build
This commit is contained in:
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f442443773
@ -172,7 +172,15 @@ status: new
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=== "Zig"
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```zig title="iteration.zig"
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[class]{}-[func]{forLoop}
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// for 循环
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fn forLoop(n: usize) i32 {
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var res: i32 = 0;
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// 循环求和 1, 2, ..., n-1, n
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for (1..n+1) |i| {
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res = res + @as(i32, @intCast(i));
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}
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return res;
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}
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```
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图 2-1 展示了该求和函数的流程框图。
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@ -368,7 +376,17 @@ status: new
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=== "Zig"
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```zig title="iteration.zig"
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[class]{}-[func]{whileLoop}
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// while 循环
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fn whileLoop(n: i32) i32 {
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var res: i32 = 0;
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var i: i32 = 1; // 初始化条件变量
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// 循环求和 1, 2, ..., n-1, n
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while (i <= n) {
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res += @intCast(i);
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i += 1;
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}
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return res;
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}
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```
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在 `while` 循环中,由于初始化和更新条件变量的步骤是独立在循环结构之外的,**因此它比 `for` 循环的自由度更高**。
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@ -575,7 +593,19 @@ status: new
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=== "Zig"
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```zig title="iteration.zig"
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[class]{}-[func]{whileLoopII}
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// while 循环(两次更新)
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fn whileLoopII(n: i32) i32 {
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var res: i32 = 0;
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var i: i32 = 1; // 初始化条件变量
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// 循环求和 1, 4, ...
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while (i <= n) {
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res += @intCast(i);
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// 更新条件变量
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i += 1;
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i *= 2;
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}
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return res;
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}
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```
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总的来说,**`for` 循环的代码更加紧凑,`while` 循环更加灵活**,两者都可以实现迭代结构。选择使用哪一个应该根据特定问题的需求来决定。
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@ -775,7 +805,21 @@ status: new
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=== "Zig"
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```zig title="iteration.zig"
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[class]{}-[func]{nestedForLoop}
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// 双层 for 循环
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fn nestedForLoop(allocator: Allocator, n: usize) ![]const u8 {
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var res = std.ArrayList(u8).init(allocator);
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defer res.deinit();
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var buffer: [20]u8 = undefined;
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// 循环 i = 1, 2, ..., n-1, n
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for (1..n+1) |i| {
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// 循环 j = 1, 2, ..., n-1, n
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for (1..n+1) |j| {
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var _str = try std.fmt.bufPrint(&buffer, "({d}, {d}), ", .{i, j});
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try res.appendSlice(_str);
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}
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}
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return res.toOwnedSlice();
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}
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```
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图 2-2 给出了该嵌套循环的流程框图。
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@ -970,7 +1014,17 @@ status: new
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=== "Zig"
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```zig title="recursion.zig"
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[class]{}-[func]{recur}
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// 递归函数
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fn recur(n: i32) i32 {
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// 终止条件
