线段树的第一次使用

• 33行之前是通用的线段树构建，下标从零开始
• 33行之后实现了：求数字序列的最长严格上升子序列，且相邻数的差不大于k。下标从1开始
• TODO：线段树的区间修改，动态开点

#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;
using ll = long long;

struct node {
    ll sum;
    int max;
    int l;
    int r;
    int lazy;
} tree[400009];

void build(int l, int r, int idx, int *nums) {
    tree[idx].l = l;
    tree[idx].r = r;
    if(l == r) {
        tree[idx].sum = nums[l];
        tree[idx].max = nums[l];
        return;
    }
    int mid = (l + r) >> 1;
    int ls = idx << 1 | 1, rs = ls + 1;
    build(l, mid, ls, nums);
    build(mid+1, r, rs, nums);
    tree[idx].sum = tree[ls].sum + tree[rs].sum;
    tree[idx].max = tree[ls].max;
    if(tree[ls].max < tree[rs].max) tree[idx].max = tree[rs].max;
} 

vector<int> tr;
// idx和l，r是成对出现的，共同变化，即上面的结构体：tr[idx]表示区间[l,r]的某个属性
int query(int ql, int qr, int idx, int l, int r) {
    if(qr == 0) return 0;
    if(ql <= l && r <= qr) return tr[idx];
    int mid = (l+r) >> 1, lson = idx << 1, rson = lson | 1;
    int res = 0;
    if(ql <= mid) res = query(ql, qr, lson, l, mid);
    if(qr > mid) {
        int tmp = query(ql, qr, rson, mid+1, r);
        if(tmp > res) res = tmp;
    }
    return res;
}
// 单值修改
void modify(int lr, int val, int idx, int l , int r) {
    if(l == r && l == lr) {
        tr[idx] = val;
        return;
    }
    int mid = (l+r) >> 1, lson = idx << 1, rson = lson | 1;
    if(lr <= mid) modify(lr, val, lson, l, mid);
    else modify(lr, val, rson, mid+1, r);
    tr[idx] = tr[lson];
    if(tr[rson] > tr[idx]) tr[idx] = tr[rson];
}

int main(int argc, char **argv) {
    vector<int> nums = {9,10,11,12,13,14, 15};
    int k = 3;
    int u = *max_element(nums.begin(), nums.end());
    tr.resize(u * 4);
    // 每个元素比他小的k个数中的最大值+1
    for(int i = 0; i < nums.size(); ++i) {
        int begin = nums[i]-k;
        if(begin < 1) begin = 1;
        int res = 1 + query(begin, nums[i]-1, 1, 1, u);
        modify(nums[i], res, 1, 1, u);
    }
    cout << tr[1] << endl;
    // int r = stoi(argv[1]);
    // build(0,r,0,nums);
    // for(int i = 0; i < 16; ++i) {
    //     cout << i << "  " << tree[i].sum << endl;
    // }
    // modify(2,2,0);
    // for(int i = 0; i <= r; ++i) {
    //     for(int j = i; j <= r; ++j) {
    //         res = 0;
    //         query(i, j, 0);
    //         printf("(%d, %d) %lld\n", i, j, res);
    //     }
    // }

    return 0;
}