위 포스트는 백준 28129 - 2022 APC가 어려웠다고요?의 풀이입니다.

핵심 아이디어#

dp[i][j] := i번째 수가 j가 되는 경우의 수

위와 같은 dp 식을 누적합으로 $O(N^2)$으로 해결할 수 있다.

코드#

cpp
1#include <bits/stdc++.h>
2
3#define endl "\n"
4#define all(v) (v).begin(), (v).end()
5#define all1(v) (v).begin()+1, (v).end()
6#define For(i, a, b) for(int i=(a); i<(b); i++)
7#define FOR(i, a, b) for(int i=(a); i<=(b); i++)
8#define Bor(i, a, b) for(int i=(a)-1; i>=(b); i--)
9#define BOR(i, a, b) for(int i=(a); i>=(b); i--)
10#define ft first
11#define sd second
12
13using namespace std;
14using ll = long long;
15using lll = __int128_t;
16using ulll = __uint128_t;
17using ull = unsigned long long;
18using ld = long double;
19using pii = pair<int, int>;
20using pll = pair<ll, ll>;
21using ti3 = tuple<int, int, int>;
22using tl3 = tuple<ll, ll, ll>;
23
24template<typename T> using ve = vector<T>;
25template<typename T> using vve = vector<vector<T>>;
26
27template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
28template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
29
30const int INF = 987654321;
31const int INF0 = numeric_limits<int>::max();
32const ll LNF = 987654321987654321;
33const ll LNF0 = numeric_limits<ll>::max();
34
35const int mxn = 3001;
36const ll mod = 1e9+7;
37
38void solve() {
39    int n, k; cin >> n >> k;
40    ve<int> a(n+1), b(n+1);
41    for(int i=1; i<=n; i++) cin >> a[i] >> b[i];
42
43    vve<ll> dp(n+1, ve<ll>(mxn, 0));
44    vve<ll> psum(n+1, ve<ll>(mxn, 0));
45    for(int i=1; i<=n; i++) {
46        if(i == 1) {
47            for(int j=a[i]; j<=b[i]; j++) {
48                dp[i][j] = 1;
49            }
50        }
51        else {
52            for(int j=a[i]; j<=b[i]; j++) {
53                int l = max(j-k,a[i-1]), r = min(j+k,b[i-1]);
54                dp[i][j] = (psum[i-1][r] - psum[i-1][l-1] + mod) % mod;
55            }
56        }
57
58        for(int j=1; j<mxn; j++) {
59            psum[i][j] = (psum[i][j-1] + dp[i][j]) % mod;
60        }
61    }
62    cout << psum[n][mxn-1] << endl;
63}
64
65int main(void) {
66    ios_base::sync_with_stdio(false);
67    cin.tie(nullptr);
68    cout.tie(nullptr);
69
70    int TC=1;
71//    cin >> TC;
72    FOR(tc, 1, TC) {
73//        cout << "Case #" << tc << ": ";
74        solve();
75    }
76
77
78    return 0;
79}