整数二分模板

模板1：满足条件的第一个数

int bianrysearch(int l, int r) {
    while (l < r) {
        int mid = l + r >> 1;
        if (check(mid)) r = mid;
        else  l = mid + 1;
    } 
    return l;
}

模板2：满足条件的最后一个数

int bianrysearch(int l, int r) {
    while (l < r) {
        int mid = l + r + 1 >> 1;
        if (check(mid)) l = mid;
        else  r = mid - 1;
    }
    return l;
}

浮点数二分模板

double bianrysearch(double l, double r) {
    double eps = 1e-6;   
    while (r - l > eps) {
        double mid = (l + r) / 2;
        if (check(mid)) r = mid;
        else l = mid;
    }
    return l;
}

一、Building an Aquarium

Building an Aquarium

思路分析

二分

具体代码

#include <cstdio>
#include <iostream>

using namespace std;
typedef long long ll;

const int N = 2e5 + 10;
ll t, n, x;
ll a[N];

bool check(ll mid) {
	ll sum = 0;
	for (int i = 1; i <= n; i++){
		if (a[i] < mid) sum += mid - a[i];
	}	
	return sum <= x;
}

int main() {
	scanf("%lld", &t);
	while (t--) {
		scanf("%lld%lld", &n, &x);
		for (int i = 1; i <= n; i++) {
			scanf("%lld", &a[i]);
		}
		ll l = 1, r = 2e9 + 10;
		while (l < r) {
			ll mid = l + r + 1 >> 1;
			if (check(mid)) l = mid;
			else r = mid - 1;
		}
		printf("%lld\n", l);
	}
	return 0;
}

二、Tracking Segments

Tracking Segments

思路分析

二分+前缀和

具体代码

#include <cstdio>
#include <iostream>
#include <cstring>

using namespace std;

typedef long long ll;

const int N = 1e5 + 10;

int t, n, m, q;
int s[N], pos[N];
ll preSum[N];

struct node{
	int x, y;
}a[N];

bool check(int mid) {
	for (int i = 1; i <= n; i++) s[i] = 0;
	for (int i = 1; i <= mid; i++)	s[pos[i]] = 1;
	for (int i = 1; i <= n; i++) {
		preSum[i] = preSum[i - 1] + s[i];
	}
	for (int i = 1; i <= m; i++) {
		if (2 * (preSum[a[i].y ] - preSum[a[i].x - 1]) > a[i].y - a[i].x + 1)	return true;
	}
	return false;
}

int main() {
	cin >> t;
	while(t--) {
		cin >> n >> m;
		for (int i = 1; i <= m; i++) {
			cin >> a[i].x >> a[i].y;
		}
		cin >> q;
		for (int i = 1; i <= q; i++) {
			cin >> pos[i];
		}
		if (!check(q)) {
			puts("-1");
			continue;
		}	
		int l = 1, r = q;
		while (l < r) {
			int mid = l + r >> 1;
			if (check(mid)) r = mid;
			else l = mid + 1;
		}
		cout << l << endl;
	}
	return 0;
}

三、Wooden Toy Festival

Wooden Toy Festival

思路分析

二分

具体代码

#include <cstdio>
#include <iostream>
#include <algorithm>

using namespace std;

const int N = 2e5 + 10;

int t, n;
int a[N];

bool check(int mid) {
	int idx = 0, t1 = a[0] + 2 * mid;
	while (a[idx] <= t1 && idx < n) idx++;
	t1 = a[idx] + 2 * mid;
	while (a[idx] <= t1 && idx < n) idx++;
	t1 = a[idx] + 2 * mid;
	while (a[idx] <= t1 && idx < n) idx++;
	if (idx == n) return true;
	return false;
}

int main() {
	cin >> t;
	while (t--) {
		cin >> n;
		int l = 0, r; 
		for (int i = 0; i < n; i++) {
			cin >> a[i];
		}
		sort(a, a + n);
		r = a[n - 1];
		while (l < r) {
			int mid = l + r >> 1;
			if (check(mid)) r = mid;
			else l = mid + 1;
		}		
		cout << l << endl;
	}
	return 0;
}

四、路标设置

路标设置

思路分析

二分，注意check函数写法

具体代码

#include <cstdio>
#include <iostream>
#include <algorithm>

using namespace std;

typedef long long ll;

const int N = 100000 + 10;
ll len, n, k;
ll a[N];

bool check(int mid) {
	ll dif = 0;
	for (int i = 1; i < n; i++) {
		dif += (a[i] - a[i - 1] - 1) / mid;
	}
	return dif <= k;
}

int main() {
	cin >> len >> n >> k;
	ll l = 1, r = len;
	for(int i = 0; i < n; i++) {
		cin >> a[i];
	} 
	sort(a, a + n);
	while (l < r) {
		ll mid = l + r >> 1;
		if (check(mid)) r = mid;
		else l = mid + 1;
	}
	cout << l << endl;
	return 0;
}

五、木材加工

木材加工

思路分析

二分

具体代码

#include <cstdio>
#include <iostream>

using namespace std;

typedef long long ll;
const int N = 1e5 + 10;

int n, k;
ll a[N];

bool check(ll mid) {
	ll sum = 0;
	for (int i = 0; i < n; i++) sum += a[i] / mid;	
	return sum >= k;
}

int main() {
	ll l = 0, r = 0;
	cin >> n >> k;
	for (int i = 0; i < n; i++) {
		scanf("%lld", &a[i]);
		r += a[i];
	} 
	while(l < r) {
		ll mid = l + r + 1 >> 1;
		if (check(mid)) l = mid; 
		else  r = mid - 1;
	}
	cout << l <<endl;
	return 0;
}