POJ3264_Balanced Lineup(区间最值查询)

最新推荐文章于 2022-12-04 09:24:17 发布

原创最新推荐文章于 2022-12-04 09:24:17 发布 · 203 阅读

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线段树同时被 2 个专栏收录

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RMQ

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本文介绍了两种高效解决区间最大值和最小值查询问题的方法：RMQ预处理算法和线段树。通过预处理和递归分解，算法能在O(log n)时间内查询任意区间的最大值和最小值，为动态数据结构和算法设计提供了实用工具。

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题意：

求给定区间内的最大值和最小值之差

思路：

RMQ

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#pragma comment(linker, "/STACK:102400000,102400000")
typedef long long LL;
const int INF = 0x3f3f3f3f;
const int maxn = 50000+5;
using namespace std;
int n,m, A[maxn];
int maxval[maxn][20], minval[maxn][20];

void RMQ_ST(){
	for(int i = 1; i <= n; ++i) maxval[i][0] = minval[i][0] = A[i];
	for(int i = 1; i <= (int)(log(n*1.0)/log(2.0)); ++i){
		for(int j = 1; j + (1<<i) - 1 <= n; ++j){
			maxval[j][i] = max(maxval[j][i-1], maxval[j + (1<<(i-1))][i-1]);
			minval[j][i] = min(minval[j][i-1], minval[j + (1<<(i-1))][i-1]);
		}
	}
}
int Query_max(int l, int r){
	int k = (int)(log(r-l+1.0)/log(2.0));
	return max(maxval[l][k], maxval[r-(1<<k)+1][k]);
}
int Query_min(int l, int r){
	int k = (int)(log(r-l+1.0)/log(2.0));
	return min(minval[l][k], minval[r-(1<<k)+1][k]);
}

int main()
{
    freopen("in.txt","r",stdin);
    
	while(scanf("%d%d",&n,&m) == 2){
		for(int i = 1; i <= n; ++i) scanf("%d", &A[i]);
		RMQ_ST();
		while(m--){
			int l,r; scanf("%d%d", &l,&r);
			int maxx = Query_max(l, r);
			int minn = Query_min(l, r);
			printf("%d\n", maxx-minn);
		}
	}
    fclose(stdin);
	return 0;
}

线段树

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
#pragma comment(linker, "/STACK:102400000,102400000")
#define lson root<<1, l, mid
#define rson root<<1 | 1, mid+1, r
typedef long long LL;
const int INF = 0x3f3f3f3f;
const int maxn = 50000+5;
using namespace std;
int n,m;
struct Node{
	int big, small;
}Tree[maxn*4];

void push_up(int root){ 
	Tree[root].big = max(Tree[root<<1].big, Tree[root<<1 | 1].big);
	Tree[root].small = min(Tree[root<<1].small, Tree[root<<1 | 1].small);
}
void Stree_build(int root, int l, int r){
	if(l == r){
		scanf("%d", &Tree[root].big); Tree[root].small = Tree[root].big;
		return;
	}
	int mid = (l+r) >> 1;
	Stree_build(lson);
	Stree_build(rson);
	push_up(root);
}

int qmax, qmin; 
void Query(int la, int rb, int l, int r, int root){
	if(la > r||rb < l) return;
	if(la <= l&&rb >= r){
		qmax = max(qmax, Tree[root].big);
		qmin = min(qmin, Tree[root].small);
		return;
	}
	int mid = (l + r) >> 1;
	if(la <= mid)
		Query(la, rb, l, mid, root<<1);
	if(rb > mid)
		Query(la, rb, mid+1, r, root<<1 | 1);
}

int main()
{
    freopen("in.txt","r",stdin);
    
	while(scanf("%d%d",&n,&m) == 2){
		Stree_build(1, 1, n);
		//printf("%d, %d\n", Tree[1].big,Tree[1].small);
		while(m--){
			int l,r; scanf("%d%d", &l,&r);
			qmax = 0; qmin = INF;
			Query(l, r, 1, n, 1);
			//printf("max = %d, min = %d\n", qmax, qmin);
			printf("%d\n", qmax - qmin);
		}
	}
    fclose(stdin);
	return 0;
}