[CF1454F] Array Partition

[CF1454F] Array Partition - ST表,二分

Description

给定序列 (a)，要求将其划分为三个非空子串（设三个子串长分别为 (x,y,z)），使得 (maxlimits_{i=1}^x a_i = minlimits_{i=x+1}^{x+y} a_i = maxlimits_{i=x+y+1}^n a_i)。

Solution

枚举 x，那么 y 会受到两个区间的限制

min 的限制区间用 ST 表 + 二分解出

max 的限制区间用后缀 max + 二分解出

#include <bits/stdc++.h>
using namespace std;

#define dbg(x) cerr << #x << ":=" << x << endl;

#define int long long
const int N = 200005;
const int M = 20;

int n, a[N], premax[N], sufmax[N], st[N][M];

int query(int l, int r)
{
    if (l > r)
        return 1e9;
    int lg = log2(r - l + 1);
    return min(st[l][lg], st[r - (1 << lg) + 1][lg]);
}

void solve()
{
    cin >> n;
    for (int i = 1; i <= n; i++)
        cin >> a[i], st[i][0] = a[i];
    for (int j = 1; j < M; j++)
        for (int i = 1; i + (1 << (j - 1)) <= n; i++)
            st[i][j] = min(st[i][j - 1], st[i + (1 << (j - 1))][j - 1]);
    for (int i = 1; i <= n; i++)
        premax[i] = max(premax[i - 1], a[i]);
    sufmax[n + 1] = 0;
    for (int i = n; i >= 1; i--)
        sufmax[i] = max(sufmax[i + 1], a[i]);
    for (int x = 1; x < n; x++)
    {
        int val = premax[x];
        int l1 = 1e9, r1 = 0, l2 = 1e9, r2 = 0;
        {
            int l = x + 1, r = n;
            while (l < r)
            {
                int mid = (l + r) / 2;
                if (query(x + 1, mid) <= val)
                    r = mid;
                else
                    l = mid + 1;
            }
            if (query(x + 1, l) == val)
                l1 = l;
        }
        {
            int l = x + 1, r = n + 1;
            while (l < r)
            {
                int mid = (l + r) / 2;
                if (query(x + 1, mid) < val)
                    r = mid;
                else
                    l = mid + 1;
            }
            if (query(x + 1, l - 1) == val)
                r1 = l - 1;
        }
        {
            int l = x + 1, r = n;
            while (l < r)
            {
                int mid = (l + r) / 2;
                if (sufmax[mid + 1] <= val)
                    r = mid;
                else
                    l = mid + 1;
            }
            if (sufmax[l + 1] == val)
                l2 = l;
        }
        {
            int l = x + 1, r = n + 1;
            while (l < r)
            {
                int mid = (l + r) / 2;
                if (sufmax[mid + 1] < val)
                    r = mid;
                else
                    l = mid + 1;
            }
            if (sufmax[l] == val)
                r2 = l - 1;
        }
        int l = max(l1, l2), r = min(r1, r2);
        if (l <= r)
        {
            // dbg(l1) dbg(l2) dbg(r1) dbg(r2)
                    cout
                << "YES" << endl;
            cout << x << " " << l - x << " " << n - l << endl;
            return;
        }
    }
    cout << "NO" << endl;
}

signed main()
{
    ios::sync_with_stdio(false);

    int t;
    cin >> t;

    while (t--)
        solve();
}