CodeForces-1216F Wi-Fi

传送门：CodeForces-1216F

思路分析

DP方程不难想，转移过程是区间最值，所以可以用线段树优化

AC代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define ll long long
#define pb push_back
#define mp make_pair
#define fun function
#define sz(x) (x).size()
#define lowbit(x) (x)&(-x)
#define all(x) (x).begin(),(x).end()
#define mem(a,b) memset(a,b,sizeof(a))

namespace FastIO {
#define BUF_SIZE 100000
#define OUT_SIZE 100000
    bool IOerror=0;
    inline char nc() {
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if(p1==pend) {
            p1=buf;
            pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if(pend==p1) {
                IOerror=1;
                return -1;
            }
        }
        return *p1++;
    }
    inline bool blank(char ch) {
        return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';
    }
    template<class T> inline bool read(T &x) {
        bool sign=0;
        char ch=nc();
        x=0;
        for(; blank(ch); ch=nc());
        if(IOerror)return false;
        if(ch=='-')sign=1,ch=nc();
        for(; ch>='0'&&ch<='9'; ch=nc())x=x*10+ch-'0';
        if(sign)x=-x;
        return true;
    }
    template<class T,class... U>bool read(T& h,U&... t) {
        return read(h)&&read(t...);
    }
#undef OUT_SIZE
#undef BUF_SIZE
};
using namespace std;
using namespace FastIO;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

#define int long long
const int INF = 1e18;
const int N = 2e5+10;

struct node{
    struct Node{
        int l,r,mid,mi;
    }tree[N<<2];
    #define ls x<<1
    #define rs x<<1|1
    void pp(int x){
        tree[x].mi=min(tree[ls].mi,tree[rs].mi);
    }
    
    void build(int x,int l,int r){
        tree[x]={l,r,l+r>>1,INF};
        if(l==r) return ;
        int mid=tree[x].mid;
        build(ls,l,mid);
        build(rs,mid+1,r);
        pp(x);
    }
    
    void modify(int x,int pos,int k){
        if(tree[x].l==pos && tree[x].r==pos){
            tree[x].mi=min(tree[x].mi,k);
            return ;
        }
        int mid=tree[x].mid;
        if(pos<=mid) modify(ls,pos,k);
        else modify(rs,pos,k);
        pp(x);
    }
    
    int query(int x,int l,int r){
        if(l<=tree[x].l && tree[x].r<=r ){
            return tree[x].mi;
        }
        int ans=INF;
        int mid=tree[x].mid;
        if(l<=mid) ans=min(ans,query(ls,l,r));
        if(r>mid) ans=min(ans,query(rs,l,r));
        return ans;
    }
    #undef ls
    #undef rs
}t0,t1;

int dp[N][2];
char s[N];

signed main() {

#ifdef xiaofan
    freopen("1.in","r",stdin);
    freopen("1.out","w",stdout);
#endif

    int n,k;
    cin>>n>>k;
    cin>>s+1;
    for(int i=1;i<=n;i++) dp[i][0]=dp[i][1]=1e18;
    dp[0][0]=0;
    t0.build(1,0,n);
    t1.build(1,0,n);
    t0.modify(1,0,0);
    for(int i=1;i<=n;i++){
        dp[i][0]=min(dp[i-1][0]+i,t1.query(1,max(0LL,i-k),i-1));
        if(s[i]=='1') dp[i][1]=min(t0.query(1,max(0LL,i-k-1),i-1),t1.query(1,max(0LL,i-k-1),i-1))+i;
        t0.modify(1,i,dp[i][0]);
        t1.modify(1,i,dp[i][1]);        
    }
    cout<<min(dp[n][0],dp[n][1])<<endl;
    




    return 0;
}