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if (n == 1) {
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return 1;
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}
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// 递:递归调用
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var res: i32 = recur(n - 1);
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// 归:返回结果
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return n + res;
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}
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```
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图 2-3 展示了该函数的递归过程。
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@ -1158,7 +1212,15 @@ status: new
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=== "Zig"
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```zig title="recursion.zig"
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[class]{}-[func]{tailRecur}
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// 尾递归函数
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fn tailRecur(n: i32, res: i32) i32 {
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// 终止条件
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if (n == 0) {
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return res;
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}
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// 尾递归调用
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return tailRecur(n - 1, res + n);
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}
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```
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尾递归的执行过程如图 2-5 所示。对比普通递归和尾递归,求和操作的执行点是不同的。
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@ -1356,7 +1418,17 @@ status: new
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=== "Zig"
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```zig title="recursion.zig"
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[class]{}-[func]{fib}
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// 斐波那契数列
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fn fib(n: i32) i32 {
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// 终止条件 f(1) = 0, f(2) = 1
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if (n == 1 or n == 2) {
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return n - 1;
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}
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// 递归调用 f(n) = f(n-1) + f(n-2)
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var res: i32 = fib(n - 1) + fib(n - 2);
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// 返回结果 f(n)
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return res;
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}
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```
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观察以上代码,我们在函数内递归调用了两个函数,**这意味着从一个调用产生了两个调用分支**。如图 2-6 所示,这样不断递归调用下去,最终将产生一个层数为 $n$ 的「递归树 recursion tree」。
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@ -1655,7 +1727,26 @@ status: new
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=== "Zig"
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```zig title="recursion.zig"
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[class]{}-[func]{forLoopRecur}
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// 使用迭代模拟递归
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fn forLoopRecur(comptime n: i32) i32 {
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// 使用一个显式的栈来模拟系统调用栈
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var stack: [n]i32 = undefined;
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var res: i32 = 0;
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// 递:递归调用
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var i: usize = n;
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while (i > 0) {
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stack[i - 1] = @intCast(i);
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i -= 1;
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}
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// 归:返回结果
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var index: usize = n;
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while (index > 0) {
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index -= 1;
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res += stack[index];
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}
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// res = 1+2+3+...+n
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return res;
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}
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```
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观察以上代码,当递归被转换为迭代后,代码变得更加复杂了。尽管迭代和递归在很多情况下可以互相转换,但也不一定值得这样做,有以下两点原因。
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@ -178,7 +178,16 @@ comments: true
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=== "Zig"
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```zig title=""
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// 在某运行平台下
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fn algorithm(n: usize) void {
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var a: i32 = 2; // 1 ns
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a += 1; // 1 ns
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a *= 2; // 10 ns
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// 循环 n 次
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for (0..n) |_| { // 1 ns
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std.debug.print("{}\n", .{0}); // 5 ns
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}
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}
