Merge pull request #262 from sjinzh/master

add zig codes for Section 'Heap' (my_heap.zig)

codes/zig/build.zig

@@ -202,6 +202,19 @@ pub fn build(b: *std.build.Builder) void {
         const run_step_heap = b.step("run_heap", "Run heap");
         run_step_heap.dependOn(&run_cmd_heap.step);
 
+        // Source File: "chapter_heap/my_heap.zig"
+        // Run Command: zig build run_my_heap
+        const exe_my_heap = b.addExecutable("my_heap", "chapter_heap/my_heap.zig");
+        exe_my_heap.addPackagePath("include", "include/include.zig");
+        exe_my_heap.setTarget(target);
+        exe_my_heap.setBuildMode(mode);
+        exe_my_heap.install();
+        const run_cmd_my_heap = exe_my_heap.run();
+        run_cmd_my_heap.step.dependOn(b.getInstallStep());
+        if (b.args) |args| run_cmd_my_heap.addArgs(args);
+        const run_step_my_heap = b.step("run_my_heap", "Run my_heap");
+        run_step_my_heap.dependOn(&run_cmd_my_heap.step);
+                     
     // Section: "Linear Search"
         // Source File: "chapter_searching/linear_search.zig"
         // Run Command: zig build run_linear_search

codes/zig/chapter_heap/my_heap.zig

@@ -0,0 +1,190 @@
+// File: my_heap.zig
+// Created Time: 2023-01-14
+// Author: sjinzh (sjinzh@gmail.com)
+
+const std = @import("std");
+const inc = @import("include");
+
+// 堆类简易实现
+// 编译期泛型
+pub fn MaxHeap(comptime T: type) type {
+    return struct {
+        const Self = @This();
+        
+        maxHeap: ?std.ArrayList(T) = null,      // 使用列表而非数组，这样无需考虑扩容问题
+
+        // 构造函数，根据输入列表建堆
+        pub fn init(self: *Self, allocator: std.mem.Allocator, nums: []const T) !void {
+            if (self.maxHeap != null) return;
+            self.maxHeap = std.ArrayList(T).init(allocator);
+            // 将列表元素原封不动添加进堆
+            try self.maxHeap.?.appendSlice(nums);
+            // 堆化除叶结点以外的其他所有结点
+            var i: usize = parent(self.size() - 1) + 1;
+            while (i > 0) : (i -= 1) {
+                try self.siftDown(i - 1);
+            }
+        }
+
+        // 析构函数，释放内存
+        pub fn deinit(self: *Self) void {
+            if (self.maxHeap != null) self.maxHeap.?.deinit();
+        }
+
+        // 获取左子结点索引
+        fn left(i: usize) usize {
+            return 2 * i + 1;
+        }
+
+        // 获取右子结点索引
+        fn right(i: usize) usize {
+            return 2 * i + 2;
+        }
+
+        // 获取父结点索引
+        fn parent(i: usize) usize {
+            // return (i - 1) / 2; // 向下整除
+            return @divFloor(i - 1, 2);
+        }
+
+        // 交换元素
+        fn swap(self: *Self, i: usize, j: usize) !void {
+            var a = self.maxHeap.?.items[i];
+            var b = self.maxHeap.?.items[j];
+            var tmp = a;
+            try self.maxHeap.?.replaceRange(i, 1, &[_]T{b});
+            try self.maxHeap.?.replaceRange(j, 1, &[_]T{tmp});
+        }
+
+        // 获取堆大小
+        pub fn size(self: *Self) usize {
+            return self.maxHeap.?.items.len;
+        }
+
+        // 判断堆是否为空
+        pub fn isEmpty(self: *Self) bool {
+            return self.size() == 0;
+        }
+
+        // 访问堆顶元素
+        pub fn peek(self: *Self) T {
+            return self.maxHeap.?.items[0];
+        }  
+
+        // 元素入堆
+        pub fn push(self: *Self, val: T) !void {
+            // 添加结点
+            try self.maxHeap.?.append(val);
+            // 从底至顶堆化
+            try self.siftUp(self.size() - 1);
