HDU3308:LCIS(线段树区间合并)
2013-11-10 15:48
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Problem Description
Given n integers.
You have two operations:
U A B: replace the Ath number by B. (index counting from 0)
Q A B: output the length of the longest consecutive increasing subsequence (LCIS) in [a, b].
Input
T in the first line, indicating the case number.
Each case starts with two integers n , m(0<n,m<=105).
The next line has n integers(0<=val<=105).
The next m lines each has an operation:
U A B(0<=A,n , 0<=B=105)
OR
Q A B(0<=A<=B< n).
Output
For each Q, output the answer.
Sample Input
Sample Output
Q是询问区间内最大的LCIS
U是更新节点
思路:简单的线段树区间合并题
Given n integers.
You have two operations:
U A B: replace the Ath number by B. (index counting from 0)
Q A B: output the length of the longest consecutive increasing subsequence (LCIS) in [a, b].
Input
T in the first line, indicating the case number.
Each case starts with two integers n , m(0<n,m<=105).
The next line has n integers(0<=val<=105).
The next m lines each has an operation:
U A B(0<=A,n , 0<=B=105)
OR
Q A B(0<=A<=B< n).
Output
For each Q, output the answer.
Sample Input
1 10 10 7 7 3 3 5 9 9 8 1 8 Q 6 6 U 3 4 Q 0 1 Q 0 5 Q 4 7 Q 3 5 Q 0 2 Q 4 6 U 6 10 Q 0 9
Sample Output
1 1 4 2 3 1 2 5
Q是询问区间内最大的LCIS
U是更新节点
思路:简单的线段树区间合并题
#include <stdio.h> #include <string.h> #include <algorithm> using namespace std; const int L = 111111; int n,m,s[L]; struct node { int l,r,c;//左右边界与连续的长度 int ln,rn;//左右边界的值 int ls,rs,ms,;//左右最大LCIS,和区间最大LCIS } a[L<<2]; void pushup(int i) { a[i].ls = a[2*i].ls; a[i].rs = a[2*i+1].rs; a[i].ln = a[2*i].ln; a[i].rn = a[2*i+1].rn; a[i].ms = max(a[2*i].ms,a[2*i+1].ms); if(a[2*i].rn<a[2*i+1].ln)//如果左子树的右边界值小于右子树的左边界值,要合并左子树的右边界和右子树的左边界进行计算 { if(a[2*i].ls == a[2*i].c) a[i].ls+=a[2*i+1].ls; if(a[2*i+1].rs == a[2*i+1].c) a[i].rs+=a[2*i].rs; a[i].ms = max(a[i].ms,a[2*i].rs+a[2*i+1].ls); } } void init(int l,int r,int i)//建树 { a[i].l = l; a[i].r = r; a[i].c = r-l+1; if(l == r) { a[i].ln = a[i].rn = s[l]; a[i].ls = a[i].rs = a[i].ms = 1; return; } int mid = (a[i].l+a[i].r)>>1; init(l,mid,2*i); init(mid+1,r,2*i+1); pushup(i); } void insert(int i,int t,int m) { if(a[i].l == a[i].r) { a[i].ln = a[i].rn = m; return; } int mid = (a[i].l+a[i].r)>>1; if(t<=mid) insert(2*i,t,m); if(t>mid) insert(2*i+1,t,m); pushup(i); } int query(int l,int r,int i)//查询最大的LCIS { if(a[i].l>=l && a[i].r<=r) { return a[i].ms; } int mid = (a[i].l+a[i].r)>>1,ans = 0; if(l<=mid) ans = max(ans,query(l,r,2*i)); if(r>mid) ans = max(ans,query(l,r,2*i+1)); if(a[2*i].rn < a[2*i+1].ln) ans = max(ans , min(mid-l+1,a[2*i].rs)+min(r-mid,a[2*i+1].ls)); return ans; } int main() { int t,i,l,r; char str[5]; scanf("%d",&t); while(t--) { scanf("%d%d",&n,&m); for(i = 1; i<=n; i++) scanf("%d",&s[i]); init(1,n,1); while(m--) { scanf("%s%d%d",str,&l,&r); if(str[0] == 'Q') printf("%d\n",query(l+1,r+1,1)); else insert(1,l+1,r); } } return 0; }
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