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```
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根据以上方法,可以得到算法运行时间为 $6n + 12$ ns :
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@ -427,7 +436,24 @@ $$
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=== "Zig"
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```zig title=""
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// 算法 A 的时间复杂度:常数阶
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fn algorithm_A(n: usize) void {
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_ = n;
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std.debug.print("{}\n", .{0});
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}
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// 算法 B 的时间复杂度:线性阶
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fn algorithm_B(n: i32) void {
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for (0..n) |_| {
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std.debug.print("{}\n", .{0});
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}
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}
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// 算法 C 的时间复杂度:常数阶
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fn algorithm_C(n: i32) void {
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_ = n;
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for (0..1000000) |_| {
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std.debug.print("{}\n", .{0});
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}
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}
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```
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图 2-7 展示了以上三个算法函数的时间复杂度。
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@ -606,7 +632,15 @@ $$
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=== "Zig"
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```zig title=""
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fn algorithm(n: usize) void {
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var a: i32 = 1; // +1
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a += 1; // +1
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a *= 2; // +1
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// 循环 n 次
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for (0..n) |_| { // +1(每轮都执行 i ++)
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std.debug.print("{}\n", .{0}); // +1
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}
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}
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```
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设算法的操作数量是一个关于输入数据大小 $n$ 的函数,记为 $T(n)$ ,则以上函数的的操作数量为:
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@ -857,7 +891,22 @@ $T(n)$ 是一次函数,说明其运行时间的增长趋势是线性的,因
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=== "Zig"
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```zig title=""
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fn algorithm(n: usize) void {
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var a: i32 = 1; // +0(技巧 1)
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a = a + @as(i32, @intCast(n)); // +0(技巧 1)
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// +n(技巧 2)
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for(0..(5 * n + 1)) |_| {
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std.debug.print("{}\n", .{0});
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}
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// +n*n(技巧 3)
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for(0..(2 * n)) |_| {
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for(0..(n + 1)) |_| {
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std.debug.print("{}\n", .{0});
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}
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}
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}
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```
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以下公式展示了使用上述技巧前后的统计结果,两者推出的时间复杂度都为 $O(n^2)$ 。
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@ -2126,16 +2126,16 @@ comments: true
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#loadThres; // 触发扩容的负载因子阈值
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#extendRatio; // 扩容倍数
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#buckets; // 桶数组
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#removed; // 删除标记
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#TOMBSTONE; // 删除标记
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/* 构造方法 */
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constructor() {
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this.#size = 0;
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this.#capacity = 4;
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this.#loadThres = 2.0 / 3.0;
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this.#extendRatio = 2;
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this.#buckets = new Array(this.#capacity).fill(null);
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this.#removed = new Pair(-1, '-1');
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this.#size = 0; // 键值对数量
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this.#capacity = 4; // 哈希表容量
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this.#loadThres = 2.0 / 3.0; // 触发扩容的负载因子阈值
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this.#extendRatio = 2; // 扩容倍数
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this.#buckets = Array(this.#capacity).fill(null); // 桶数组
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this.#TOMBSTONE = new Pair(-1, '-1'); // 删除标记
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}
