Codeforces Round 951 (Div. 2) C、D（构造、线段树）

1979C - Earning on Bets

构造题：观察到k范围很小，首先考虑最终硬币总数可以是多少，我们可以先假设最终的硬币总数为所有k取值的最小公倍数，这样只需要满足每个结果添加1枚硬币即可赚到硬币。

cpp 复制代码

// Problem: C. Earning on Bets
// Contest: Codeforces - Codeforces Round 951 (Div. 2)
// URL: https://codeforces.com/contest/1979/problem/C
// Memory Limit: 256 MB
// Time Limit: 2000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
using namespace std;
#define LL long long
#define pb push_back
#define x first
#define y second 
#define endl '\n'
#define int long long
const LL maxn = 4e05+7;
const LL N = 5e05+10;
const LL mod = 1e09+7;
const int inf = 0x3f3f3f3f;
const LL llinf = 5e18;
typedef pair<int,int>pl;
priority_queue<LL , vector<LL>, greater<LL> >mi;//小根堆
priority_queue<LL> ma;//大根堆
LL gcd(LL a, LL b){
	return b > 0 ? gcd(b , a % b) : a;
}

LL lcm(LL a , LL b){
	return a / gcd(a , b) * b;
}
int n , m;
vector<int>a(N , 0);
void init(int n){
	for(int i = 0 ; i <= n ; i ++){
		a[i] = 0;
	}
}
void solve() 
{
	int n;
	cin >> n;
	LL ans = 1;
	for(int i = 2 ; i <= 20 ; i ++){
		ans = lcm(ans , i);
	}
	int tot = 0;
	for(int i = 0 ; i < n ; i ++){
		cin >> a[i];
		tot += ans / a[i];
	}
	int res = ans - tot;
	if(res < n){
		cout << -1 << endl;
	}
	else{
		for(int i = 0 ; i < n - 1; i ++){
			cout << ans / a[i] + 1 << " ";
			res--;
		}
		cout << ans / a[n - 1] + res << endl;
	}
}            
signed main() 
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cout.precision(10);
    int t=1;
	cin>>t;
    while(t--)
    {
    	solve();
    }
    return 0;
}

1979D - Fixing a Binary String

题意：

翻译有误，请看英文题面

思路：典型的一个区间合并求数量问题，我们可以直接构造两颗线段树解决。

cpp 复制代码

// Problem: D. Fixing a Binary String
// Contest: Codeforces - Codeforces Round 951 (Div. 2)
// URL: https://codeforces.com/contest/1979/problem/D
// Memory Limit: 256 MB
// Time Limit: 2000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

#include <bits/stdc++.h>
using namespace std;
#define LL long long
#define pb push_back
#define x first
#define y second 
#define endl '\n'
const LL maxn = 4e05+7;
const LL N = 5e05+10;
const LL mod = 1e09+7;
const int inf = 0x3f3f3f3f;
const LL llinf = 5e18;
typedef pair<int,int>pl;
priority_queue<LL , vector<LL>, greater<LL> >mi;//小根堆
priority_queue<LL> ma;//大根堆
LL gcd(LL a, LL b){
	return b > 0 ? gcd(b , a % b) : a;
}

LL lcm(LL a , LL b){
	return a / gcd(a , b) * b;
}
int n , m;
vector<int>a(N , 0);
void init(int n){
	for(int i = 0 ; i <= n ; i ++){
		a[i] = 0;
	}
}

template<class Info>
struct SegmentTree {
    int n;
    std::vector<Info> info;
    SegmentTree() : n(0) {}
    SegmentTree(int n_, Info v_ = Info()) {
        init(n_, v_);
    }
    template<class T>
    SegmentTree(std::vector<T> init_) {
        init(init_);
    }

    template<class T>
    void init(std::vector<T> init_) {
        n = init_.size();
        info.assign(4 << std::__lg(n), Info());
        std::function<void(int, int, int)> build = [&](int p, int l, int r) {
            if (r - l == 1) {
                info[p] = init_[l];
                return;
            }
            int m = (l + r) / 2;
            build(2 * p, l, m);
            build(2 * p + 1, m, r);
            pull(p);
        };
        build(1, 0, n);
    }
    void pull(int p) {
        info[p] = info[2 * p] + info[2 * p + 1];
    }
    void modify(int p, int l, int r, int x, const Info &v) {
        if (r - l == 1) {
            info[p] = info[p] + v;
            return;
        }
        int m = (l + r) / 2;
        if (x < m) {
            modify(2 * p, l, m, x, v);
        } else {
            modify(2 * p + 1, m, r, x, v);
        }
        pull(p);
    }
    void modify(int p, const Info &v) {
        modify(1, 0, n, p, v);
    }
    Info rangeQuery(int p, int l, int r, int x, int y) {
        if (l >= y || r <= x) {
            return Info();
        }
        if (l >= x && r <= y) {
            return info[p];
        }
        int m = (l + r) / 2;
        return rangeQuery(2 * p, l, m, x, y) + rangeQuery(2 * p + 1, m, r, x, y);
    }
    Info rangeQuery(int l, int r) {
        return rangeQuery(1, 0, n, l, r);
    }
    template<class F>
    int findFirst(int p, int l, int r, int x, int y, F pred) {
        if (l >= y || r <= x || !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findFirst(2 * p, l, m, x, y, pred);
        if (res == -1) {
            res = findFirst(2 * p + 1, m, r, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findFirst(int l, int r, F pred) {
        return findFirst(1, 0, n, l, r, pred);
    }
    template<class F>
    int findLast(int p, int l, int r, int x, int y, F pred) {
        if (l >= y || r <= x || !pred(info[p])) {
            return -1;
        }
        if (r - l == 1) {
            return l;
        }
        int m = (l + r) / 2;
        int res = findLast(2 * p + 1, m, r, x, y, pred);
        if (res == -1) {
            res = findLast(2 * p, l, m, x, y, pred);
        }
        return res;
    }
    template<class F>
    int findLast(int l, int r, F pred) {
        return findLast(1, 0, n, l, r, pred);
    }
};

