Realm

1package collatz
2
3import (
4	"chain"
5	"sort"
6	"strconv"
7	"strings"
8
9	"gno.land/p/moul/md/v0"
10	"gno.land/p/nt/avl/v0"
11)
12
13// selfPath is this realm's own page. A root-relative link resolves against
14// the domain, not the realm, so every link back into it names it in full.
15const selfPath = "/r/moul/x/daily/collatz/v1"
16
17// maxIters caps the Collatz walk so a hostile / huge input cannot loop
18// forever on-chain. No known n stays below this bound and fails to reach 1.
19const maxIters = 1000000
20
21// MaxResults bounds the leaderboard's state: anyone may Compute, and each new
22// n is a new entry the root page sorts.
23const MaxResults = 1000
24
25// maxSeqLen caps how many terms Render("/<n>") will print.
26const maxSeqLen = 500
27
28// Result is one recorded submission.
29type Result struct {
30	N     int64
31	Steps int
32	Peak  int64
33	Who   address
34}
35
36// results maps a decimal-string key of N -> Result. avl.Tree keeps a
37// deterministic order for iteration inside Render.
38var results avl.Tree
39
40// maxOdd is the largest odd term whose successor 3n+1 still fits in an
41// int64. Past it the step wraps: 6148914691236517205 maps to exactly 2^64,
42// which is 0, and the walk then spins on 0 until maxIters.
43const maxOdd = (1<<63 - 1 - 1) / 3
44
45// stopping returns the number of steps to reach 1 and the peak value seen,
46// walking the Collatz (hailstone) map. ok is false when a term would overflow
47// int64, in which case steps and peak describe the walk up to that term. It
48// never mutates state.
49func stopping(n int64) (steps int, peak int64, ok bool) {
50	peak = n
51	cur := n
52	for cur != 1 {
53		if steps >= maxIters {
54			break
55		}
56		if cur%2 == 0 {
57			cur = cur / 2
58		} else {
59			if cur > maxOdd {
60				return steps, peak, false
61			}
62			cur = 3*cur + 1
63		}
64		if cur > peak {
65			peak = cur
66		}
67		steps++
68	}
69	return steps, peak, true
70}
71
72// Compute walks the hailstone sequence for n and records the result
73// attributed to the caller. It is a crossing (state-mutating) func.
74func Compute(cur realm, n int) {
75	if !cur.IsCurrent() {
76		panic("collatz: spoofed realm")
77	}
78	caller := cur.Previous().Address()
79	if n <= 0 {
80		panic("n must be > 0")
81	}
82	nn := int64(n)
83	steps, peak, ok := stopping(nn)
84	if !ok {
85		// Recording it would put a wrapped walk on the leaderboard, forever.
86		panic("collatz: the walk from " + strconv.FormatInt(nn, 10) + " overflows int64")
87	}
88
89	res := Result{N: nn, Steps: steps, Peak: peak, Who: caller}
90	key := strconv.FormatInt(nn, 10)
91	if !results.Has(key) && results.Size() >= MaxResults {
92		panic("collatz: the leaderboard is full at " + strconv.Itoa(MaxResults) + " entries")
93	}
94	results.Set(key, res)
95
96	chain.Emit(
97		"Computed",
98		"n", key,
99		"steps", strconv.Itoa(steps),
100		"peak", strconv.FormatInt(peak, 10),
101		"who", caller.String(),
102	)
103}
104
105// byLongest implements sort.Interface, ordering results by steps desc,
106// then peak desc, then n asc for stability.
107type byLongest []Result
108
109func (b byLongest) Len() int      { return len(b) }
110func (b byLongest) Swap(i, j int) { b[i], b[j] = b[j], b[i] }
111func (b byLongest) Less(i, j int) bool {
112	if b[i].Steps != b[j].Steps {
113		return b[i].Steps > b[j].Steps
114	}
115	if b[i].Peak != b[j].Peak {
116		return b[i].Peak > b[j].Peak
117	}
118	return b[i].N < b[j].N
119}
120
121// Render shows the leaderboard at root, or the full hailstone sequence for a
122// given n at path "/<n>".
123func Render(path string) string {
124	p := strings.TrimPrefix(path, "/")
125	if p == "" {
126		return renderLeaderboard()
127	}
128	return renderSequence(p)
129}
130
131func renderLeaderboard() string {
132	all := make([]Result, 0, results.Size())
133	results.Iterate("", "", func(_ string, v interface{}) bool {
134		all = append(all, v.(Result))
135		return false
136	})
137
138	var sb strings.Builder
139	sb.WriteString("# Collatz Explorer\n\n")
140	sb.WriteString("Hailstone-sequence explorer. Call `Compute(n)` to record a run, ")
141	sb.WriteString("or view a full sequence at `/<n>`.\n\n")
142
143	if len(all) == 0 {
144		sb.WriteString("_No sequences submitted yet._\n")
145		return sb.String()
146	}
147
148	sort.Stable(byLongest(all))
149
150	sb.WriteString("## Leaderboard — longest sequences\n\n")
151	sb.WriteString("| # | n | steps | peak | who |\n")
152	sb.WriteString("|---|---|-------|------|-----|\n")
153	limit := len(all)
154	if limit > 20 {
155		limit = 20
156	}
157	for i := 0; i < limit; i++ {
158		r := all[i]
159		sb.WriteString("| " + strconv.Itoa(i+1) + " | ")
160		sb.WriteString("[" + strconv.FormatInt(r.N, 10) + "](" + selfPath + ":" + strconv.FormatInt(r.N, 10) + ") | ")
161		sb.WriteString(strconv.Itoa(r.Steps) + " | ")
162		sb.WriteString(strconv.FormatInt(r.Peak, 10) + " | ")
163		sb.WriteString(r.Who.String() + " |\n")
164	}
165	sb.WriteString("\n_" + strconv.Itoa(len(all)) + " sequence(s) recorded._\n")
166	return sb.String()
167}
168
169func renderSequence(p string) string {
170	n, err := strconv.ParseInt(p, 10, 64)
171	var sb strings.Builder
172	if err != nil || n <= 0 {
173		sb.WriteString("# Invalid n\n\n" + md.InlineCode(p) + " is not a positive integer.\n")
174		return sb.String()
175	}
176
177	sb.WriteString("# Hailstone sequence for " + strconv.FormatInt(n, 10) + "\n\n")
178
179	seq := make([]int64, 0, 64)
180	cur := n
181	var peak int64 = n
182	truncated := false
183	overflow := false
184	for {
185		seq = append(seq, cur)
186		if cur == 1 {
187			break
188		}
189		if len(seq) >= maxSeqLen {
190			truncated = true
191			break
192		}
193		if cur%2 == 0 {
194			cur = cur / 2
195		} else {
196			if cur > maxOdd {
197				overflow = true
198				break
199			}
200			cur = 3*cur + 1
201		}
202		if cur > peak {
203			peak = cur
204		}
205	}
206
207	parts := make([]string, len(seq))
208	for i, v := range seq {
209		parts[i] = strconv.FormatInt(v, 10)
210	}
211	sb.WriteString(strings.Join(parts, " → "))
212	sb.WriteString("\n\n")
213	sb.WriteString("- steps: " + strconv.Itoa(len(seq)-1) + "\n")
214	sb.WriteString("- peak: " + strconv.FormatInt(peak, 10) + "\n")
215	if overflow {
216		sb.WriteString("\n_Stopped: the next term would overflow int64._\n")
217	}
218	if truncated {
219		sb.WriteString("\n_Sequence truncated at " + strconv.Itoa(maxSeqLen) + " terms._\n")
220	}
221	return sb.String()
222}
223