js +++ b/codes/javascript/chapter_sorting/heap_sort.js @@ -5,7 +5,7 @@ */ /* 堆的长度为 n ,从节点 i 开始,从顶至底堆化 */ -function sift_down(nums, n, i) { +function siftDown(nums, n, i) { while (true) { // 判断节点 i, l, r 中值最大的节点,记为 ma let l = 2 * i + 1; @@ -29,21 +29,21 @@ function sift_down(nums, n, i) { } /* 堆排序 */ -function heap_sort(nums) { +function heapSort(nums) { // 建堆操作:堆化除叶节点以外的其他所有节点 for (let i = Math.floor(nums.length / 2) - 1; i >= 0; i--) { - sift_down(nums, nums.length, i); + siftDown(nums, nums.length, i); } // 从堆中提取最大元素,循环 n-1 轮 for (let i = nums.length - 1; i > 0; i--) { // 交换根节点与最右叶节点(即交换首元素与尾元素) [nums[0], nums[i]] = [nums[i], nums[0]]; // 以根节点为起点,从顶至底进行堆化 - sift_down(nums, i, 0); + siftDown(nums, i, 0); } } /* Driver Code */ const nums = [4, 1, 3, 1, 5, 2]; -heap_sort(nums); -console.log("堆排序完成后 nums =", nums); +heapSort(nums); +console.log('堆排序完成后 nums =', nums); diff --git a/codes/javascript/chapter_sorting/selection_sort.js b/codes/javascript/chapter_sorting/selection_sort.js index 5afcfb418..9383e23f8 100644 --- a/codes/javascript/chapter_sorting/selection_sort.js +++ b/codes/javascript/chapter_sorting/selection_sort.js @@ -5,7 +5,7 @@ */ /* 选择排序 */ -function selection_sort(nums) { +function selectionSort(nums) { let n = nums.length; // 外循环:未排序区间为 [i, n-1] for (let i = 0; i < n - 1; i++) { @@ -13,7 +13,7 @@ function selection_sort(nums) { let k = i; for (let j = i + 1; j < n; j++) { if (nums[j] < nums[k]) { - k = j; // 记录最小元素的索引 + k = j; // 记录最小元素的索引 } } // 将该最小元素与未排序区间的首个元素交换 @@ -23,5 +23,5 @@ function selection_sort(nums) { /* Driver Code */ const nums = [4, 1, 3, 1, 5, 2]; -selection_sort(nums); -console.log("选择排序完成后 nums =", nums); +selectionSort(nums); +console.log('选择排序完成后 nums =', nums); diff --git a/codes/typescript/chapter_searching/binary_search_edge.ts b/codes/typescript/chapter_searching/binary_search_edge.ts index f7136b1a4..c46bcee9c 100644 --- a/codes/typescript/chapter_searching/binary_search_edge.ts +++ b/codes/typescript/chapter_searching/binary_search_edge.ts @@ -5,7 +5,7 @@ */ /* 二分查找最左一个元素 */ -function binary_search_left_edge(nums: number[], target: number): number { +function binarySearchLeftEdge(nums: number[], target: number): number { let i = 0, j = nums.length - 1; // 初始化双闭区间 [0, n-1] while (i <= j) { let m = Math.floor((i + j) / 2); // 计算中点索引 m @@ -24,7 +24,7 @@ function binary_search_left_edge(nums: number[], target: number): number { } /* 二分查找最右一个元素 */ -function binary_search_right_edge(nums: number[], target: number): number { +function binarySearchRightEdge(nums: number[], target: number): number { let i = 0, j = nums.length - 1; // 初始化双闭区间 [0, n-1] while (i <= j) { let m = Math.floor((i + j) / 2); // 计算中点索引 m @@ -47,9 +47,9 @@ let target: number = 6; const nums: number[] = [1, 3, 6, 6, 6, 6, 6, 10, 12, 15]; // 二分查找最左一个元素 -let index_left: number = binary_search_left_edge(nums, target); +let index_left: number = binarySearchLeftEdge(nums, target); console.log("数组中最左一个元素 6 的索引 = ", index_left); // 二分查找最右一个元素 -let index_right: number = binary_search_right_edge(nums, target); +let index_right: number = binarySearchRightEdge(nums, target); console.log("数组中最右一个元素 6 的索引 = ", index_right); diff --git a/codes/typescript/chapter_sorting/heap_sort.ts b/codes/typescript/chapter_sorting/heap_sort.ts index 9023ee429..d9669f5d9 100644 --- a/codes/typescript/chapter_sorting/heap_sort.ts +++ b/codes/typescript/chapter_sorting/heap_sort.ts @@ -5,7 +5,7 @@ */ /* 堆的长度为 n ,从节点 i 开始,从顶至底堆化 */ -function sift_down(nums: number[], n: number, i: number): void { +function siftDown(nums: number[], n: number, i: number): void { while (true) { // 判断节点 i, l, r 中值最大的节点,记为 ma let l = 2 * i + 1; @@ -29,23 +29,23 @@ function sift_down(nums: number[], n: number, i: number): void { } /* 堆排序 */ -function heap_sort(nums: number[]): void { +function heapSort(nums: number[]): void { // 建堆操作:堆化除叶节点以外的其他所有节点 for (let i = Math.floor(nums.length / 2) - 1; i >= 0; i--) { - sift_down(nums, nums.length, i); + siftDown(nums, nums.length, i); } // 从堆中提取最大元素,循环 n-1 轮 for (let i = nums.length - 1; i > 0; i--) { // 交换根节点与最右叶节点(即交换首元素与尾元素) [nums[0], nums[i]] = [nums[i], nums[0]]; // 以根节点为起点,从顶至底进行堆化 - sift_down(nums, i, 0); + siftDown(nums, i, 0); } } /* Driver Code */ const nums: number[] = [4, 1, 3, 1, 5, 2]; -heap_sort(nums); -console.log("堆排序完成后 nums =", nums); +heapSort(nums); +console.log('堆排序完成后 nums =', nums); -export { }; +export {}; diff --git a/codes/typescript/chapter_sorting/selection_sort.ts b/codes/typescript/chapter_sorting/selection_sort.ts index 792f89ff5..1f0817824 100644 --- a/codes/typescript/chapter_sorting/selection_sort.ts +++ b/codes/typescript/chapter_sorting/selection_sort.ts @@ -5,7 +5,7 @@ */ /* 选择排序 */ -function selection_sort(nums: number[]): void { +function selectionSort(nums: number[]): void { let n = nums.length; // 外循环:未排序区间为 [i, n-1] for (let i = 0; i < n - 1; i++) { @@ -13,7 +13,7 @@ function selection_sort(nums: number[]): void { let k = i; for (let j = i + 1; j < n; j++) { if (nums[j] < nums[k]) { - k = j; // 记录最小元素的索引 + k = j; // 记录最小元素的索引 } } // 将该最小元素与未排序区间的首个元素交换 @@ -23,7 +23,7 @@ function selection_sort(nums: number[]): void { /* Driver Code */ const nums: number[] = [4, 1, 3, 1, 5, 2]; -selection_sort(nums); -console.log("选择排序完成后 nums =", nums); +selectionSort(nums); +console.log('选择排序完成后 nums =', nums); -export { }; +export {}; diff --git a/docs/chapter_computational_complexity/time_complexity.md b/docs/chapter_computational_complexity/time_complexity.md index 259540fc1..761b694c7 100755 --- a/docs/chapter_computational_complexity/time_complexity.md +++ b/docs/chapter_computational_complexity/time_complexity.md @@ -592,7 +592,7 @@ $T(n)$ 是一次函数,说明时间增长趋势是线性的,因此可以得 根据定义,确定 $f(n)$ 之后,我们便可得到时间复杂度 $O(f(n))$ 。那么如何确定渐近上界 $f(n)$ 呢?总体分为两步:首先统计操作数量,然后判断渐近上界。 -### 1) 统计操作数量 +### 第一步:统计操作数量 针对代码,逐行从上到下计算即可。然而,由于上述 $c \cdot f(n)$ 中的常数项 $c$ 可以取任意大小,**因此操作数量 $T(n)$ 中的各种系数、常数项都可以被忽略**。根据此原则,可以总结出以下计数简化技巧: @@ -808,7 +808,7 @@ $$ } ``` -### 2) 判断渐近上界 +### 第二步:判断渐近上界 **时间复杂度由多项式 $T(n)$ 中最高阶的项来决定**。这是因为在 $n$ 趋于无穷大时,最高阶的项将发挥主导作用,其他项的影响都可以被忽略。 diff --git a/docs/chapter_data_structure/number_encoding.assets/1s_2s_complement.png b/docs/chapter_data_structure/number_encoding.assets/1s_2s_complement.png index ccc56863226e3b725f51deac83b403cfc2a2f554..c20f0859b7feb668e2dcb9276765d066c9338f48 100644 GIT binary patch literal 62416 zcmeFZbzD?y7e6|bbVzq7B_Q1`qI4)N-6|c@%rHubQi61gl(a~vbPV0n-3*-r+>Ph> zo}=%*zkC0`uYP2P?cUFRVm)hp*LSV;1gopc;bKu@fj}T!1$o)0AP^ex6}cY+8TgQ< zQ$zwjkX)Y1$$$!bsn>yD{4I4AtW;D$Y`}L65E>F82<7G$;4cV?^5?@hk0>Hh{pb5r zB-X$00on|D0Yd$GKM3>;_`LaJ0{pvq=C4nbG^Br8Ohf*4HyS7n<=1!Qe&B8pMD~FX z@PX+lujc{+;kDfSLyBg{qXPO3QjmS1>4CI0jXqA@>U-)mtp0!yLsJ@;F=37VjV#HC 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