HDU 5323 Solve this interesting problem(dfs结合线段树特点剪枝)
2016-07-23 21:04
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Problem Description
Have you learned something about segment tree? If not, don’t worry, I will explain it for you.
Segment Tree is a kind of binary tree, it can be defined as this:
- For each node u in Segment Tree, u has two values: Lu and Ru.
- If Lu=Ru,
u is a leaf node.
- If Lu≠Ru,
u has two children x and y,with Lx=Lu,Rx=⌊Lu+Ru2⌋,Ly=⌊Lu+Ru2⌋+1,Ry=Ru.
Here is an example of segment tree to do range query of sum.
Given two integers L and R, Your task is to find the minimum non-negative n satisfy that: A Segment Tree with root node's value Lroot=0 and Rroot=n contains
a node u with Lu=L and Ru=R.
Input
The input consists of several test cases.
Each test case contains two integers L and R, as described above.
0≤L≤R≤109
LR−L+1≤2015
Output
For each test, output one line contains one integer. If there is no such n, just output -1.
Sample Input
6 7
10 13
10 11
Sample Output
7
-1
12
Author
ZSTU
Source
2015 Multi-University Training Contest 3
题意:
给出区间[l,r]要求找到一棵线段树,使[l,r]是线段树上的一个区间,求满足的线段树中最大区间[0,n]的n
如果有多解,取最小的解
分析:
显然需要自下而上的搜索线段树,对于区间[l,r],它可能是它爸爸的左儿子,也可能是它爸爸的右儿子
当它是左儿子,它爸爸的区间左端点为l,右端点有两种情况(因为对于式子 mid = (l+r)/2 , 同样的mid 有两个(l+r)/2满足条件)
: rx1 = 2*r - l 或者 rx2 = 2*r +1 - l
同理,当它是右儿子,它爸爸的区间右端点为r,左端点为: lx1 = 2*(l-1)-r 或 lx2 = 2*(l-1)+1-r
剪枝:1.当前搜索的区间右端点已经大于已知的答案则无需继续,继续下去再找到的答案也必然比已知的答案大
2.根据 线段树左儿子不可能比右儿子表示的区间长度小 的特点,故当l<(r-l+1)时返回
Have you learned something about segment tree? If not, don’t worry, I will explain it for you.
Segment Tree is a kind of binary tree, it can be defined as this:
- For each node u in Segment Tree, u has two values: Lu and Ru.
- If Lu=Ru,
u is a leaf node.
- If Lu≠Ru,
u has two children x and y,with Lx=Lu,Rx=⌊Lu+Ru2⌋,Ly=⌊Lu+Ru2⌋+1,Ry=Ru.
Here is an example of segment tree to do range query of sum.
Given two integers L and R, Your task is to find the minimum non-negative n satisfy that: A Segment Tree with root node's value Lroot=0 and Rroot=n contains
a node u with Lu=L and Ru=R.
Input
The input consists of several test cases.
Each test case contains two integers L and R, as described above.
0≤L≤R≤109
LR−L+1≤2015
Output
For each test, output one line contains one integer. If there is no such n, just output -1.
Sample Input
6 7
10 13
10 11
Sample Output
7
-1
12
Author
ZSTU
Source
2015 Multi-University Training Contest 3
题意:
给出区间[l,r]要求找到一棵线段树,使[l,r]是线段树上的一个区间,求满足的线段树中最大区间[0,n]的n
如果有多解,取最小的解
分析:
显然需要自下而上的搜索线段树,对于区间[l,r],它可能是它爸爸的左儿子,也可能是它爸爸的右儿子
当它是左儿子,它爸爸的区间左端点为l,右端点有两种情况(因为对于式子 mid = (l+r)/2 , 同样的mid 有两个(l+r)/2满足条件)
: rx1 = 2*r - l 或者 rx2 = 2*r +1 - l
同理,当它是右儿子,它爸爸的区间右端点为r,左端点为: lx1 = 2*(l-1)-r 或 lx2 = 2*(l-1)+1-r
剪枝:1.当前搜索的区间右端点已经大于已知的答案则无需继续,继续下去再找到的答案也必然比已知的答案大
2.根据 线段树左儿子不可能比右儿子表示的区间长度小 的特点,故当l<(r-l+1)时返回
#include<iostream> #include<cstdio> #include<algorithm> using namespace std; typedef long long ll; ll ans; void dfs(ll l,ll r) { if (l == 0) { if (ans == -1) ans = r; else ans = min(ans,r); return; } if (l < 0) return; if (ans != -1&&r >= ans) return;//剪枝1 //剪枝2:l<(r-l+1)无解,因为线段树左儿子不可能比右儿子表示的区间长度小 if (l < (r-l+1)) return ; //枚举区间[l,r]上一层的区间,[l,r]可能是其爸爸的左儿子,也可能是其爸爸的右儿子 //对于式子(l+r)/2 = mid,同样的mid 有2个(l+r)/2满足条件 ll lx1 = 2*(l-1) - r; ll lx2 = (2*(l-1))+1 - r; ll rx1 = 2*r - l; ll rx2 = 2*r+1 - l; dfs(lx1,r); dfs(lx2,r); dfs(l,rx1); dfs(l,rx2); } int main() { ll l,r; while (~scanf("%I64d %I64d",&l,&r)) { ans = -1; dfs(l,r); printf("%I64d\n",ans); } return 0; }
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