add python code

public/py/ch2/allpai/permutations.py

@@ -0,0 +1,34 @@
+"""
+全排列生成 — 递归交换法
+生成 n 个元素的所有排列 (n!)
+"""
+
+def permute(arr, start, end):
+    """递归生成全排列"""
+    if start == end:
+        print("".join(map(str, arr)))
+    else:
+        for i in range(start, end + 1):
+            arr[start], arr[i] = arr[i], arr[start]
+            permute(arr, start + 1, end)
+            arr[start], arr[i] = arr[i], arr[start]  # 回溯
+
+def permute_unique(arr, start, end):
+    """生成去重全排列"""
+    if start == end:
+        print("".join(map(str, arr)))
+    else:
+        seen = set()
+        for i in range(start, end + 1):
+            if arr[i] not in seen:
+                seen.add(arr[i])
+                arr[start], arr[i] = arr[i], arr[start]
+                permute_unique(arr, start + 1, end)
+                arr[start], arr[i] = arr[i], arr[start]
+
+if __name__ == "__main__":
+    print("全排列 [1,2,3]:")
+    permute([1, 2, 3], 0, 2)
+
+    print("\n去重全排列 [1,1,2]:")
+    permute_unique([1, 1, 2], 0, 2)

public/py/ch2/digui/print_number.py

@@ -0,0 +1,25 @@
+"""
+递归示例 — 递归打印整数各位数字
+"""
+
+def print_digits(n):
+    """递归按位打印整数（高位到低位）"""
+    if n < 10:
+        print(n, end=" ")
+    else:
+        print_digits(n // 10)
+        print(n % 10, end=" ")
+
+def print_triangle(n, current=1):
+    """递归打印星号三角形"""
+    if current > n:
+        return
+    print("*" * current)
+    print_triangle(n, current + 1)
+
+if __name__ == "__main__":
+    n = 12345
+    print(f"递归打印 {n} 的各位数字:")
+    print_digits(n)
+    print("\n\n递归三角形 (n=5):")
+    print_triangle(5)

public/py/ch2/halfsearch/binary_search.py

@@ -0,0 +1,43 @@
+"""
+二分查找 — 在有序数组中查找目标值
+时间复杂度 O(log n)
+"""
+
+def binary_search_recursive(arr, target, left, right):
+    """递归版二分查找"""
+    if left > right:
+        return -1
+
+    mid = left + (right - left) // 2
+
+    if arr[mid] == target:
+        return mid
+    elif arr[mid] > target:
+        return binary_search_recursive(arr, target, left, mid - 1)
+    else:
+        return binary_search_recursive(arr, target, mid + 1, right)
+
+def binary_search_iterative(arr, target):
+    """迭代版二分查找"""
+    left, right = 0, len(arr) - 1
+
+    while left <= right:
+        mid = left + (right - left) // 2
+        if arr[mid] == target:
+            return mid
+        elif arr[mid] > target:
+            right = mid - 1
+        else:
+            left = mid + 1
+
+    return -1
+
+if __name__ == "__main__":
+    arr = [1, 3, 5, 7, 9, 11, 13, 15]
+    target = 7
+
+    idx1 = binary_search_recursive(arr, target, 0, len(arr) - 1)
+    idx2 = binary_search_iterative(arr, target)
+
+    print(f"数组: {arr}")
+    print(f"查找 {target}: 递归版结果索引={idx1}, 迭代版结果索引={idx2}")

public/py/ch2/mergesort/mergesort.py

@@ -0,0 +1,50 @@
+"""
+归并排序 — 分治法的经典应用
+时间复杂度 O(n log n)，空间复杂度 O(n)
+"""
+
+def merge(arr, left, mid, right):
+    """合并两个有序子数组"""
+    # 创建临时数组
+    L = arr[left:mid + 1]
+    R = arr[mid + 1:right + 1]
+
+    i = j = 0
+    k = left
+
+    # 合并两个有序数组
+    while i < len(L) and j < len(R):
+        if L[i] <= R[j]:
+            arr[k] = L[i]
+            i += 1
+        else:
+            arr[k] = R[j]
+            j += 1
+        k += 1
+
+    # 复制剩余元素
+    while i < len(L):
+        arr[k] = L[i]
+        i += 1
+        k += 1
+    while j < len(R):
+        arr[k] = R[j]
+        j += 1
+        k += 1
+
+def merge_sort(arr, left, right):
+    """归并排序主函数"""
+    if left < right:
+        mid = (left + right) // 2
+        merge_sort(arr, left, mid)
+        merge_sort(arr, mid + 1, right)
+        merge(arr, left, mid, right)
+
+def sort(arr):
+    merge_sort(arr, 0, len(arr) - 1)
+
+if __name__ == "__main__":
+    data = [38, 27, 43, 3, 9, 82, 10]
+    print("排序前:", data)
+    sort(data)
+    print("排序后:", data)

public/py/ch2/quicksort/quicksort.py

@@ -0,0 +1,33 @@
+"""
+快速排序 — 分治策略
+平均时间复杂度 O(n log n)，最坏 O(n²)
+"""
+
+def partition(arr, low, high):
+    """划分：选择基准，将小于基准的放左边，大于的放右边"""
+    pivot = arr[high]  # 选最后一个元素作为基准
+    i = low - 1
+
+    for j in range(low, high):
+        if arr[j] <= pivot:
+            i += 1
+            arr[i], arr[j] = arr[j], arr[i]
+
+    arr[i + 1], arr[high] = arr[high], arr[i + 1]
+    return i + 1
+
+def quick_sort(arr, low, high):
+    """快速排序递归实现"""
+    if low < high:
+        pi = partition(arr, low, high)
+        quick_sort(arr, low, pi - 1)
+        quick_sort(arr, pi + 1, high)
+
+def sort(arr):
+    quick_sort(arr, 0, len(arr) - 1)
+
+if __name__ == "__main__":
+    data = [10, 7, 8, 9, 1, 5]
+    print("排序前:", data)
+    sort(data)
+    print("排序后:", data)