Range Minimum/Maximum Query (RMQ) - Sparse Table 算法

/*
* =====================================================================================
*
*       Filename:  RMQ_st.CPP
*
*    Description:  Range Min/Max Query - st algorithm
*
*        Version:  1.0
*        Created:  07/13/11 13:33:45
*       Revision:  none
*       Compiler:  gcc
*
*         Author:  nomad2
*
* =====================================================================================
*/

#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;

const int N = 200001;

int a
, d[20];
int st
[20];

void readIn(int n)
{
int i;
for(i = 0; i < n; i++)
{
scanf("%d", &a[i]);
}
}

void initRMQ(int n)
{
int i, j;
for(d[0] = 1, i = 1; i < 21; i++)
{
d[i] = 2 * d[i-1];
}

for(i = 0; i < n; i++)
{
st[i][0] = a[i];
}

int k = int(log(double(n))/log(2)) + 1;
for(j = 1; j < k; j++)
{
for(int i = 0; i < n; i++)
{
if(i + d[j-1] - 1 < n)
{
st[i][j] = max(st[i][j-1], st[i + d[j-1]][j-1]);
}
else
{
break; // st[i][j] = st[i][j-1];
}
}
}
for(int i = 0; i < n; i++)
{
for(int j = 0; j < k; j++)
{
printf("%d ", st[i][j]);
}
printf("\n");
}
}

void query(int Q)
{
int i;
for(i = 0; i < Q; i++)
{
int x, y, k;
scanf("%d%d", &x, &y);
k = int(log(double(y-x+1))/log(2.0));
printf("%d\n", max(st[x][k], st[y - d[k]+1][k]));
}
}

int main()
{
int n, Q;
while(scanf("%d%d", &n, &Q) != EOF)
{
readIn(n);
initRMQ(n);
query(Q);
}
return 0;
}

[pa004306: ]
>> cat input1
8 3
4 5 7 2 1 3 6 9
1 2
2 4
3 7
[pa004306: ]
>> cat input1 |./a.exe
4 5 7
5 7 7
7 7 7
2 2 6
1 3 9
3 6 9
6 9 9
9 9 0
7
7
9

#include <cstdio>
#include <algorithm>

using namespace std;

const int N = 100;
int st[20]
, ln
, val
;

int n = 9;

void initrmq(int n)
{
int i, j, k, sk;
ln[0] = ln[1] = 0;
for(i = 0; i < n; i++)
{
st[0][i] = val[i];
}
for(i = 1, k = 2; k < n; i++, k <<= 1)
{
printf("k is %d\n", k);
for(j = 0, sk = (k>>1); j < n; j++, sk++)
{
st[i][j] = st[i-1][j];
if(sk < n && st[i][j] > st[i-1][sk])
{
st[i][j] = st[i-1][sk];
}
}
ln[0] = -1;
for(j = (k>>1); j < k; j++)
{
ln[j] = ln[(k>>1)-1] + 1;
}
}
ln[0] = 0;
/*
for(j = (k>>1) + 1; j <= k; j++)
{
ln[j] = ln[k>>1] + 1;
}  */
}

void print()
{
for(int i = 0; i < 5; i++)
{
for(int j = 0; j < n; j++)
{
printf("%d ", st[i][j]);
}
printf("\n");
}
printf("ln is ");
for(int i = 0; i < n; i++)
{
printf("%d ", ln[i]);
}
printf("\n");
}

// min of (val[x]...val[y])
int query(int x, int y)
{
int bl = ln[y-x+1];
return min(st[bl][x], st[bl][y-(1<<bl)+1]);
}

int main()
{
int v[] = {9, 5, 6, 7, 8, 3, 4, 2, 1};
n = sizeof(v)/sizeof(int);
for(int i = 0; i < n; i++)
{
val[i] = v[i];
}
initrmq(n);
print();

for(int x = 0; x < n; x++)
{
//for(int y = x; y < n; y++)
int y = x + 1;
{
printf("min between %d and %d is %d\n", x, y, query(x, y));
}
}
}