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  • Codeforces 1129D Isolation dp + 分块 (看题解)

    Isolation

    感觉没有见过这种分块优化的题目啊。。

    dp转移很容易就能得出来, 然后分块维护块内信息, 在末尾加入一个数的时候更新块内信息, 更新当前合法的dp值得和。

    #include<bits/stdc++.h>
    #define LL long long
    #define LD long double
    #define ull unsigned long long
    #define fi first
    #define se second
    #define mk make_pair
    #define PLL pair<LL, LL>
    #define PLI pair<LL, int>
    #define PII pair<int, int>
    #define SZ(x) ((int)x.size())
    #define ALL(x) (x).begin(), (x).end()
    #define fio ios::sync_with_stdio(false); cin.tie(0);
    
    using namespace std;
    
    const int N = 1e5 + 7;
    const int inf = 0x3f3f3f3f;
    const LL INF = 0x3f3f3f3f3f3f3f3f;
    const int mod = 998244353;
    const double eps = 1e-8;
    const double PI = acos(-1);
    
    template<class T, class S> inline void add(T &a, S b) {a += b; if(a >= mod) a -= mod;}
    template<class T, class S> inline void sub(T &a, S b) {a -= b; if(a < 0) a += mod;}
    template<class T, class S> inline bool chkmax(T &a, S b) {return a < b ? a = b, true : false;}
    template<class T, class S> inline bool chkmin(T &a, S b) {return a > b ? a = b, true : false;}
    
    mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
    
    const int B = 350;
    
    int n, k, a[N];
    int belong[N], bl[N], br[N];
    int prePos[N], Map[N];
    int c[400][N], lazy[400], g[N];
    int dp[N], sumdp;
    
    void changeUp(int L, int R) {
        if(L > R) return;
        if(belong[L] == belong[R]) {
            for(int i = L; i <= R; i++) {
                if(g[i] + lazy[belong[i]] == k) sub(sumdp, dp[i]);
                sub(c[belong[i]][g[i]], dp[i]);
                g[i]++;
                add(c[belong[i]][g[i]], dp[i]);
            }
        } else {
            for(int i = L; i <= br[belong[L]]; i++) {
                if(g[i] + lazy[belong[L]] == k) sub(sumdp, dp[i]);
                sub(c[belong[i]][g[i]], dp[i]);
                g[i]++;
                add(c[belong[i]][g[i]], dp[i]);
            }
            for(int i = bl[belong[R]]; i <= R; i++) {
                if(g[i] + lazy[belong[R]] == k) sub(sumdp, dp[i]);
                sub(c[belong[i]][g[i]], dp[i]);
                g[i]++;
                add(c[belong[i]][g[i]], dp[i]);
            }
            for(int i = belong[L] + 1; i <= belong[R] - 1; i++) {
                sub(sumdp, c[i][k - lazy[i]]);
                lazy[i]++;
            }
        }
    }
    
    void changeDn(int L, int R) {
        if(L > R) return;
        if(belong[L] == belong[R]) {
            for(int i = L; i <= R; i++) {
                if(g[i] + lazy[belong[i]] == k + 1) add(sumdp, dp[i]);
                sub(c[belong[i]][g[i]], dp[i]);
                g[i]--;
                add(c[belong[i]][g[i]], dp[i]);
            }
        } else {
            for(int i = L; i <= br[belong[L]]; i++) {
                if(g[i] + lazy[belong[L]] == k + 1) add(sumdp, dp[i]);
                sub(c[belong[i]][g[i]], dp[i]);
                g[i]--;
                add(c[belong[i]][g[i]], dp[i]);
            }
            for(int i = bl[belong[R]]; i <= R; i++) {
                if(g[i] + lazy[belong[R]] == k + 1) add(sumdp, dp[i]);
                sub(c[belong[i]][g[i]], dp[i]);
                g[i]--;
                add(c[belong[i]][g[i]], dp[i]);
            }
            for(int i = belong[L] + 1; i <= belong[R] - 1; i++) {
                add(sumdp, c[i][k + 1 - lazy[i]]);
                lazy[i]--;
            }
        }
    }
    
    int main() {
        memset(bl, 0x3f, sizeof(bl));
        memset(br, 0xc0, sizeof(br));
        scanf("%d%d", &n, &k);
        for(int i = 0; i <= n; i++) {
            belong[i] = i / B;
            chkmin(bl[belong[i]], i);
            chkmax(br[belong[i]], i);
        }
        dp[0] = 1;
        c[0][0] = 1;
        sumdp = 1;
    
        for(int i = 1; i <= n; i++) {
            scanf("%d", &a[i]);
            prePos[i] = Map[a[i]];
            Map[a[i]] = i;
        }
        for(int i = 1; i <= n; i++) {
            int pos = prePos[i];
            int ppos = prePos[pos];
            changeUp(pos, i - 1);
            changeDn(ppos, pos - 1);
            dp[i] = sumdp;
            add(sumdp, dp[i]);
            add(c[belong[i]][0], dp[i]);
        }
        printf("%d
    ", dp[n]);
        return 0;
    }
    
    /*
    */
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  • 原文地址:https://www.cnblogs.com/CJLHY/p/11138726.html
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