Range Minimum Query-优快云博客

本文介绍了一种使用稀疏表算法解决区间最小值查询问题的方法。该算法通过预处理数组生成稀疏表，使得在给定的两个索引之间的元素中找到最小值的位置变得高效。通过C++实现并展示了算法的工作原理。

Range Minimum Query is used on arrays to find the position of an element with the minimum value between two specified indices. This problem can be solved in many different ways, such as dynamic programming, segment tree, ect. Here shows the C++ implementation of so-called sparse table algorithm.

#include <cmath> #include <fstream> #include <iomanip> #include <iostream> using namespace std; int intArray[] = { 2, 4, 3, 1, 6, 7, 8, 9, 1, 7, }; int size = sizeof(intArray) / sizeof(int); int sparseTableSearch(int *intArray, int size, int left, int right); int main() { ofstream outfile; outfile.open("table.txt"); if(!outfile) { cerr << "can not open input file." << endl; return -1; } for(int i = 0; i < size; ++i) { for(int j = 0; j < size; ++j) { if(i <= j) outfile << setw(2) << sparseTableSearch(intArray, size, i, j); else outfile << setw(2) << " "; } outfile << endl; } outfile << endl; outfile.close(); return 0; } int sparseTableSearch(int *intArray, int size, int left, int right) { static bool first = true; static int **table = new int*[size]; if(first) { int N = (int)(log((double)size) / log(2.0)); for(int i = 0; i < size; ++i) { table[i] = new int[N]; table[i][0] = i; } for(int j = 1; j <= N; ++j) { for(int i = 0; i + (1 << j) - 1 < size ; ++i) { if(intArray[table[i][j - 1]] < intArray[table[i + (1 << (j - 1))][j - 1]]) table[i][j] = table[i][j - 1]; else table[i][j] = table[i + (1 << (j - 1))][j - 1]; } } first = false; } int k = (int)(log(double(right - left + 1)) / log(2.0)); if(intArray[table[left][k]] < intArray[table[right - (1 << k) + 1][k]]) return table[left][k]; else return table[right - (1 << k) + 1][k]; }

The file output:

0 0 0 3 3 3 3 3 8 8 1 2 3 3 3 3 3 8 8 2 3 3 3 3 3 8 8 3 3 3 3 3 8 8 4 4 4 4 8 8 5 5 5 8 8 6 6 8 8 7 8 8 8 8 9