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/* 哈希函数 */
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@ -2148,22 +2148,48 @@ comments: true
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return this.#size / this.#capacity;
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}
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/* 搜索 key 对应的桶索引 */
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#findBucket(key) {
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let index = this.#hashFunc(key);
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let firstTombstone = -1;
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// 线性探测,当遇到空桶时跳出
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while (this.#buckets[index] !== null) {
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// 若遇到 key ,返回对应桶索引
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if (this.#buckets[index].key === key) {
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// 若之前遇到了删除标记,则将键值对移动至该索引
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if (firstTombstone !== -1) {
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this.#buckets[firstTombstone] = this.#buckets[index];
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this.#buckets[index] = this.#TOMBSTONE;
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return firstTombstone; // 返回移动后的桶索引
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}
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return index; // 返回桶索引
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}
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// 记录遇到的首个删除标记
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if (
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firstTombstone === -1 &&
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this.#buckets[index] === this.#TOMBSTONE
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) {
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firstTombstone = index;
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}
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// 计算桶索引,越过尾部返回头部
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index = (index + 1) % this.#capacity;
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}
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// 若 key 不存在,则返回添加点的索引
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return firstTombstone === -1 ? index : firstTombstone;
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}
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/* 查询操作 */
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get(key) {
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const index = this.#hashFunc(key);
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// 线性探测,从 index 开始向后遍历
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for (let i = 0; i < this.#capacity; i++) {
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// 计算桶索引,越过尾部返回头部
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const j = (index + i) % this.#capacity;
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// 若遇到空桶,说明无此 key ,则返回 null
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if (this.#buckets[j] === null) return null;
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// 若遇到指定 key ,则返回对应 val
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if (
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this.#buckets[j].key === key &&
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this.#buckets[j].key !== this.#removed.key
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)
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return this.#buckets[j].val;
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// 搜索 key 对应的桶索引
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const index = this.#findBucket(key);
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// 若找到键值对,则返回对应 val
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if (
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this.#buckets[index] !== null &&
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this.#buckets[index] !== this.#TOMBSTONE
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) {
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return this.#buckets[index].val;
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}
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// 若键值对不存在,则返回 null
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return null;
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}
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@ -2173,45 +2199,32 @@ comments: true
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if (this.#loadFactor() > this.#loadThres) {
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this.#extend();
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}
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const index = this.#hashFunc(key);
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// 线性探测,从 index 开始向后遍历
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for (let i = 0; i < this.#capacity; i++) {
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// 计算桶索引,越过尾部返回头部
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let j = (index + i) % this.#capacity;
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// 若遇到空桶、或带有删除标记的桶,则将键值对放入该桶
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if (
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this.#buckets[j] === null ||
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this.#buckets[j].key === this.#removed.key
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) {
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this.#buckets[j] = new Pair(key, val);
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this.#size += 1;
