《算法竞赛进阶指南》0x00倍增

数列区间最大值

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

const int N = 1e5 + 10;
int n, m, a[N];
int f[N][20];		//f[i][j]：a[i]...a[i + 2^j - 1]范围里的最小值 

int main() {
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i ++) {
		scanf("%d", &a[i]);
		f[i][0] = a[i];
	}

	int t = log2(n);
	for (int j = 1; j <= t; j ++) {
		for (int i = 1; i + (1 << j) - 1 <= n; i ++) {
			int k = j - 1;
			f[i][j] = max(f[i][k], f[i + (1 << k)][k]);
		}
	}
	
	while (m --) {
		int x, y;
		scanf("%d%d", &x, &y);
		int k = log2(y - x + 1);
		int maxx = max(f[x][k], f[y + 1 - (1 << k)][k]);
		printf("%d\n", maxx);
	}
	
	return 0;
}

天才的记忆

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

const int N = 2e5 + 10;
int n, m, a[N];
int f[N][20];		//f[i][j]：a[i]...a[i + 2^j - 1]范围里的最小值 

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i ++) {
		scanf("%d", &a[i]);
		f[i][0] = a[i];
	}
	
	int t = log2(n);
	for (int j = 1; j <= t; j ++) {
		for (int i = 1; i + (1 << j) - 1 <= n; i ++) {
			int k = j - 1;
			f[i][j] = max(f[i][k], f[i + (1 << k)][k]);
		}
	}
	
	scanf("%d", &m);
	while (m --) {
		int x, y;
		scanf("%d%d", &x, &y);
		int k = log2(y - x + 1);
		int maxx = max(f[x][k], f[y + 1 - (1 << k)][k]);
		printf("%d\n", maxx);
	}
	
	return 0;
}

最敏捷的机器人

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

const int N = 1e5 + 10;
int n, m, a[N];
int f[N][20];		//f[i][j]：a[i]...a[i + 2^j - 1]范围里的最大值 
int g[N][20];		//g[i][j]：a[i]...a[i + 2^j - 1]范围里的最小值 

int main() {
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= n; i ++) {
		scanf("%d", &a[i]);
		f[i][0] = a[i];
		g[i][0] = a[i];
	}
	
	int t = log2(n);
	for (int j = 1; j <= t; j ++) {
		for (int i = 1; i + (1 << j) - 1 <= n; i ++) {
			f[i][j] = max(f[i][j - 1], f[i + (1 << j - 1)][j - 1]);
			g[i][j] = min(g[i][j - 1], g[i + (1 << j - 1)][j - 1]);
		}
	}
	
	for (int i = 1; i <= n - m + 1; i ++) {
		//1 ~ m, 2 ~ m + 1,..., i ~ m + i - 1
		//(m + i - 1) - 1 << k + 1
		//
		int k = log2(m);
		int maxx = max(f[i][k], f[m + i - (1 << k)][k]);
		int minn = min(g[i][k], g[m + i - (1 << k)][k]);
		printf("%d %d\n", maxx, minn);
	}
	
	return 0;
}

Balanced Lineup

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

const int N = 5e4 + 10;
int n, Q, x;
int f[N][20], g[N][20];	//最矮，最高 

int main() {
	scanf("%d%d", &n, &Q);
	for (int i = 1; i <= n; i ++) {
		scanf("%d", &x);
		f[i][0] = g[i][0] = x;
	}
	
	int t = log2(n);
	for (int j = 1; j <= t; j ++) {
		for (int i = 1; i + (1 << j) - 1 <= n; i ++) {
			int k = j - 1;
			f[i][j] = min(f[i][k], f[i + (1 << k)][k]);
			g[i][j] = max(g[i][k], g[i + (1 << k)][k]);
		}
	}
	
	while (Q --) {
		int a, b;
		scanf("%d%d", &a, &b);
		int k = log2(b - a + 1);
		int minn = min(f[a][k], f[b + 1 - (1 << k)][k]);
		int maxx = max(g[a][k], g[b + 1 - (1 << k)][k]);
		printf("%d\n", maxx - minn);
	}

	return 0;
}