给定一个01串$S_{1\cdots n}$和$Q$个操作.操作有两种类型:1.将$[l,r]$区间的数取反(将其中的$0$变成$1$,$1$变成$0$).2.询问字符串$S$的子串$S_{l\cdots r}$有多少个不同的子序列.由于答案可能很大,请将答案对$10^9+7$取模.在数学中,某个序列的子序列是从最初序列通过去除某些元素但不破坏余下元素的相对位置(在前或在后)而形成的新序列. 先不管修改,看一看怎么DP找出子序列个数 $f_{i,j}(1\leq i\leq n,j\in\{0,…

Subsequence Count Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 256000/256000 K (Java/Others) Problem Description Given a binary string S[1,...,N] (i.e. a sequence of 0's and 1's), and Q queries on the string. There are two types of querie…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6155 题意: 题解来自:http://www.cnblogs.com/iRedBean/p/7398272.html 先考虑dp求01串的不同子序列的个数. dp[i][j]表示用前i个字符组成的以j为结尾的01串个数. 如果第i个字符为0,则dp[i][0] = dp[i-1][1] + dp[i-1][0] + 1,dp[i][1] = dp[i-1][1] 如果第i个字符为1,则dp[i][1…

Time Limit: 1000 ms   Memory Limit: 256 MB Description 给定一个01串 $S_{1 \cdots n}$ 和 $Q$ 个操作. 操作有两种类型: 1.将 $[l, r]$ 区间的数取反(将其中的0变成1,1变成0). 2.询问字符串 $S$ 的子串 $S_{l \cdots r}$ 有多少个不同的子序列.由于答案可能很大,请将答案对 $10^9 + 7$ 取模. 在数学中,某个序列的子序列是从最初序列通过去除某些元素但不破坏余下元素的相对位置…

题目链接 首先考虑询问[1,n]怎么做 设 f[i][0/1]表示[1,i]以0/1结尾的不同子序列个数 则 \(if(A[i]) f[i][1] = f[i-1][0] + f[i-1][1] + 1 , f[i][0] = f[i-1][0]\) \(\ \ if(!A[i]) f[i][0] = f[i-1][0] + f[i-1][1] + 1 , f[i][1] = f[i-1][1]\) 很整齐,我们来写成矩阵的样子: \(f[i,0]\ f[i,1]\ 1=f[i-1,0]\ f[…

题意 给定一个长度为 \(n\) 的 \(01\) 串,完成 \(m\) 种操作--操作分两种翻转 \([l,r]\) 区间中的元素.求区间 \([l,r]\) 有多少个不同的子序列. \(1 \leq n,m \leq 10^5\) 思路 看到这种题目,应该条件反射的去想一下线段树. 但首先还是从一个询问开始,对于一个长度为 \(n\) 的串,设 \(dp_{i,j}\) 为前 \(i\) 位组成的序列中,以 \(j\) 结尾的串的个数,若串的第 \(i\) 位为 \(j\) 有递推式: \(…

Problem Description Given a binary string S[1,...,N] (i.e. a sequence of 0's and 1's), and Q queries on the string.There are two types of queries:1. Flipping the bits (i.e., changing all 1 to 0 and 0 to 1) between l and r (inclusive).2. Counting the…

DP式很容易得到,发现是线性递推形式,于是可以矩阵加速.又由于是区间形式,所以用线段树维护. https://www.cnblogs.com/Miracevin/p/9124511.html 关键在于证明区间操作中,可以直接在打标记的位置翻转矩阵两行两列. 上面网址用代数形式证了一遍,这里考虑从矩阵本身解释. 由线代内容可知,将一个矩阵作初等行变换,相当于将其左乘一个作了相应初等列变换的单位矩阵.同理将一个矩阵作初等列变换,相当于将其又乘一个作了相应初等行变换的单位矩阵. 这里,左乘的矩阵$T=…

题目大意: 给定一个01序列,支持以下两种操作: 1.区间反转: 2.区间求不同的子序列数量. 思路: 首先我们考虑区间反转,这是一个经典的线段树操作. 接下来考虑求不同的子序列数量,在已知当前区间的情况下,我们有如下$O(n)$的动态规划:| $f_{i,0}=f_{i-1,0}+f_{i-1,1}+1,f_{i,1}=f_{i-1,1}//第i位为0$ $f_{i,1}=f_{i-1,0}+f_{i-1,1}+1,f_{i,0}=f_{i-1,0}//第i位为1$ 这样的动态规划显然无法直接…

话说这题比赛时候过的好少,连题都没读TOT 先考虑dp求01串的不同子序列的个数. dp[i][j]表示用前i个字符组成的以j为结尾的01串个数. 如果第i个字符为0,则dp[i][0] = dp[i-1][1] + dp[i-1][0] + 1,dp[i][1] = dp[i-1][1] 如果第i个字符为1,则dp[i][1] = dp[i-1][1] + dp[i-1][0] + 1,dp[i][0] = dp[i-1][0] 显然这是线性递推,我们考虑如何用矩阵表示这种递推关系. 下面分别…

