启发式分治:2019牛客多校第三场 G题 Removing Stones

问题可以转换为求有多少个区间数字的总和除2向下取整大于等于最大值。或者解释为有多少个区间数字的总和大于等于最大值的两倍(但是若区间数字总和为奇数,需要算作减1)

启发式分治:
首先按最大值位置分治,遍历长度较短的一边,枚举它为一个端点,另一边二分算贡献即可。
复杂度大概\(nlog(n)^2\)

#pragma comment(linker, "/STACK:102400000,102400000")
#include<bits/stdc++.h>
#define fi first
#define se second
#define endl '\n'
#define o2(x) (x)*(x)
#define BASE_MAX 30
#define mk make_pair
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define clr(a, b) memset((a),(b),sizeof((a)))
#define iis std::ios::sync_with_stdio(false); cin.tie(0)
#define my_unique(x) sort(all(x)),x.erase(unique(all(x)),x.end())
using namespace std;
#pragma optimize("-O3")
typedef long long LL;
typedef pair<int, int> pii;
inline LL read() {
    LL x = 0;int f = 0;
    char ch = getchar();
    while (ch < '0' || ch > '9') f |= (ch == '-'), ch = getchar();
    while (ch >= '0' && ch <= '9') x = (x << 3) + (x << 1) + ch - '0', ch = getchar();
    return x = f ? -x : x;
}
inline void write(LL x) {
    if (x == 0) {putchar('0'), putchar('\n');return;}
    if (x < 0) {putchar('-');x = -x;}
    static char s[23];
    int l = 0;
    while (x != 0)s[l++] = x % 10 + 48, x /= 10;
    while (l)putchar(s[--l]);
    putchar('\n');
}
int lowbit(int x) { return x & (-x); }
template<class T>T big(const T &a1, const T &a2) { return a1 > a2 ? a1 : a2; }
template<typename T, typename ...R>T big(const T &f, const R &...r) { return big(f, big(r...)); }
template<class T>T sml(const T &a1, const T &a2) { return a1 < a2 ? a1 : a2; }
template<typename T, typename ...R>T sml(const T &f, const R &...r) { return sml(f, sml(r...)); }
void debug_out() { cerr << '\n'; }
template<typename T, typename ...R>void debug_out(const T &f, const R &...r) {cerr << f << " ";debug_out(r...);}
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]: ", debug_out(__VA_ARGS__);

#define print(x) write(x);
typedef unsigned long long uLL;
const LL INFLL = 0x3f3f3f3f3f3f3f3fLL;
const int HMOD[] = {1000000009, 1004535809};
const LL BASE[] = {1572872831, 1971536491};
const int mod = 998244353;
const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int MXN = 3e5 + 7;

int n, q;
LL ar[MXN], dp[MXN][20], pos[MXN][20];
LL sum[MXN], ans, ret;
void init() {
    for(int j = 1; j < 20; ++j) {
        if((1<<(j-1)) > n) break;
        for(int i = 1; i + (1<<j) - 1 <= n; ++i) {
            if(dp[i][j-1] >= dp[i+(1<<(j-1))][j-1]) {
                dp[i][j] = dp[i][j-1];
                pos[i][j] = pos[i][j-1];
            }else {
                dp[i][j] = dp[i+(1<<(j-1))][j-1];
                pos[i][j] = pos[i+(1<<(j-1))][j-1];
            }
        }
    }
}
inline int query(int l, int r) {
    int k = log(r - l + 1) / log(2);
    if (dp[l][k] >= dp[r - (1 << k) + 1][k]) return pos[l][k];
    return pos[r - (1 << k) + 1][k];
}
void solve(int l, int r) {
    if(l >= r) return;
    if(l + 1 == r) {
        ans += (ar[l] == ar[r]);
        return;
    }
    int mid = query(l, r);
//    debug(mid)
    if(r - mid > mid - l) {
        for(int i = l ; i <= mid; ++i) {
            int L = mid + 1, R = r, M, res = mid;
            if(i != mid) L = mid, res = mid - 1;
            while(L <= R) {
                M = (L + R) >> 1;
                ret = sum[M] - sum[i-1];
                if(ret & 1) -- ret;
                if(ret < 2 * ar[mid]) res = M, L = M + 1;
                else R = M - 1;
            }
            ans += r - res;
//            debug(i, res)
        }
    }else {
        for(int i = mid; i <= r; ++i) {
            int L = l, R = mid - 1, M, res = mid;
            if(i != mid) R = mid, res = mid + 1;
            while(L <= R) {
                M = (L + R) >> 1;
                ret = sum[i] - sum[M-1];
                if(ret & 1) -- ret;
                if(ret < 2 * ar[mid]) res = M, R = M - 1;
                else L = M + 1;
            }
            ans += res - l;
//            debug(i, res)
        }
    }
    solve(l, mid - 1), solve(mid + 1, r);
}
int main() {
#ifndef ONLINE_JUDGE
    freopen("/home/cwolf9/CLionProjects/ccc/in.txt", "r", stdin);
    //freopen("/home/cwolf9/CLionProjects/ccc/out.txt", "w", stdout);
#endif
    int tim = read();
    while(tim --) {
        n = read();
//        debug("***")
        ans = 0;
        for(int i = 1; i <= n; ++i) ar[i] = read(), sum[i] = sum[i-1] + ar[i], dp[i][0] = ar[i], pos[i][0] = i;
        init();
        solve(1, n);
        print(ans)
//    debug(ans)
    }
#ifndef ONLINE_JUDGE
    cout << "time cost:" << clock() << "ms" << endl;
#endif
    return 0;
}

https://codeforces.com/blog/entry/44351

posted @ 2019-07-31 22:28 Cwolf9 阅读(...) 评论(...) 编辑 收藏

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