+        }  
+
+        // 从结点 i 开始，从底至顶堆化
+        fn siftUp(self: *Self, i_: usize) !void {
+            var i = i_;
+            while (true) {
+                // 获取结点 i 的父结点
+                var p = parent(i);
+                // 当“越过根结点”或“结点无需修复”时，结束堆化
+                if (p < 0 or self.maxHeap.?.items[i] <= self.maxHeap.?.items[p]) break;
+                // 交换两结点
+                try self.swap(i, p);
+                // 循环向上堆化
+                i = p;
+            }
+        }
+
+        // 元素出堆
+        pub fn poll(self: *Self) !T {
+            // 判断处理
+            if (self.isEmpty()) unreachable;
+            // 交换根结点与最右叶结点（即交换首元素与尾元素）
+            try self.swap(0, self.size() - 1);
+            // 删除结点
+            var val = self.maxHeap.?.pop();
+            // 从顶至底堆化
+            try self.siftDown(0);
+            // 返回堆顶元素
+            return val;
+        } 
+
+        // 从结点 i 开始，从顶至底堆化
+        fn siftDown(self: *Self, i_: usize) !void {
+            var i = i_;
+            while (true) {
+                // 判断结点 i, l, r 中值最大的结点，记为 ma
+                var l = left(i);
+                var r = right(i);
+                var ma = i;
+                if (l < self.size() and self.maxHeap.?.items[l] > self.maxHeap.?.items[ma]) ma = l;
+                if (r < self.size() and self.maxHeap.?.items[r] > self.maxHeap.?.items[ma]) ma = r;
+                // 若结点 i 最大或索引 l, r 越界，则无需继续堆化，跳出
+                if (ma == i) break;
+                // 交换两结点
+                try self.swap(i, ma);
+                // 循环向下堆化
+                i = ma;
+            }
+        }
+
+        fn lessThan(context: void, a: T, b: T) std.math.Order {
+            _ = context;
+            return std.math.order(a, b);
+        }
+
+        fn greaterThan(context: void, a: T, b: T) std.math.Order {
+            return lessThan(context, a, b).invert();
+        }
+
+        // 打印堆（二叉树）
+        pub fn print(self: *Self, mem_allocator: std.mem.Allocator) !void {
+            const PQgt = std.PriorityQueue(T, void, greaterThan);
+            var queue = PQgt.init(std.heap.page_allocator, {});
+            defer queue.deinit();
+            try queue.addSlice(self.maxHeap.?.items);
+            try inc.PrintUtil.printHeap(T, mem_allocator, queue);
+        } 
+    };
+}
+
+// Driver Code
+pub fn main() !void {
+    // 初始化内存分配器
+    var mem_arena = std.heap.ArenaAllocator.init(std.heap.page_allocator);
+    defer mem_arena.deinit();
+    const mem_allocator = mem_arena.allocator();
+
+    // 初始化大顶堆
+    var maxHeap = MaxHeap(i32){};
+    try maxHeap.init(std.heap.page_allocator, &[_]i32{ 9, 8, 6, 6, 7, 5, 2, 1, 4, 3, 6, 2 });
+    defer maxHeap.deinit();
+    std.debug.print("\n输入列表并建堆后\n", .{});
+    try maxHeap.print(mem_allocator);
+
+    // 获取堆顶元素
+    var peek = maxHeap.peek();
+    std.debug.print("\n堆顶元素为 {}\n", .{peek});
+
+    // 元素入堆
+    const val = 7;
+    try maxHeap.push(val);
+    std.debug.print("\n元素 {} 入堆后\n", .{val});
+    try maxHeap.print(mem_allocator);
+
+    // 堆顶元素出堆
+    peek = try maxHeap.poll();
+    std.debug.print("\n堆顶元素 {} 出堆后\n", .{peek});
+    try maxHeap.print(mem_allocator);
+
+    // 获取堆的大小
+    var size = maxHeap.size();
+    std.debug.print("\n堆元素数量为 {}", .{size});
+
+    // 判断堆是否为空
+    var isEmpty = maxHeap.isEmpty();
+    std.debug.print("\n堆是否为空 {}\n", .{isEmpty});
+
+    const getchar = try std.io.getStdIn().reader().readByte();
+    _ = getchar;
+}
+