guest@cp-base:~/home/strings$
templates/hashed-deque.cpp
compilable
$cat templates/hashed-deque

Hashed Deque

Deque with O(1) rolling polynomial double hash for constant-time equality comparison.

[Strings]|
Jul 9, 2026
|explanatory_notes.md|
#hashing#deque#rolling-hash#equality
Log in to track progress, save custom versions, and organize into collections.Log In
$cat source_code/
cpp
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

struct HashedDeque {
    static const int MAXN = 500005;
    static const ll BASE = 1000000007;
    static ll mod[2], pw[MAXN][2], inv[MAXN][2];
    static bool inited;

    deque<ll> dq;
    ll val[2] = {};
    int len = 0;

    static ll power(ll b, ll e, ll m) {
        ll r = 1; b %= m;
        while (e > 0) { if (e & 1) r = r * b % m; b = b * b % m; e >>= 1; }
        return r;
    }

    static void init() {
        if (inited) return; inited = true;
        mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
        auto nextPrime = [](ll x) { while (true) { bool ok = x > 1; for (ll i = 2; i * i <= x && ok; i++) ok = x % i != 0; if (ok) return x; x++; } };
        mod[0] = nextPrime(900000000LL + rng() % 100000000);
        mod[1] = nextPrime(900000000LL + rng() % 100000000);
        while (mod[1] == mod[0]) mod[1] = nextPrime(900000000LL + rng() % 100000000);
        for (int j = 0; j < 2; j++) {
            pw[0][j] = inv[0][j] = 1;
            ll invB = power(BASE, mod[j] - 2, mod[j]);
            for (int i = 1; i < MAXN; i++) {
                pw[i][j] = pw[i-1][j] * BASE % mod[j];
                inv[i][j] = inv[i-1][j] * invB % mod[j];
            }
        }
    }

    HashedDeque() { init(); }

    void pushBack(ll x) {
        for (int j = 0; j < 2; j++)
            val[j] = (val[j] * BASE + x) % mod[j];
        dq.push_back(x); len++;
    }

    void pushFront(ll x) {
        for (int j = 0; j < 2; j++)
            val[j] = (x * pw[len][j] + val[j]) % mod[j];
        dq.push_front(x); len++;
    }

    void popBack() {
        ll x = dq.back(); dq.pop_back(); len--;
        for (int j = 0; j < 2; j++)
            val[j] = (val[j] - x % mod[j] + mod[j]) % mod[j] * inv[1][j] % mod[j];
    }

    void popFront() {
        ll x = dq.front(); dq.pop_front(); len--;
        for (int j = 0; j < 2; j++)
            val[j] = (val[j] - x * pw[len][j] % mod[j] + mod[j]) % mod[j];
    }

    int size() const { return len; }
    bool operator==(const HashedDeque &o) const { return len == o.len && val[0] == o.val[0] && val[1] == o.val[1]; }
};

ll HashedDeque::mod[2];
ll HashedDeque::pw[HashedDeque::MAXN][2];
ll HashedDeque::inv[HashedDeque::MAXN][2];
bool HashedDeque::inited = false;
71 linesutf-8
$cat explanation_notes.md
notes_viewer --renderedmarkdown (math enabled)

Hashed Deque

A double-ended queue that maintains a rolling polynomial hash, enabling O(1)O(1) equality comparison between two deques.

Hash Updates

For sequence a0,a1,…,an−1a_0, a_1, \dots, a_{n-1} with hash H=∑ai⋅bn−1−i mod mH = \sum a_i \cdot b^{n-1-i} \bmod m:

  • Push back (xx): H′=H⋅b+xH' = H \cdot b + x

  • Push front (xx): H′=x⋅blen+HH' = x \cdot b^{\text{len}} + H

  • Pop back (an−1a_{n-1}): H′=(H−an−1)⋅b−1H' = (H - a_{n-1}) \cdot b^{-1}

  • Pop front (a0a_0): H′=H−a0⋅blen−1H' = H - a_0 \cdot b^{\text{len}-1}

    • All operations O(1)O(1) using precomputed powers and modular inverses.

    When to Use

  • O(1)O(1) equality comparison of two sequences

  • Sliding window hashing with push/pop from both ends

  • Palindrome checking on a deque

    • Anti-Hack

    Two random prime moduli selected at runtime. Double hashing reduces collision probability.

    Complexity

  • Push / Pop — O(1)O(1)

  • Equality check — O(1)O(1)

  • Initialization — O(N)O(N) for power/inverse precomputation