题意 给定一个 \(01\) 串 \(S_{1...n}\) 和 \(Q\) 个操作. 操作有 \(2\) 种类型: 1. 将 \([l,r]\) 区间所有数取反(\(0→1,\space 1→0\)) 2. 询问字符串 \(S\) 的子串 \(S_{l...r}\) 有多少个不同的子序列,答案模 \(10^9+7\). 在数学中,某个序列的子序列是从最初序列通过去除某些元素但不破坏余下元素的相对位置(在前或在后)而形成的新序列. \(n,q\le 10^5\) 题解 注意子序列的定义,不是子串…

题目链接 http://acm.hdu.edu.cn/showproblem.php?pid=6155 题解 DP+线代好题.(考场上过多时间刚前两题,没怎么想这题--) 首先列出一个DP式: 设\(dp[i][j]\)表示到第\(i\)位最后一位是\(j\)有多少个本质不同的子序列(最后一位不一定取到第\(i\)位),考虑转移: 假设\(a_i=0\), 那么\(dp[i][0]=2\times dp[i-1][0]+dp[i-1][1]-dp[i-1][0]+1=dp[i-1][0]+dp[…

题意:01串,操作1:把l r区间的0变1,1变0:操作2:求出l r区间的子序列种数 思路:设DP[i][j]为到i为止以j结尾的种数,假设j为0,那么dp[i][0] = dp[i - 1][1] + dp[i -1][0] (0结尾新串) + dp[i - 1][0] (0结尾旧串) - dp[i - 1][0] (重复) + 1(0本身被重复时去除). 那么可以得到转移时的矩阵 $$ \left( \begin{matrix} dp[i - 1][0] & dp[i - 1][1] &am…

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A sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same. For example, these are arithmetic sequences: 1, 3, 5, 7, 9 7, 7, 7, 7 3, -1, -5, -9 The follo…

3638: Cf172 k-Maximum Subsequence Sum Time Limit: 50 Sec  Memory Limit: 256 MBSubmit: 174  Solved: 92[Submit][Status][Discuss] Description 给一列数,要求支持操作: 1.修改某个数的值 2.读入l,r,k,询问在[l,r]内选不相交的不超过k个子段,最大的和是多少. Input The first line contains integer n (1 ≤ n …

We define a harmonious array is an array where the difference between its maximum value and its minimum value is exactly 1.Now, given an integer array, you need to find the length of its longest harmonious subsequence among all its possible subsequen…

We define a harmonious array is an array where the difference between its maximum value and its minimum value is exactly 1. Now, given an integer array, you need to find the length of its longest harmonious subsequence among all its possible subseque…

Given an unsorted array of integers, find the length of longest increasing subsequence. Example: Input: [10,9,2,5,3,7,101,18] Output: 4 Explanation: The longest increasing subsequence is [2,3,7,101], therefore the length is 4. Note: There may be more…

Given an unsorted array return whether an increasing subsequence of length 3 exists or not in the array. Formally the function should: Return true if there exists i, j, k such that arr[i] < arr[j] < arr[k] given 0 ≤ i < j < k ≤ n-1 else return…

A sequence of numbers is called a wiggle sequence if the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with fewer than two…

Given a string s and a string t, check if s is subsequence of t. You may assume that there is only lower case English letters in both s and t. t is potentially a very long (length ~= 500,000) string, and s is a short string (<=100). A subsequence of…

A sequence of numbers is called arithmetic if it consists of at least three elements and if the difference between any two consecutive elements is the same. For example, these are arithmetic sequences: 1, 3, 5, 7, 9 7, 7, 7, 7 3, -1, -5, -9 The follo…

Given a string s, find the longest palindromic subsequence's length in s. You may assume that the maximum length of s is 1000. Example 1:Input: "bbbab" Output: 4 One possible longest palindromic subsequence is "bbbb". Example 2:Input:…

Given a group of two strings, you need to find the longest uncommon subsequence of this group of two strings. The longest uncommon subsequence is defined as the longest subsequence of one of these strings and this subsequence should not be any subseq…

Given a list of strings, you need to find the longest uncommon subsequence among them. The longest uncommon subsequence is defined as the longest subsequence of one of these strings and this subsequence should not be any subsequence of the other stri…

We define a harmonious array is an array where the difference between its maximum value and its minimum value is exactly 1. Now, given an integer array, you need to find the length of its longest harmonious subsequence among all its possible subseque…

Given an unsorted array of integers, find the number of longest increasing subsequence. Example 1: Input: [1,3,5,4,7] Output: 2 Explanation: The two longest increasing subsequence are [1, 3, 4, 7] and [1, 3, 5, 7].  Example 2: Input: [2,2,2,2,2] Outp…

Given an unsorted array of integers, find the length of longest continuous increasing subsequence (subarray). Example 1: Input: [1,3,5,4,7] Output: 3 Explanation: The longest continuous increasing subsequence is [1,3,5], its length is 3. Even though…

Given a string S, find the number of different non-empty palindromic subsequences in S, and return that number modulo 10^9 + 7. A subsequence of a string S is obtained by deleting 0 or more characters from S. A sequence is palindromic if it is equal…