二分查找与二分答案

壹·二分查找

一、基础

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;

int x, n, mid, high, low = 1;

int main() {
	scanf("%d %d", &x, &n);
	high = n;
	
	while(low < high) {
		mid = (high+low)/2;
		if(mid < x) 
			low = mid+1;
		else 
			high = mid;
	}
	
	printf("%d right", x);
	return 0;
}

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;

int x, n, mid, high, low = 1;

int main() {
	scanf("%d %d", &x, &n);
	high = n;
	
	while(low < high) {
		mid = (high+low+1)/2;
		if(mid > x) 
			high = mid-1;
		else 
			low = mid;
	}
	
	printf("%d right", x);
	return 0;
}

二、进阶

1. 查找第一个大于 $x$ 的数

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;

int l = 1, r, mid, n, s;
int a[20005];

void bs(){
	while(l<r) {
		mid= (l+r)/2;
		if(a[mid] > s)
			r = mid;
		else l = mid+1;
	}
}

int main() {
	scanf("%d", &n);
	r = n+1;
	for(int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
	}
	scanf("%d", &s);
	
	sort(a+1, a+1+n);
	bs();
	
	(l > r)? printf("No\n"): printf("%d", a[l]);
	return 0;
}

2. 查找第一个大于等于 $x$ 的数

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;

int l = 1, r, mid, n, s;
int a[20005];

void bs(){
	while(l<r) {
		mid= (l+r)/2;
		if(a[mid] >= s)
			r = mid;
		else l = mid+1;
	}
}

int main() {
	scanf("%d", &n);
	r = n+1;
	for(int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
	}
	scanf("%d", &s);
	
	sort(a+1, a+1+n);
	bs();
	
	(l > r)? printf("No\n"): printf("%d", a[l]);
	return 0;
}

3. 查找第一个小于 $x$ 的数

// 第一个小于 
#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;

int l = 1, r, mid, n, s;
int a[20005];

void bs(){
	while(l<r) {
		mid= (l+r+1)/2;
		if(a[mid] >= s)
			r = mid-1;
		else l = mid;
	}
}

int main() {
	scanf("%d", &n);
	r = n+1;
	for(int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
	}
	scanf("%d", &s);
	
	sort(a+1, a+1+n);
	bs();
	
	(l < 1)? printf("No\n"): printf("%d", a[l]);
	return 0;
}

4. 查找第一个小于等于 $x$ 的数

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cstring>
using namespace std;

int l = 1, r, mid, n, s;
int a[20005];

void bs(){
	while(l<r) {
		mid= (l+r+1)/2;
		if(a[mid] <= s)
			r = mid-1;
		else l = mid;
	}
}

int main() {
	scanf("%d", &n);
	r = n+1;
	for(int i = 1; i <= n; i++) {
		scanf("%d", &a[i]);
	}
	scanf("%d", &s);
	
	sort(a+1, a+1+n);
	bs();
	
	(l < 1)? printf("No\n"): printf("%d", a[l]);
	return 0;
}

贰·二分答案