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Diff for: ‎第一章代码.ipynb

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"# 第一章代码"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 算法1.1"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[11, 12, 22, 25, 25, 64]\n"
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]
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}
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],
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"source": [
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"# author: Zeqi Zhu ([email protected])\n",
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"# 选择排序算法\n",
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"def selection_sort(A):\n",
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" n = len(A)\n",
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" for i in range(n - 1):\n",
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" # Find the minimum element in the remaining unsorted array\n",
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" cur_min_pos = i\n",
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" for j in range(i + 1, n):\n",
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" if A[j] < A[cur_min_pos]:\n",
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" cur_min_pos = j\n",
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" # Swap the found minimum element with the first element\n",
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" A[i], A[cur_min_pos] = A[cur_min_pos], A[i]\n",
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" return A\n",
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"\n",
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"# Example usage:\n",
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"example_array = [64, 25, 25, 12, 22, 11]\n",
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"sorted_array = selection_sort(example_array)\n",
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"print(sorted_array)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
@@ -28,7 +69,7 @@
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}
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],
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"source": [
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"# author: ZhuZeqi ([email protected])\n",
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"# author: Zeqi Zhu ([email protected])\n",
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"# 插入排序算法\n",
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"\n",
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"def insertion_sort(A):\n",

Diff for: ‎第三章代码.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# 第三章代码"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 算法3.1: MergeSort"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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"# author: Zeqi Zhu ([email protected])\n",
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"\n",
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"def merge_sort(A, l, r):\n",
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" if l < r:\n",
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" # Same as (l+r)//2, but avoids overflow for large l and r\n",
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" mid = l + (r - l) // 2\n",
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"\n",
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" # Sort first and second halves\n",
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" merge_sort(A, l, mid)\n",
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" merge_sort(A, mid + 1, r)\n",
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" merge(A, l, mid, r)\n",
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"\n",
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" return A"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 算法3.2: Merge "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[5, 6, 7, 11, 12, 12, 13]\n"
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]
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}
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],
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"source": [
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"def merge(arr, l, m, r):\n",
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" n1 = m - l + 1\n",
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" n2 = r - m\n",
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" B = [0] * (n1 + n2) # Temporary array B\n",
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"\n",
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" i, j, k = l, m + 1, 0 # Initial indexes\n",
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"\n",
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" # Merge the subarrays into B\n",
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" while i <= m and j <= r:\n",
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" if arr[i] <= arr[j]:\n",
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" B[k] = arr[i]\n",
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" i += 1\n",
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" else:\n",
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" B[k] = arr[j]\n",
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" j += 1\n",
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" k += 1\n",
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"\n",
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" # Copy the remaining elements of left subarray, if there are any\n",
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" while i <= m:\n",
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" B[k] = arr[i]\n",
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" i += 1\n",
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" k += 1\n",
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"\n",
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" # Copy the remaining elements of right subarray, if there are any\n",
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" while j <= r:\n",
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" B[k] = arr[j]\n",
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" j += 1\n",
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" k += 1\n",
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"\n",
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" # Copy the merged elements back into original array arr\n",
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" for i in range(l, r + 1):\n",
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" arr[i] = B[i - l]\n",
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"\n",
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" return arr\n",
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"\n",
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"# Example usage:\n",
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"example_array = [12, 12, 11, 13, 5, 6, 7]\n",
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"sorted_array = merge_sort(example_array, 0, len(example_array) - 1)\n",
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"print(sorted_array) # Output: [5, 6, 7, 11, 12, 12, 13]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 算法3.3: Inversion-BruteForce"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"3\n"
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]
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}
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],
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"source": [
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"def count_inversions_bruteforce(arr):\n",
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" n = len(arr)\n",
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" sum = 0\n",
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" for i in range(n):\n",
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" for j in range(i + 1, n):\n",
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" if arr[i] > arr[j]:\n",
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" sum += 1\n",
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" return sum\n",
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"\n",
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"# Example usage:\n",
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"example_array = [2, 4, 1, 3, 5]\n",
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"print(count_inversions_bruteforce(example_array)) # Output: 3"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 算法3.4: MergeCount "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [],
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"source": [
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"def merge_count(arr, l, mid, r):\n",
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" i = l\n",
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" j = mid + 1\n",
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" k = 0\n",
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" inv_count = 0 # This will hold the count of inversions\n",
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" B = [0] * (r - l + 1) # Temporary array B\n",
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" \n",
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" # Merge the subarrays and count inversions\n",
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" while i <= mid and j <= r:\n",
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" if arr[i] > arr[j]:\n",
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" B[k] = arr[j]\n",
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" # The number of inversions is the number of elements remaining in the left subarray\n",
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" inv_count += (mid - i + 1)\n",
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" k += 1\n",
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" j += 1\n",
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" else:\n",
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" B[k] = arr[i]\n",
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" k += 1\n",
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" i += 1\n",
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" \n",
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" # Copy the remaining elements of left subarray, if there are any\n",
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" while i <= mid:\n",
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" B[k] = arr[i]\n",
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" i += 1\n",
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" k += 1\n",
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" \n",
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" # Copy the remaining elements of right subarray, if there are any\n",
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" while j <= r:\n",
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" B[k] = arr[j]\n",
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" j += 1\n",
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" k += 1\n",
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" \n",
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" # Copy the merged elements back into original array arr\n",
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" for i in range(0, k):\n",
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" arr[l + i] = B[i]\n",
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" \n",
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" return inv_count\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## 算法3.5: CountInver"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"(45, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10])\n"
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]
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}
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],
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"source": [
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"def count_inver(arr, l, r):\n",
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" if l >= r:\n",
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" return 0, arr[l:r+1]\n",
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" \n",
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" mid = (l + r) // 2\n",
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" s1, left_half = count_inver(arr, l, mid)\n",
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" s2, right_half = count_inver(arr, mid + 1, r)\n",
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" s3 = merge_count(arr, l, mid, r) # merge_count function from previous implementation\n",
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" total = s1 + s2 + s3\n",
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" \n",
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" return total, arr[l:r+1]\n",
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"\n",
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"\n",
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"# Example usage:\n",
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"example_array = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]\n",
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"print(count_inver(example_array, 0, len(example_array) - 1)) # Output: 45\n",
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"\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "py38_torch",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.18"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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