RMQ(Range Minimum Query)问题(转)】的更多相关文章

Range Minimum Query (RMQ) Write a program which manipulates a sequence A = {a0,a1,...,an−1} with the following operations: find(s,t): report the mimimum element in as,as+1,...,at. update(i,x): change ai to x. Note that the initial values of ai (i=0,1…
作者:danielp 出处:http://community.topcoder.com/tc?module=Static&d1=tutorials&d2=lowestCommonAncestor Introduction  Notations  Range Minimum Query (RMQ)      Trivial algorithms for RMQ      A <O(N), O(sqrt(N))> solution      Sparse Table (ST) al…
RMQ ( 范围最小值查询 ) 问题是一种动态查询问题,它不需要修改元素,但要及时回答出数组 A 在区间 [l, r] 中最小的元素值. RMQ(Range Minimum/Maximum Query):对于长度为n的数列A,回答若干询问RMQ(A,i,j)(i,j<=n),返回数列A中下标在i,j之间的最小/大值. 对于 RMQ ,我们通常关心两方面的算法效率:预处理时间和查询时间.解决一般 RMQ 问题的三种方法胜者树 (Winner Tree) O(n)-O(logn)稀疏表 (Spars…
使用线段树预处理.能够使得查询RMQ时间效率在O(lgn). 线段树是记录某范围内的最小值. 标准的线段树应用. Geeks上仅仅有两道线段树的题目了.并且没有讲到pushUp和pushDown操作.仅仅是线段树的入门了. 參考:http://www.geeksforgeeks.org/segment-tree-set-1-range-minimum-query/ 我改动了一下他的程序,使用pushUp操作.事实上也是非常easy的一个小函数.并且手动计算了下,认为他的动态分配内存,计算须要的树…
问题描述 RMQ问题是求给定区间中的最值问题.对于长度为n的数列A,回答若干查询RMQ(A, i, j).返回数组A中下标在[i,j]里的最小值的下标. 比如数列 5,8,1,3,6,4,9,5,7      那么RMQ(2,4) = 3, RMQ(6,9) = 6.   解决问题 最简单的解法时间复杂度是O(n),就是对于每一个查询遍历一遍数组.但是当n非常大的时候,并且查询次数非常多的时候,这个解决方案就不是那么高效了. 使用线段树(以后会讲)可以将时间复杂度优化到O(logn),通过在线段…
给定一个数组,求出给定区间[l,r]中元素的最大值或最小值或者最值的索引. 一看到这个题目,简单,看我暴力出奇迹.暴力当然是可行的.但是时间复杂度很高(O(n^2)).线段树,树状数组也可以解决这个问题,复杂度(O(nlogn))的预处理,最终查询为O(次数*logn). 而今天用ST(Sparse_Table)算法,也是O(nlogn)的预处理,但是是单次查询为O(1),挺高效的. 我们现在给定一组数据 n==9,元素为2,4,6,8,9,1,2,3,4.一个二维数组f[MAX][MAX];假…
int rangeMinQuery(int segTree[], int qlow, int qhigh, int low, int high, int pos) { if (qlow <= low && qhigh >= high) return segTree[pos]; if (qlow > high || qhigh < low) return maxVal; int mid = (low + high) / 2; return min(rangeMinQu…
Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, co…
Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. The update(i, val) function modifies nums by updating the element at index i to val. Example: Given nums = [1, 3, 5] sumRange(0, 2) -> 9 update(1, 2…
Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2, co…
Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. Example: Given nums = [-2, 0, 3, -5, 2, -1] sumRange(0, 2) -> 1 sumRange(2, 5) -> -1 sumRange(0, 5) -> -3 Note: You may assume that the array do…
Range Add Query 数列 A = {a1,a2,...,an} に対し.次の2つの操作を行うプログラムを作成せよ. add(s,t,x): as,as+1,...,at にxを加算する. get(i): aiの値を出力する. ただし.ai (i=1,2,...,n)は.0 で初期化されているものとする. 入力 n q query1 query2 : queryq 1行目にAの要素数n, クエリの数qが与えられる.続くq行に i 番目のクエリ queryi が与えられる.queryi …
Range Update Query 数列 A = {a0,a1 ,...,an−1} に対し.次の2つの操作を行うプログラムを作成せよ. update(s,t,x): as,as+1,...,at をxに変更する. find(i): ai の値を出力する. ただし.ai (i=0,1,...,n−1)は.231-1で初期化されているものとする. 入力 n q query1 query2 : queryq 1行目にAの要素数n, クエリの数qが与えられる.続くq行にi 番目のクエリ queryi…
static void range_test(Args _args) { Query                   Query; QueryRun                QueryRun; QueryBuildDataSource    qbr; CustTable custtable; //QueryBuildRange         qbr; Range                   range = 'den-000004'; int                  …
Range Sum Query 2D - Mutable Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). The above rectangle (with the red border) is defined by (row1,…
