POJ 3468 A Simple Problem with Integers-优快云博客

本文链接：https://blog.youkuaiyun.com/NMfloat/article/details/46870895

本文详细解读了段树数据结构及其在 POJ 3468 题目的应用。通过提供代码实现、核心概念解释和实例分析，帮助读者理解如何高效地使用段树解决区间更新和查询问题。

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Segment Tree.

The portal:http://poj.org/problem?id=3468

#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <iostream>

const int MAXN = 100005;

struct Node {
	int Left;
	int Right;
	long long value;
	long long lazy;
}Segment_Tree[MAXN<<2];

long long a[MAXN];
int cnt ;

void Push_Up(int Now) {
	Segment_Tree[Now].value = Segment_Tree[Now<<1].value + Segment_Tree[Now<<1|1].value;
}

void Push_Down(int Now) {
	if(Segment_Tree[Now].lazy){
		Segment_Tree[Now << 1].lazy += Segment_Tree[Now].lazy;
		Segment_Tree[Now << 1|1].lazy  += Segment_Tree[Now].lazy;
		Segment_Tree[Now << 1].value += Segment_Tree[Now].lazy * (Segment_Tree[Now<<1].Right - Segment_Tree[Now<<1].Left + 1);
		Segment_Tree[Now << 1|1].value += Segment_Tree[Now].lazy * (Segment_Tree[Now<<1|1].Right - Segment_Tree[Now<<1|1].Left + 1);
		Segment_Tree[Now].lazy = 0;
	}
}

void Build_Tree(int Left,int Right,int Now) {
	Segment_Tree[Now].lazy = 0;
	Segment_Tree[Now].Left = Left;
	Segment_Tree[Now].Right = Right;
	if(Left == Right) {
		Segment_Tree[Now].value = a[cnt++];
		return ;
	}
	int Mid = (Left + Right) >> 1;
	Build_Tree(Left,Mid,Now<<1);
	Build_Tree(Mid+1,Right,Now<<1|1);
	Push_Up(Now);
}

void Update_Tree(int Left,int Right,int Now,int Update_left,int Update_right,long long lazy_value) {
	if(Left >= Update_left && Right <= Update_right) {
		Segment_Tree[Now].lazy += lazy_value;
		Segment_Tree[Now].value += lazy_value * (Right - Left +1);
		return ;
	}
	int Mid = (Left + Right) >> 1;
	Push_Down(Now);
	if(Mid >= Update_left) {
		Update_Tree(Left,Mid,Now<<1,Update_left,Update_right,lazy_value);
	}
	if(Mid < Update_right) {
		Update_Tree(Mid+1,Right,Now<<1|1,Update_left,Update_right,lazy_value);
	}
	Push_Up(Now);
}

long long Query_Tree(int Left,int Right,int Now,int Left_Edge,int Right_Edge) {
	long long Query_Ans = 0;
	if(Left >= Left_Edge && Right <= Right_Edge) {
		return Segment_Tree[Now].value;
	}
	int Mid = (Left + Right) >> 1;
	Push_Down(Now);
	if(Mid >= Left_Edge) {
		Query_Ans += Query_Tree(Left,Mid,Now<<1,Left_Edge,Right_Edge);
	}
	if(Mid < Right_Edge) {
		Query_Ans += Query_Tree(Mid+1,Right,Now<<1|1,Left_Edge,Right_Edge);
	}
	return Query_Ans;
}

void Deal_with() {
	int n,m;
	while(~scanf("%d %d",&n,&m)) {
		for(int i = 1 ; i <= n ; i ++) {
			scanf("%lld",a+i);
		}
		cnt = 1;
		Build_Tree(1,n,1);
		char tempc;
		int Left,Right;
		long long value;
		for(int i = 1 ; i <= m ; i ++) {
			getchar();
			scanf("%c %d %d",&tempc,&Left,&Right);
			if(tempc == 'Q') {
				printf("%lld\n",Query_Tree(1,n,1,Left,Right));
			}
			else {
				scanf("%lld",&value);
				Update_Tree(1,n,1,Left,Right,value);
			}
		}
	}
}

int main(void) {
	//freopen("a.in","r",stdin);
	Deal_with();
	return 0;
}