結果
問題 |
No.3119 A Little Cheat
|
ユーザー |
|
提出日時 | 2025-04-20 18:59:25 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 73 ms / 2,000 ms |
コード長 | 4,817 bytes |
コンパイル時間 | 2,074 ms |
コンパイル使用メモリ | 206,356 KB |
実行使用メモリ | 7,844 KB |
最終ジャッジ日時 | 2025-04-20 18:59:33 |
合計ジャッジ時間 | 6,634 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 49 |
ソースコード
#include <bits/stdc++.h> using namespace std; using ll = long long; static const ll MOD = 998244353; inline ll mod_add(ll a, ll b) { a += b; if (a >= MOD) a -= MOD; return a; } inline ll mod_mul(ll a, ll b) { return (a % MOD) * (b % MOD) % MOD; } inline ll overlap(int a1, int b1, int a2, int b2) { int lo = max(a1, a2); int hi = min(b1, b2); return (lo <= hi) ? (hi - lo + 1) : 0; } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); int N, M; cin >> N >> M; vector<int> A(N); for(int i = 0; i < N; i++){ cin >> A[i]; } // Precompute powers of M mod MOD vector<ll> powM(N+1, 1); ll M_mod = M % MOD; for(int i = 1; i <= N; i++){ powM[i] = mod_mul(powM[i-1], M_mod); } // 1) Base score: sum (M - A[i]) * M^(N-1) ll base = 0; for(int i = 0; i < N; i++){ base = mod_add(base, mod_mul((M - A[i] + MOD) % MOD, powM[N-1])); } if(N == 1){ cout << base << "\n"; return 0; } // DP states: counts of prefixes ending in small/mid/large region int t0 = min(A[0], A[1]); int T0 = max(A[0], A[1]); ll dp_sm = t0; ll dp_md = T0 - t0; ll dp_lg = M - T0; ll X = 0; for(int i = 0; i < N - 1; i++){ // current thresholds int ti = min(A[i], A[i+1]); int Ti = max(A[i], A[i+1]); int sm_i = ti; int md_i = Ti - ti; int lg_i = M - Ti; // number of free tail choices ll tail = (i + 2 <= N) ? powM[N - i - 2] : 1LL; // add contribution for first improvement at i if(A[i] < A[i+1]){ // improve by moving into mid_i ll ways = mod_add(dp_sm, dp_lg); X = mod_add(X, mod_mul(mod_mul(ways, md_i), tail)); } else { // improve by moving into sm_i or lg_i ll ways = dp_md % MOD; ll sum = (sm_i + lg_i) % MOD; X = mod_add(X, mod_mul(mod_mul(ways, sum), tail)); } // no need to update dp after last pair if(i == N - 2) break; // thresholds for next position int tn = min(A[i+1], A[i+2]); int Tn = max(A[i+1], A[i+2]); int sm_n = tn; int md_n = Tn - tn; int lg_n = M - Tn; // build allowed ranges for B_{i+1} to avoid early improvement // for each previous region "sm","md","lg" vector<pair<int,int>> allow_sm, allow_md, allow_lg; if(A[i] < A[i+1]){ // cannot choose B_{i+1} in mid_i when coming from sm or lg allow_sm = {{1, ti}, {Ti+1, M}}; allow_lg = allow_sm; allow_md = {{1, M}}; } else { // cannot choose B_{i+1} in sm_i/lg_i when coming from md allow_md = {{ti+1, Ti}}; allow_sm = {{1, M}}; allow_lg = allow_sm; } // next intervals classification vector<pair<int,int>> next_sm = {{1, tn}}; vector<pair<int,int>> next_md = {{tn+1, Tn}}; vector<pair<int,int>> next_lg = {{Tn+1, M}}; ll new_sm = 0, new_md = 0, new_lg = 0; // transition from "sm" region for(auto &seg : allow_sm){ for(auto &nx : next_sm){ new_sm += dp_sm * overlap(seg.first, seg.second, nx.first, nx.second); } for(auto &nx : next_md){ new_md += dp_sm * overlap(seg.first, seg.second, nx.first, nx.second); } for(auto &nx : next_lg){ new_lg += dp_sm * overlap(seg.first, seg.second, nx.first, nx.second); } } // from "md" region for(auto &seg : allow_md){ for(auto &nx : next_sm){ new_sm += dp_md * overlap(seg.first, seg.second, nx.first, nx.second); } for(auto &nx : next_md){ new_md += dp_md * overlap(seg.first, seg.second, nx.first, nx.second); } for(auto &nx : next_lg){ new_lg += dp_md * overlap(seg.first, seg.second, nx.first, nx.second); } } // from "lg" region for(auto &seg : allow_lg){ for(auto &nx : next_sm){ new_sm += dp_lg * overlap(seg.first, seg.second, nx.first, nx.second); } for(auto &nx : next_md){ new_md += dp_lg * overlap(seg.first, seg.second, nx.first, nx.second); } for(auto &nx : next_lg){ new_lg += dp_lg * overlap(seg.first, seg.second, nx.first, nx.second); } } dp_sm = new_sm % MOD; dp_md = new_md % MOD; dp_lg = new_lg % MOD; } ll answer = mod_add(base, X); cout << answer << "\n"; return 0; }