RMQ问题 acm.mipt 105题解

2014-11-24 10:39:59 · 作者: · 浏览: 0

题目:

RMQ problem
Time limit = 5 second(s)

Memory limit = 32000 Kb

You are given large array of real numbers:
a[0], a[1], ..., a[N-1]

Range Minimal Query problem:

Problem RMQ(i,j) = "find minimum of a[i], a[i+1], ..., a[j-1]".

Your program should solve given set of RMQ problems.

Input. Input data has the following format:

N
a[0] a[1] ... a[N-1]
M
i1 j1
i2 j2
...

iM jM

Here N ≤ 250000, M ≤ 500000, 0 ≤ ik < N, 0 < jk ≤ N, ik < jk.

Output. Your program should output M numbers b1, b2, ..., bM delimited by space, where

bk = MIN (a[ik], a[ik + 1], ..., a[jk — 1]).

Input#1
10
1 2 3 4 5 6 7 8 9 10
16
0 1
0 2
0 3
0 4
3 4
3 5
3 6
3 7
3 8
3 9
3 10
0 10
9 10
8 10
7 10
5 6
Output#1
1.000000
1.000000
1.000000
1.000000
4.000000
4.000000
4.000000
4.000000
4.000000
4.000000
4.000000
1.000000
10.000000
9.000000
8.000000
6.000000

Input#2
10
3.86934 7.28362 2.15556 14.75963 0.33240 17.12550 -0.71121 13.90834 -1.13470 5.99831
11
6 10
0 1
5 10
1 9
0 6
0 10
2 5
3 10
5 9
0 8
2 10
Output#2
-1.134700
3.869340
-1.134700
-1.134700
0.332400
-1.134700
0.332400
-1.134700
-1.134700
-0.711210
-1.134700

代码:
[cpp]
#include
#include
#include
using namespace std;

#define N 250010
int n,m;
int x,y;
float A[N];
int M[N][19];

void process()
{
for(int i=0;i {
M[i][0] = i;
}
for(int j=1;(1< {
for(int i=0;i+(1< {
if(A[M[i][j-1]] {
M[i][j] = M[i][j-1];
}
else
{
M[i][j] = M[i+(1<<(j-1))][j-1];
}
}
}
}

float query(int x,int y)
{
int k;
k = (int)(log(y-x+1)/log(2));

return A[M[x][k]] }

int main()
{
/*#ifndef ONLINE_JUDGE
freopen("in.txt","r",stdin);
#endif*/
scanf("%d",&n);
for(int i=0;i {
scanf(" %f",&A[i]);
}
process();
scanf(" %d",&m);

for(int i=0;i {
scanf(" %d%d",&x,&y);
printf("%f\n",query(x,y-1));
}
return 0;

}