原题链接在这里:https://leetcode.com/problems/range-sum-query-2d-mutable/ 题目: Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). The above rectangle (…
Range Sum Query - Immutable Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. Example: Given nums = [-2, 0, 3, -5, 2, -1] sumRange(0, 2) -> 1 sumRange(2, 5) -> -1 sumRange(0, 5) -> -3 Note: You…
Very similar to Range Sum Query - Immutable, but we now need to compute a 2d accunulated-sum. In fact, if you work in computer vision, you may know a name for such an array --- Integral Image. To solve this problem, Stefan has already posted a very e…
Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). Range Sum Query 2D The above rectangle (with the red border) is defined by (row1, col1) = (…
题目: Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). The above rectangle (with the red border) is defined by (row1, col1) = (2, 1) and (row2…
Range Sum Query 2D - Mutable Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). The above rectangle (with the red border) is defined by (row1,…
303. Range Sum Query - Immutable class NumArray { private: vector<int> v; public: NumArray(vector<int> &nums) { int n = nums.size(); v = vector<int>(n + 1); int sum = 0; for (int i = 1; i <= n; ++i) { sum += nums[i - 1]; v[i] = su…
893F - Subtree Minimum Query 题意 给出一棵树,每次询问 \(x\) \(k\),求以 \(x\) 为根结点的子树中的结点到结点 \(x\) 的距离小于等于 \(k\) 的结点权值最小值. 分析 可持久化线段树,对每个结点都建树,然后尽可能复用子孙结点的线段树. 对于一般的线段树,我们并不需要记录左右子结点的标号,因为如果当前节点标号为 \(rt\) ,则左右子结点标号为 \(2 * rt\) 和 \(2 * rt + 1\) .对于本题,若有 \(u\) 是 \(v…
[cf contest 893(edu round 33)] F - Subtree Minimum Query time limit per test 6 seconds memory limit per test 512 megabytes input standard input output standard output You are given a rooted tree consisting of n vertices. Each vertex has a number writ…
Immutable [抄题]: Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. Example: Given nums = [-2, 0, 3, -5, 2, -1] sumRange(0, 2) -> 1 sumRange(2, 5) -> -1 sumRange(0, 5) -> -3 [暴力解法]: 时间分析:n 空间分析:n…
Range Sum Query - Mutable 题解 原创文章,拒绝转载 题目来源:https://leetcode.com/problems/range-sum-query-mutable/description/ Description Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. The update(i, val) functi…
CF893F Subtree Minimum Query 输入输出格式 输入格式: The first line contains two integers \(n\) and \(r\) ( \(1<=r<=n<=100000\) ) - the number of vertices in the tree and the index of the root, respectively. The second line contains n integers \(a_{1},a_{2}…
题目 Given a 2D matrix matrix, find the sum of the elements inside the rectangle defined by its upper left corner (row1, col1) and lower right corner (row2, col2). Range Sum Query 2D The above rectangle (with the red border) is defined by (row1, col1)…
一. 题目描写叙述 Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. The update(i, val) function modifies nums by updating the element at index i to val. Example: Given nums = [1, 3, 5] sumRange(0, 2) -> 9 u…
Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. The update(i, val) function modifies nums by updating the element at index i to val. Example: Given nums = [1, 3, 5] sumRange(0, 2) -> 9 update(1, 2…