【AtCoder】ARC085

C - HSI

题解

\(E = 1900 * (N - M) + 100 * M + \frac{1}{2^{M}} E\)

\(E = 2^{M}(1900 * (N - M) + 100 * M)\)

代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define pdi pair<db,int>
#define mp make_pair
#define pb push_back
#define enter putchar('\n')
#define space putchar(' ')
#define eps 1e-8
#define mo 974711
#define MAXN 100005
//#define ivorysi
using namespace std;
typedef long long int64;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;char c = getchar();T f = 1;
    while(c < '0' || c > '9') {
	if(c == '-') f = -1;
	c = getchar();
    }
    while(c >= '0' && c <= '9') {
	res = res * 10 + c - '0';
	c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) {
	out(x / 10);
    }
    putchar('0' + x % 10);
}
int N,M;
void Solve() {
    read(N);read(M);
    int ans = M * 1900 + (N - M) * 100;
    for(int i = 1 ; i <= M ; ++i) ans *= 2;
    out(ans);enter;
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    Solve();
    return 0;
}

D - ABS

简单的minmax搜索，就是dp[i][0/1]表示前一张牌是第i张，0是X局面，1是Y局面

每次在X层取max，在Y层取min

代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define pdi pair<db,int>
#define mp make_pair
#define pb push_back
#define enter putchar('\n')
#define space putchar(' ')
#define eps 1e-8
#define mo 974711
#define MAXN 2005
//#define ivorysi
using namespace std;
typedef long long int64;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;char c = getchar();T f = 1;
    while(c < '0' || c > '9') {
	if(c == '-') f = -1;
	c = getchar();
    }
    while(c >= '0' && c <= '9') {
	res = res * 10 + c - '0';
	c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) {
	out(x / 10);
    }
    putchar('0' + x % 10);
}
int N,Z,W;
int a[MAXN],dp[MAXN][2];
int dfs(int on,int t) {
    if(dp[t][on] != -1) return dp[t][on];
    dp[t][on] = abs(a[t] - a[N]);
    for(int i = 1 ; i < N - t ; ++i) {
	if(on == 0) dp[t][on] = max(dp[t][on],dfs(on ^ 1,t + i));
	else dp[t][on] = min(dp[t][on],dfs(on ^ 1,t + i));
    }
    return dp[t][on];
}
void Solve() {
    read(N);read(Z);read(W);
    a[0] = W;
    for(int i = 1 ; i <= N ; ++i) read(a[i]);
    memset(dp,-1,sizeof(dp));
    out(dfs(0,0));
    enter;
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    Solve();
    return 0;
}

E - MUL

题解

相当于把边权取反后求一个最大权闭合子图

代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define pdi pair<db,int>
#define mp make_pair
#define pb push_back
#define enter putchar('\n')
#define space putchar(' ')
#define eps 1e-8
#define mo 974711
#define MAXN 105
//#define ivorysi
using namespace std;
typedef long long int64;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;char c = getchar();T f = 1;
    while(c < '0' || c > '9') {
	if(c == '-') f = -1;
	c = getchar();
    }
    while(c >= '0' && c <= '9') {
	res = res * 10 + c - '0';
	c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) {
	out(x / 10);
    }
    putchar('0' + x % 10);
}
int N;
struct node {
    int to,next;
    int64 cap;
}E[MAXN * MAXN * 2];
int sumE = 1,head[MAXN],S,T;
int64 a[MAXN];
void add(int u,int v,int64 c) {
    E[++sumE].to = v;
    E[sumE].next = head[u];
    E[sumE].cap = c;
    head[u] = sumE;
}
void addtwo(int u,int v,int64 c) {
    add(u,v,c);add(v,u,0);
}
int gap[MAXN],dis[MAXN],last[MAXN];
int64 sap(int u,int64 aug) {
    if(u == T) return aug;
    int64 flow = 0;
    for(int i = last[u] ; i ; i = E[i].next) {
	int v = E[i].to;
	if(E[i].cap > 0) {
	    if(dis[v] + 1 == dis[u]) {
		int64 t = sap(v,min(E[i].cap,aug - flow));
		E[i].cap -= t;E[i ^ 1].cap += t;
		flow += t;
		if(flow == aug) return flow;
		if(dis[S] >= T) return flow;
	    }
	}
    }
    if(--gap[dis[u]++] == 0) dis[S] = T;
    ++gap[dis[u]];
    last[u] = head[u];
    return flow;
}
void Solve() {
    read(N);
    int64 ans = 0,tmp = 0;
    for(int i = 1 ; i <= N ; ++i) {
	read(a[i]);
	ans += a[i];
    }
    S = N + 1,T = N + 2;
    for(int i = 1 ; i <= N ; ++i) {
	if(a[i] > 0) addtwo(i,T,a[i]);
	else if(a[i] < 0) {
	    addtwo(S,i,-a[i]);
	    tmp -= a[i];
	}
    }
    for(int i = 1 ; i <= N ; ++i) {
	int t = 2 * i;
	while(t <= N) {
	    addtwo(i,t,2e9);
	    t += i;
	}
    }
    for(int i = 1 ; i <= N + 2 ; ++i) last[i] = head[i];
    while(dis[S] < T) tmp -= sap(S,1e18);
    ans += tmp;
    out(ans);enter;
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    Solve();
    return 0;
}