struct Info {
	int left0 = 0, left1 = 0;
	int right0 = 0, right1 = 0;
	int cnt = 0;
	int act = 0;
};

Info operator + (Info a, Info b) {
	if(a.act == 0){
		return b;
	}
	if(b.act == 0){
		return a;
	}
	Info c;
	c.left0 = a.left0;
	c.left1 = a.left1;
	c.right0 = b.right0;
	c.right1 = b.right1;
	c.act = a.act + b.act;
	c.cnt = a.cnt + b.cnt;
	if(a.right0 > 0 && b.left0 > 0){
		int tmp = a.right0 + b.left0;
		if(tmp > m){
			c.cnt = -1;
		}
		if(tmp == m){
			c.cnt++;
		}
		if(a.right0 == a.act){
			c.left0 = a.act + b.left0;
		}
		if(b.left0 == b.act){
			c.right0 = a.right0 + b.act;
		}
		if(a.right0 != a.act && b.left0 != b.act && tmp != m){
			c.cnt = -1;
		}
	}
	else if(a.right1 > 0 && b.left1 > 0){
		int tmp = a.right1 + b.left1;
		if(tmp > m){
			c.cnt = -1;
		}
		if(tmp == m){
			c.cnt++;
		}
		if(a.right1 == a.act){
			c.left1 = a.act + b.left1;
		}
		if(b.left1 == b.act){
			c.right1 = b.act + a.right1; 
		}
		if(a.right1 != a.act && b.left1 != b.act && tmp != m){
			c.cnt = -1;
		}
	}
	else if(a.right0 > 0 && b.left1 > 0){
		int tmp1 = a.right0;
		int tmp2 = b.left1;
		if(b.left1 == b.act){
			c.right1 = b.act;
		}
		else if(b.left1 != m){
			c.cnt = -1;
		}
		if(a.right0 == a.act){
			c.left0 = a.act;
		}
		else if(a.right0 != m){
			c.cnt = -1;
		}
	}
	else if(a.right1 > 0 && b.left0 > 0){
		int tmp1 = a.right1;
		int tmp2 = b.left0;
		if(b.left0 == b.act){
			c.right0 = b.act;
		}
		else if(b.left0 != m){
			c.cnt = -1;
		}
		if(a.right1 == a.act){
			c.left1 = a.act;
		}
		else if(a.right1 != m){
			c.cnt = -1;
		}	
	}
	return c;
}

void solve() 
{
	cin >> n >> m;
	string s;
	cin >> s;
	vector<Info>v;
	for(int i = 0 ; i < n ; i ++){
		Info tmp;
		if(s[i] == '1'){
			tmp.cnt = 0;
			tmp.act = 1;
			tmp.left1 = 1;
			tmp.right1 = 1;
			tmp.left0 = 0;
			tmp.right0 = 0;
			if(m == 1){
				tmp.cnt = 1;
			}
		}
		else{
			tmp.cnt = 0;
			tmp.act = 1;
			tmp.left1 = 0;
			tmp.right1 = 0;
			tmp.left0 = 1;
			tmp.right0 = 1;	
			if(m == 1){
				tmp.cnt = 1;
			}		
		}
		v.pb(tmp);
	}
	vector<Info>vv;
	for(int i = n - 1 ; i >= 0 ; i --){
		Info tmp;
		if(s[i] == '1'){
			tmp.cnt = 0;
			tmp.act = 1;
			tmp.left1 = 1;
			tmp.right1 = 1;
			tmp.left0 = 0;
			tmp.right0 = 0;
			if(m == 1){
				tmp.cnt = 1;
			}				
		}
		else{
			tmp.cnt = 0;
			tmp.act = 1;
			tmp.left1 = 0;
			tmp.right1 = 0;
			tmp.left0 = 1;
			tmp.right0 = 1;	
			if(m == 1){
				tmp.cnt = 1;
			}				
		}
		vv.pb(tmp);		
	}
	SegmentTree	<Info> seg(v);
	SegmentTree<Info>seg2(vv);
	for(int i = 1 ; i <= n ; i ++){
		Info tmp1 = seg.rangeQuery(i , n);
		Info tmp2 = seg2.rangeQuery(n - i , n);
		Info tmp3 = tmp1 + tmp2;
		if(tmp3.cnt == n / m){
			cout << i << endl;
			return;
		}
	}
	cout << -1 << endl;
}            
int main() 
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    cout.precision(10);
    int t=1;
	cin>>t;
    while(t--)
    {
    	solve();
    }
    return 0;
}