Implementation：Segment Tree 线段树

早就听人提起过线段树，今天有题搞不出来，讨论上说要用一下线段树，看了下，本质上是空间划分索引，只不过是一维上面的，如果在二维则是四叉树，三维则是八叉树，如果可以动态调整那么跟R-Tree就很相似了，他们都可以对范围查询做出响应。参照书上写了一个，虽然不多，但是渣渣也写的很是费力

#include <iostream>
#include <cstdlib>
#include <vector>

using namespace std;

class SegmentTree {
    private:
        int *mem;
        int capacity;
        int storage_size;
    private:
        void init_level_update() {
            int k = capacity - ;
            while (--k >= ) {
                int L = (k<<) + ;
                int R = L + ;
                mem[k]= min(mem[L], mem[R]);
            }
        }

        int query(int a, int b, int idx, int L, int R) {
            if (b <= L || a >= R) return INT_MAX;
            if (a <= L && R <= b) return mem[idx];

            int ml = query(a, b, (idx<<) + , L, (L+R)/);
            int mr = query(a, b, (idx<<) + , (L+R)/, R);
            return min(ml, mr);
        }

        void init_mem(int _capacity) {
            if (_capacity <= ) {
                capacity = ;
                return;
            }
            int n = ;
            while (n < _capacity) n<<=;
            capacity = n;
            storage_size = capacity *  - ;
            mem = new int[storage_size];

            int k = ;
            while (k < storage_size) mem[k++] = INT_MAX;
        }
    public:
        SegmentTree(int _capacity) {
            init_mem(_capacity);
        }
        SegmentTree(vector<int>::iterator begin, vector<int>::iterator end) {
            capacity = end - begin;
            init_mem(capacity);

            int k = capacity - ;
            vector<int>::iterator iter = begin;
            while (iter != end) mem[k++] = *iter++;

            init_level_update();
        }
        ~SegmentTree() {
            delete[] mem;
        }

        // update value in original data index
        void update(int idx, int val) {
            if (idx >= capacity || idx < ) return;
            int k = idx + capacity - ; // internal storage index
            mem[k] = val;
            while (k > ) {
                k = (k - ) >> ;
                int L = (k << ) + ;
                int R = L + ;
                mem[k] = min (mem[L], mem[R]);
            }
        }

        // retrive the min value in index range [a, b)
        int query(int a, int b) {
            return query(a, b, , , capacity);
        }

        void print_mem(const char* msg) {
            cout<<msg<<endl;
            for (int i=; i<(capacity*-); i++) {
                cout<<mem[i]<<" ";
            }
            cout<<endl;
        }
};

void test(const char* msg, SegmentTree& seg_tree, int* data, int size) {
    cout<<msg<<endl;
    for (int i=; i<=size; i++) {
        for (int j=i+; j<=size; j++) {
            int tmin = seg_tree.query(i, j);
            cout<<"min of ("<<i<<","<<j<<") = "<<tmin<<endl;
            int amin = INT_MAX;
            for (int k=i; k<j; k++) if (data[k] < amin) amin = data[k];
            if (amin != tmin)
                cout<<"fail"<<endl;
            else
                cout<<"ok"<<endl;
        }
    }
}
int main() {
    int h[] = {, , , , , , };
    int size= sizeof(h) / sizeof(int);
    vector<int> hs(h, h + size);

    SegmentTree seg_tree(hs.begin(), hs.end());
    test("Test construction with data :", seg_tree, h, size);

    SegmentTree init_empty_tree(size);
    for (int i=; i<size; i++) init_empty_tree.update(i, h[i]);
    test("Test construction without data", init_empty_tree, h, size);

    system("pause");
    return ;
}

下面是一个带有返回最小值索引值的改进版本

class SegmentTree {
    private:
        int *mem;
        int *idx;
        int capacity;
        int storage_size;

    private:
        void init_level_update() {
            int k = capacity - ;
            while (--k >= ) {
                int L = (k<<) + ;
                int R = L + ;
                if (mem[L] < mem[R]) {
                    mem[k] = mem[L];
                    idx[k] = idx[L];
                } else {
                    mem[k] = mem[R];
                    idx[k] = idx[R];
                }
            }
        }

        pair<int, int> query(int a, int b, int idx, int L, int R) {
            if (b <= L || a >= R) return make_pair(INT_MAX, -);
            if (a <= L && R <= b) return make_pair(mem[idx], this->idx[idx]);

            pair<int, int> ml = query(a, b, (idx<<) + , L, (L+R)/);
            pair<int, int> mr = query(a, b, (idx<<) + , (L+R)/, R);
            return ml.first < mr.first ? ml : mr;
        }

        void init_mem(int _capacity) {
            if (_capacity <= ) {
                capacity = ;
                return;
            }
            int n = ;
            while (n < _capacity) n<<=;
            capacity = n;
            storage_size = capacity *  - ;
            mem = new int[storage_size];
            idx = new int[storage_size];

            int k = ;
            while (k < storage_size) mem[k++] = INT_MAX;
            k = capacity - ;
            int i = ;
            while (k < storage_size) idx[k++] = i++;
        }
    public:
        SegmentTree(int _capacity) {
            init_mem(_capacity);
        }
        SegmentTree(vector<int>::iterator begin, vector<int>::iterator end) {
            capacity = end - begin;
            init_mem(capacity);

            int k = capacity - ;
            vector<int>::iterator iter = begin;
            while (iter != end) mem[k++] = *iter++;

            init_level_update();
        }

        ~SegmentTree() {
            delete[] mem;
            delete[] idx;
        }

        // update value in original data index
        void update(int index, int val) {
            if (index >= capacity || idx < ) return;
            int k = index + capacity - ; // internal storage index
            mem[k] = val;
            while (k > ) {
                k = (k - ) >> ;
                int L = (k << ) + ;
                int R = L + ;
                if (mem[L] < mem[R]) {
                    mem[k] = mem[L];
                    idx[k] = idx[L];
                } else {
                    mem[k] = mem[R];
                    idx[k] = idx[R];
                }
            }
        }

        // retrive the min value in index range [a, b)
        pair<int, int> query(int a, int b) {
            return query(a, b, , , capacity);
        }

        void print_mem(const char* msg) {
            cout<<msg<<endl;
            for (int i=; i<(capacity*-); i++) {
                cout<<mem[i]<<" ";
            }

            for (int i=; i<capacity *  - ; i++) {
                cout<<idx[i]<<",";
            }
            cout<<endl;
        }
};

参考：

　　挑战程序设计竞赛第二版