범위 최소 / 최대 쿼 리 (RMQ) - 스 파스 테이블 알고리즘

/*
 * =====================================================================================
 *
 *       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[N], d[20];
int st[N][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("
");
	}
}

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
", 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][N], ln[N], val[N];

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
", 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("
");
	}
	printf("ln is ");
	for(int i = 0; i < n; i++)
	{
		printf("%d ", ln[i]);	
	}
	printf("
");
}

// 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
", x, y, query(x, y));
		}
	}
}