Codeforce E. Lucky Queries line segment tree practice

E. Lucky Queries

Petya loves lucky numbers very much. everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. for example, numbers 47,744, 4 are lucky and 5, 17,467 are not.

Petya brought home stringSWith the lengthN. The string only consists of lucky digits. The digits are numbered from the left to the right starting with 1. Now Petya showould executeMQueries of the following form:

• SwitchL R-"Switch" digits (I. e. replace them with their opposites) at all positions with indexes fromLToR, Random sive: each digit 4 is replaced with 7 and each digit 7 is replaced with 4 (1? ≤?L? ≤?R? ≤?N);
• Count-find and print on the screen the length of the longest non-decreasing subsequence of stringS.

  Subsequence of a stringSIs a string that can be obtained fromSBy removing zero or more of its elements. A string is called non-decreasing if each successive digit is not less than the previous one.

  Help Petya process the requests.

  Input

  The first line contains two integersNAndM(1? ≤?N? ≤? 106 ,? 1? ≤?M? ≤? 3. 105)-the length of the stringSAnd the number of queries correspondingly. The second line containsNLucky digits without spaces-Petya's initial string. NextMLines contain queries in the form described in the statement.

  Output

  For each query count print an answer on a single line.

  Sample test (s) input

  2 347countswitch 1 2count

  Output

  21

  The data volume is large, and the query speed can be greatly improved by using the line segment tree.

  The key difficulty of this question is the dynamic update of the Line Segment tree. You need to set a Lazy flag, that is, you do not need to update all vertices each time, but wait until the next time you need to query this vertex, update the two child nodes at this point.

  For the logical relationship, study the code carefully. The logic is still very difficult.

  The line segment tree has two points:

  1. Binary Tree

  2 Lazy flag Dynamic Update Interval

  # Include
     
      
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  Using namespace std; class LuckyQueries {int n, tSize; char * str; struct Node {int L4, L7, L47, L74; bool lazy ;}; Node * segTree; void updateNode (int id, int left, int right) {segTree [id]. l4 = segTree [left]. l4 + segTree [right]. l4; segTree [id]. l7 = segTree [left]. l7 + segTree [right]. l7; int a = segTree [left]. l47 + segTree [right]. l7; int B = segTree [left]. l4 + segTree [right]. l47; segTree [id]. l47 = max (a, B); a = seg Tree [left]. l74 + segTree [right]. l4; B = segTree [left]. l7 + segTree [right]. l74; segTree [id]. l74 = max (a, B); segTree [id]. lazy = false;} void conHelper (int low, int up, int id = 0) {if (low = up) {if (str [low] = '4 ') {segTree [id]. l4 = 1, segTree [id]. l7 = 0; segTree [id]. l47 = 1, segTree [id]. l74 = 0;} else {segTree [id]. l4 = 0, segTree [id]. l7 = 1; segTree [id]. l47 = 0, segTree [id]. l74 = 1;} segTree [id]. lazy = fa Lse; return;} int mid = low + (up-low)> 1); int left = id * 2 + 1; int right = id * 2 + 2; conHelper (low, mid, left); conHelper (mid + 1, up, right); updateNode (id, left, right);} void conTree () {int h = (int) ceil (double) log (double (n)/log (2.0) + 1; tSize = (int) pow (2.0, double (h)-1; segTree = (Node *) malloc (sizeof (Node) * tSize); conHelper (0, n-1);} inline int getLongestIncease () {return max (segTree [0]. l4, max (SegTree [0]. L47, segTree [0]. L7);} void invert (int root) {segTree [root]. lazy =! SegTree [root]. lazy; swap (segTree [root]. l4, segTree [root]. l7); swap (segTree [root]. l47, segTree [root]. l74);} void updateTree (const int low, const int up, int tLow, int tUp, int root = 0) {if (tUp <low | up <tLow) // error | to & {return;} if (low <= tLow & tUp <= up) {invert (root); return ;} int tMid = tLow + (tUp-tLow)> 1); int left = root * 2 + 1; int right = root * 2 + 2; if (segTree [root]. lazy) {segTree [root]. Lazy = false; invert (left); invert (right);} updateTree (low, up, tLow, tMid, left); updateTree (low, up, tMid + 1, tUp, right); updateNode (root, left, right);} public: LuckyQueries () {int m; scanf ("% d", & n, & m ); getchar (); // do not forget to remove a linefeed str = (char *) malloc (sizeof (char) * (n + 1); gets (str ); conTree (); char command [8]; for (int I = 0; I <m; I ++) {char c = getchar (); if ('c' = c) {printf ("% d \ n", getLongestIncease ()); Gets (command); // gets row} else {while (c! = '') C = getchar (); int low, up; scanf (" % d ", & low, & up); updateTree (low-1, up-1, 0, n-1); if (I + 1! = M) getchar ();}}}~ LuckyQueries () {if (str) free (str); if (segTree) free (segTree );}};