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return;
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}
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// 若遇到指定 key ,则更新对应 val
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if (this.#buckets[j].key === key) {
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this.#buckets[j].val = val;
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return;
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}
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// 搜索 key 对应的桶索引
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const index = this.#findBucket(key);
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// 若找到键值对,则覆盖 val 并返回
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if (
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this.#buckets[index] !== null &&
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this.#buckets[index] !== this.#TOMBSTONE
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) {
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this.#buckets[index].val = val;
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return;
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}
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// 若键值对不存在,则添加该键值对
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this.#buckets[index] = new Pair(key, val);
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this.#size++;
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}
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/* 删除操作 */
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remove(key) {
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const index = this.#hashFunc(key);
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// 线性探测,从 index 开始向后遍历
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||||
for (let i = 0; i < this.#capacity; i++) {
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// 计算桶索引,越过尾部返回头部
|
||||
const j = (index + i) % this.#capacity;
|
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// 若遇到空桶,说明无此 key ,则直接返回
|
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if (this.#buckets[j] === null) {
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return;
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}
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// 若遇到指定 key ,则标记删除并返回
|
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if (this.#buckets[j].key === key) {
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this.#buckets[j] = this.#removed;
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this.#size -= 1;
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return;
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}
|
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// 搜索 key 对应的桶索引
|
||||
const index = this.#findBucket(key);
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// 若找到键值对,则用删除标记覆盖它
|
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if (
|
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this.#buckets[index] !== null &&
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||||
this.#buckets[index] !== this.#TOMBSTONE
|
||||
) {
|
||||
this.#buckets[index] = this.#TOMBSTONE;
|
||||
this.#size--;
|
||||
}
|
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}
|
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@ -2221,11 +2234,11 @@ comments: true
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const bucketsTmp = this.#buckets;
|
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// 初始化扩容后的新哈希表
|
||||
this.#capacity *= this.#extendRatio;
|
||||
this.#buckets = new Array(this.#capacity).fill(null);
|
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this.#buckets = Array(this.#capacity).fill(null);
|
||||
this.#size = 0;
|
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// 将键值对从原哈希表搬运至新哈希表
|
||||
for (const pair of bucketsTmp) {
|
||||
if (pair !== null && pair.key !== this.#removed.key) {
|
||||
if (pair !== null && pair !== this.#TOMBSTONE) {
|
||||
this.put(pair.key, pair.val);
|
||||
}
|
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}
|
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@ -2234,10 +2247,12 @@ comments: true
|
||||
/* 打印哈希表 */
|
||||
print() {
|
||||
for (const pair of this.#buckets) {
|
||||
if (pair !== null) {
|
||||
console.log(pair.key + ' -> ' + pair.val);
|
||||
} else {
|
||||
if (pair === null) {
|
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console.log('null');
|
||||
} else if (pair === this.#TOMBSTONE) {
|
||||
console.log('TOMBSTONE');
|
||||
} else {
|
||||
console.log(pair.key + ' -> ' + pair.val);
|
||||
}
|
||||
}
|
||||
}
|
||||
@ -2249,111 +2264,124 @@ comments: true
|
||||
```typescript title="hash_map_open_addressing.ts"
|
||||
/* 开放寻址哈希表 */
|
||||
class HashMapOpenAddressing {
|
||||
#size: number; // 键值对数量
|
||||
#capacity: number; // 哈希表容量
|
||||
#loadThres: number; // 触发扩容的负载因子阈值
|
||||
#extendRatio: number; // 扩容倍数
|
||||
#buckets: Pair[]; // 桶数组
|
||||
#removed: Pair; // 删除标记
|
||||
private size: number; // 键值对数量
|
||||
private capacity: number; // 哈希表容量
|
||||
private loadThres: number; // 触发扩容的负载因子阈值
|
||||
private extendRatio: number; // 扩容倍数
|
||||
private buckets: Array<Pair | null>; // 桶数组
|
||||
private TOMBSTONE: Pair; // 删除标记
|
||||
|
||||
/* 构造方法 */
|
||||
constructor() {
|
||||
this.#size = 0;
|
||||
this.#capacity = 4;
|
||||
this.#loadThres = 2.0 / 3.0;
|
||||
this.#extendRatio = 2;
|
||||
this.#buckets = new Array(this.#capacity).fill(null);
|
||||
this.#removed = new Pair(-1, '-1');
|
||||
this.size = 0; // 键值对数量
|
||||
this.capacity = 4; // 哈希表容量
|
||||
this.loadThres = 2.0 / 3.0; // 触发扩容的负载因子阈值
|
||||
this.extendRatio = 2; // 扩容倍数
|
||||
this.buckets = Array(this.capacity).fill(null); // 桶数组
|
||||
this.TOMBSTONE = new Pair(-1, '-1'); // 删除标记
|
||||
}
