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https://github.com/krahets/hello-algo.git
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e720aa2d24
* Sync recent changes to the revised Word. * Revised the preface chapter * Revised the introduction chapter * Revised the computation complexity chapter * Revised the chapter data structure * Revised the chapter array and linked list * Revised the chapter stack and queue * Revised the chapter hashing * Revised the chapter tree * Revised the chapter heap * Revised the chapter graph * Revised the chapter searching * Reivised the sorting chapter * Revised the divide and conquer chapter * Revised the chapter backtacking * Revised the DP chapter * Revised the greedy chapter * Revised the appendix chapter * Revised the preface chapter doubly * Revised the figures
77 lines
2.3 KiB
Zig
77 lines
2.3 KiB
Zig
// File: coin_change.zig
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// Created Time: 2023-07-15
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// Author: sjinzh (sjinzh@gmail.com)
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const std = @import("std");
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// 零钱兑换：动态规划
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fn coinChangeDP(comptime coins: []i32, comptime amt: usize) i32 {
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comptime var n = coins.len;
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comptime var max = amt + 1;
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// 初始化 dp 表
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var dp = [_][amt + 1]i32{[_]i32{0} ** (amt + 1)} ** (n + 1);
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// 状态转移：首行首列
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for (1..amt + 1) |a| {
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dp[0][a] = max;
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}
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// 状态转移：其余行和列
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for (1..n + 1) |i| {
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for (1..amt + 1) |a| {
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if (coins[i - 1] > @as(i32, @intCast(a))) {
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// 若超过目标金额，则不选硬币 i
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dp[i][a] = dp[i - 1][a];
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} else {
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// 不选和选硬币 i 这两种方案的较小值
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dp[i][a] = @min(dp[i - 1][a], dp[i][a - @as(usize, @intCast(coins[i - 1]))] + 1);
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}
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}
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}
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if (dp[n][amt] != max) {
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return @intCast(dp[n][amt]);
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} else {
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return -1;
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}
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}
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// 零钱兑换：空间优化后的动态规划
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fn coinChangeDPComp(comptime coins: []i32, comptime amt: usize) i32 {
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comptime var n = coins.len;
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comptime var max = amt + 1;
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// 初始化 dp 表
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var dp = [_]i32{0} ** (amt + 1);
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@memset(&dp, max);
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dp[0] = 0;
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// 状态转移
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for (1..n + 1) |i| {
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for (1..amt + 1) |a| {
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if (coins[i - 1] > @as(i32, @intCast(a))) {
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// 若超过目标金额，则不选硬币 i
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dp[a] = dp[a];
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} else {
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// 不选和选硬币 i 这两种方案的较小值
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dp[a] = @min(dp[a], dp[a - @as(usize, @intCast(coins[i - 1]))] + 1);
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}
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}
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}
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if (dp[amt] != max) {
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return @intCast(dp[amt]);
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} else {
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return -1;
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}
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}
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// Driver Code
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pub fn main() !void {
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comptime var coins = [_]i32{ 1, 2, 5 };
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comptime var amt: usize = 4;
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// 动态规划
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var res = coinChangeDP(&coins, amt);
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std.debug.print("凑到目标金额所需的最少硬币数量为 {}\n", .{res});
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// 空间优化后的动态规划
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res = coinChangeDPComp(&coins, amt);
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std.debug.print("凑到目标金额所需的最少硬币数量为 {}\n", .{res});
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_ = try std.io.getStdIn().reader().readByte();
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}
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