hello-algo/codes/zig/chapter_dynamic_programming/climbing_stairs_constraint_dp.zig

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// File: climbing_stairs_constraint_dp.zig
// Created Time: 2023-07-15
// Author: sjinzh (sjinzh@gmail.com)
const std = @import("std");
// 带约束爬楼梯:动态规划
fn climbing_stairs_constraint_dp(comptime n: usize) i32 {
if (n == 1 or n == 2) {
return @intCast(n);
}
// 初始化 dp 表,用于存储子问题的解
var dp = [_][3]i32{ [_]i32{ -1, -1, -1 } } ** (n + 1);
// 初始状态:预设最小子问题的解
dp[1][1] = 1;
dp[1][2] = 0;
dp[2][1] = 0;
dp[2][2] = 1;
// 状态转移:从较小子问题逐步求解较大子问题
for (3..n + 1) |i| {
dp[i][1] = dp[i - 1][2];
dp[i][2] = dp[i - 2][1] + dp[i - 2][2];
}
return dp[n][1] + dp[n][2];
}
// Driver Code
pub fn main() !void {
comptime var n: usize = 9;
var res = climbing_stairs_constraint_dp(n);
std.debug.print("爬 {} 阶楼梯共有 {} 种方案\n", .{ n, res });
_ = try std.io.getStdIn().reader().readByte();
}