|
||||
|
||||
/* 哈希函数 */
|
||||
#hashFunc(key: number): number {
|
||||
return key % this.#capacity;
|
||||
private hashFunc(key: number): number {
|
||||
return key % this.capacity;
|
||||
}
|
||||
|
||||
/* 负载因子 */
|
||||
#loadFactor(): number {
|
||||
return this.#size / this.#capacity;
|
||||
private loadFactor(): number {
|
||||
return this.size / this.capacity;
|
||||
}
|
||||
|
||||
/* 搜索 key 对应的桶索引 */
|
||||
private findBucket(key: number): number {
|
||||
let index = this.hashFunc(key);
|
||||
let firstTombstone = -1;
|
||||
// 线性探测,当遇到空桶时跳出
|
||||
while (this.buckets[index] !== null) {
|
||||
// 若遇到 key ,返回对应桶索引
|
||||
if (this.buckets[index]!.key === key) {
|
||||
// 若之前遇到了删除标记,则将键值对移动至该索引
|
||||
if (firstTombstone !== -1) {
|
||||
this.buckets[firstTombstone] = this.buckets[index];
|
||||
this.buckets[index] = this.TOMBSTONE;
|
||||
return firstTombstone; // 返回移动后的桶索引
|
||||
}
|
||||
return index; // 返回桶索引
|
||||
}
|
||||
// 记录遇到的首个删除标记
|
||||
if (
|
||||
firstTombstone === -1 &&
|
||||
this.buckets[index] === this.TOMBSTONE
|
||||
) {
|
||||
firstTombstone = index;
|
||||
}
|
||||
// 计算桶索引,越过尾部返回头部
|
||||
index = (index + 1) % this.capacity;
|
||||
}
|
||||
// 若 key 不存在,则返回添加点的索引
|
||||
return firstTombstone === -1 ? index : firstTombstone;
|
||||
}
|
||||
|
||||
/* 查询操作 */
|
||||
get(key: number): string | null {
|
||||
const index = this.#hashFunc(key);
|
||||
// 线性探测,从 index 开始向后遍历
|
||||
for (let i = 0; i < this.#capacity; i++) {
|
||||
// 计算桶索引,越过尾部返回头部
|
||||
const j = (index + i) % this.#capacity;
|
||||
// 若遇到空桶,说明无此 key ,则返回 null
|
||||
if (this.#buckets[j] === null) return null;
|
||||
// 若遇到指定 key ,则返回对应 val
|
||||
if (
|
||||
this.#buckets[j].key === key &&
|
||||
this.#buckets[j].key !== this.#removed.key
|
||||
)
|
||||
return this.#buckets[j].val;
|
||||
// 搜索 key 对应的桶索引
|
||||
const index = this.findBucket(key);
|
||||
// 若找到键值对,则返回对应 val
|
||||
if (
|
||||
this.buckets[index] !== null &&
|
||||
this.buckets[index] !== this.TOMBSTONE
|
||||
) {
|
||||
return this.buckets[index]!.val;
|
||||
}
|
||||
// 若键值对不存在,则返回 null
|
||||
return null;
|
||||
}
|
||||
|
||||
/* 添加操作 */
|
||||
put(key: number, val: string): void {
|
||||
// 当负载因子超过阈值时,执行扩容
|
||||
if (this.#loadFactor() > this.#loadThres) {
|
||||
this.#extend();
|
||||
if (this.loadFactor() > this.loadThres) {
|
||||
this.extend();
|
||||
}
|
||||
const index = this.#hashFunc(key);
|
||||
// 线性探测,从 index 开始向后遍历
|
||||
for (let i = 0; i < this.#capacity; i++) {
|
||||
// 计算桶索引,越过尾部返回头部
|
||||
let j = (index + i) % this.#capacity;
|
||||
// 若遇到空桶、或带有删除标记的桶,则将键值对放入该桶
|
||||
if (
|
||||
this.#buckets[j] === null ||
|
||||
this.#buckets[j].key === this.#removed.key
|
||||
) {
|
||||
this.#buckets[j] = new Pair(key, val);
|
||||
this.#size += 1;
|
||||
return;
|
||||
}
|
||||
// 若遇到指定 key ,则更新对应 val
|
||||
if (this.#buckets[j].key === key) {
|
||||
this.#buckets[j].val = val;
|
||||
return;
|
||||
}
|
||||
// 搜索 key 对应的桶索引
|
||||
const index = this.findBucket(key);
|
||||
// 若找到键值对,则覆盖 val 并返回
|
||||
if (
|
||||
this.buckets[index] !== null &&
|
||||
this.buckets[index] !== this.TOMBSTONE
|
||||
) {
|
||||
this.buckets[index]!.val = val;
|
||||
return;
|
||||
}
|
||||
// 若键值对不存在,则添加该键值对
|
||||
this.buckets[index] = new Pair(key, val);
|
||||
this.size++;
|
||||
}
|
||||
|
||||
/* 删除操作 */
|
||||
remove(key: number): void {
|
||||
const index = this.#hashFunc(key);
|
||||
// 线性探测,从 index 开始向后遍历
|
||||
for (let i = 0; i < this.#capacity; i++) {
|
||||
// 计算桶索引,越过尾部返回头部
|
||||
const j = (index + i) % this.#capacity;
|
||||
// 若遇到空桶,说明无此 key ,则直接返回
|
||||
if (this.#buckets[j] === null) {
|
||||
return;
|
||||
}
|
||||
// 若遇到指定 key ,则标记删除并返回
|
||||
if (this.#buckets[j].key === key) {
|
||||
this.#buckets[j] = this.#removed;
|
||||
this.#size -= 1;
|
||||
return;
|
||||
}
|
||||
// 搜索 key 对应的桶索引
|
||||
const index = this.findBucket(key);
|
||||
// 若找到键值对,则用删除标记覆盖它
|
||||
if (
|
||||
this.buckets[index] !== null &&
|
||||
this.buckets[index] !== this.TOMBSTONE
|
||||
) {
|
||||
this.buckets[index] = this.TOMBSTONE;
|
||||
this.size--;
|
||||
}
|
||||
}
|
||||
|
||||
/* 扩容哈希表 */
|
||||
#extend(): void {
|
||||
private extend(): void {
|
||||
// 暂存原哈希表
|
||||
const bucketsTmp = this.#buckets;
|
||||
const bucketsTmp = this.buckets;
|
||||
// 初始化扩容后的新哈希表
|
||||
this.#capacity *= this.#extendRatio;
|
||||
this.#buckets = new Array(this.#capacity).fill(null);
|
||||
this.#size = 0;
|
||||
this.capacity *= this.extendRatio;
|
||||
this.buckets = Array(this.capacity).fill(null);
|
||||
this.size = 0;
|
||||
// 将键值对从原哈希表搬运至新哈希表
|
||||
for (const pair of bucketsTmp) {
|
||||
if (pair !== null && pair.key !== this.#removed.key) {
|
||||
if (pair !== null && pair !== this.TOMBSTONE) {
|
||||
this.put(pair.key, pair.val);
|
||||
}
|
||||
}
|
||||
@ -2361,11 +2389,13 @@ comments: true
|
||||
|
||||
/* 打印哈希表 */
|
||||
print(): void {
|
||||
for (const pair of this.#buckets) {
|
||||
if (pair !== null) {
|
||||
console.log(pair.key + ' -> ' + pair.val);
|
||||
} else {
|
||||
for (const pair of this.buckets) {
|
||||
if (pair === null) {
|
||||
console.log('null');
|
||||
} else if (pair === this.TOMBSTONE) {
|
||||
console.log('TOMBSTONE');
|
||||
} else {
|
||||
console.log(pair.key + ' -> ' + pair.val);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
@ -308,13 +308,9 @@ comments: true
|
||||
for (auto kv: map) {
|
||||
cout << kv.first << " -> " << kv.second << endl;
|
||||
}
|
||||
// 单独遍历键 key
|
||||
for (auto kv: map) {
|
||||
cout << kv.first << endl;
|
||||
}
|
||||
// 单独遍历值 value
|
||||
for (auto kv: map) {
|
||||
cout << kv.second << endl;
|
||||
// 使用迭代器遍历 key->value
|
||||
for (auto iter = map.begin(); iter != map.end(); iter++) {
|
||||
cout << iter->first << "->" << iter->second << endl;
|
||||
}
|
||||
```
|
||||
|
||||
|
Loading…
Reference in New Issue
Block a user