F - NRE

题解

本来想着外国人真是瞧不起中国的数据结构水平啊看我用数据结构艹过去这题

结果题解就是数据结构= =

就是把区间按右端点排序，然后每次扫到一个右端点用左端点取更新它

同时把这个区间的左端点\(dp[l - 1] - (l - 1) + sum[l - 1]\)的值更新给\([l,r]\)

一个点的dp值认为是在不断的dp时的dp值，还有是线段树里的最小值加上这个点的\(r - sum[r]\)

代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define pdi pair<db,int>
#define mp make_pair
#define pb push_back
#define enter putchar('\n')
#define space putchar(' ')
#define eps 1e-8
#define mo 974711
#define MAXN 200005
//#define ivorysi
using namespace std;
typedef long long int64;
typedef double db;
template<class T>
void read(T &res) {
    res = 0;char c = getchar();T f = 1;
    while(c < '0' || c > '9') {
	if(c == '-') f = -1;
	c = getchar();
    }
    while(c >= '0' && c <= '9') {
	res = res * 10 + c - '0';
	c = getchar();
    }
    res *= f;
}
template<class T>
void out(T x) {
    if(x < 0) {x = -x;putchar('-');}
    if(x >= 10) {
	out(x / 10);
    }
    putchar('0' + x % 10);
}
int N,Q;
int dp[MAXN],b[MAXN];
int sum[MAXN],cnt[MAXN];
vector<int> ed[MAXN];
struct node {
    int l,r,cov;
}tr[MAXN * 4];
void build(int u,int l,int r) {
    tr[u].l = l;tr[u].r = r;tr[u].cov = 2 * N;
    if(l == r) return;
    int mid = (l + r) >> 1;
    build(u << 1,l,mid);
    build(u << 1 | 1,mid + 1,r);
}
void Change(int u,int l,int r,int v) {
    if(tr[u].l == l && tr[u].r == r) {
	tr[u].cov = min(tr[u].cov,v);
	return;
    }
    int mid = (tr[u].l + tr[u].r) >> 1;
    if(r <= mid) Change(u << 1,l,r,v);
    else if(l > mid) Change(u << 1 | 1,l,r,v);
    else {Change(u << 1,l,mid,v);Change(u << 1 | 1,mid + 1,r,v);}
}
int Query(int u,int pos,int v) {
    if(tr[u].l == tr[u].r) {
	v = min(v,tr[u].cov);
	return v + tr[u].l - sum[tr[u].l];
    }
    int mid = (tr[u].l + tr[u].r) >> 1;
    if(pos <= mid) return Query(u << 1,pos,min(v,tr[u].cov));
    else return Query(u << 1 | 1,pos,min(v,tr[u].cov));
}
void Solve() {
    read(N);
    for(int i = 1 ; i <= N ; ++i) {
	read(b[i]);
	sum[i] = sum[i - 1] + b[i];
    }
    read(Q);
    int l,r;
    build(1,0,N);
    for(int i = 1 ; i <= Q ; ++i) {
	read(l);read(r);
	ed[r].pb(l);
    }
    dp[0] = 0;
    for(int i = 1 ; i <= N ; ++i) {
	dp[i] = i;
	if(b[i] == 0) dp[i] = min(dp[i - 1],dp[i]);
	else dp[i] = min(dp[i - 1] + 1,dp[i]);
	for(auto t : ed[i]) {
	    dp[i] = min(min(Query(1,t - 1,2 * N),dp[t - 1]) + (i - t + 1) - (sum[i] - sum[t - 1]),dp[i]);
	}
	for(auto t : ed[i]) {
	    int a = min(Query(1,t - 1,2 * N),dp[t - 1]);
	    Change(1,t,i,a - (t - 1) + sum[t - 1]);
	}
    }
    out(dp[N]);enter;
}
int main() {
#ifdef ivorysi
    freopen("f1.in","r",stdin);
#endif
    Solve();
    return 0;
}