Codeforce E. Lucky Queries 線段樹實踐

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 string s with the length of n. The string only consists of lucky digits. The digits are numbered from the left to the right starting with 1. Now Petya should execute m queries of the following form:

• switch l r — "switch" digits (i.e. replace them with their opposites) at all positions with indexes from l to r, inclusive: 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 string s.

  Subsequence of a string s is a string that can be obtained from s by 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 integers n and m (1?≤?n?≤?106,?1?≤?m?≤?3·105) — the length of the string s and the number of queries correspondingly. The second line contains n lucky digits without spaces — Petya's initial string. Next m lines 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 3
  47
  count
  switch 1 2
  count
  

  output

  2
  1

  數據量好大，使用線段樹查詢可以大大提高速度。

  本題關鍵難點是線段樹的動態更新，需要設置一個Lazy標志，就是不需要每次更新所有點，而是等到下次需要查詢到這個點的時候，更新這個點的兩個孩子節點。

  其中的邏輯關系，需要好好研究研究代碼吧。 沒搞清其中的邏輯，還是十分有難度的。

  線段樹本題就兩個點了：

  1 二分法操作樹

  2 Lazy標志動態更新區間

  #include 
  #include 
  #include 
  #include 
  #include 
  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 = segTree[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 = false;
  			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)//錯寫||成&&
  		{
  			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 %d", &n, &m);
  		getchar();//別忘記了去掉一個換行符
  
  		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一行
  			}
  			else
  			{
  				while (c != ' ') c = getchar();
  
  				int low, up;
  				scanf("%d %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);
  	}
  };