离散化

与哈希类似，但是离散化是保序的，可以用二分。

vector<int> alls; // 存储所有待离散化的值
sort(alls.begin(), alls.end()); // 将所有值排序
alls.erase(unique(alls.begin(), alls.end()), alls.end());   // 去掉重复元素

// 二分求出x对应的离散化的值
int find(int x) // 找到第一个大于等于x的位置
{
    int l = 0, r = alls.size() - 1;
    while (l < r)
    {
        int mid = l + r >> 1;
        if (alls[mid] >= x) r = mid;
        else l = mid + 1;
    }
    return r + 1; // 映射到1, 2, ...n，即下标从1开始
}

应用：区间和

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

using namespace std;

typedef pair<int, int> PII;

const int N = 300010;
int n, m;
int a[N], s[N];
vector<int> alls;
vector<PII> add, query;

int find(int x) {
    int l = 0, r = alls.size() - 1;
    while(l < r) {
        int mid = l + r >> 1;
        if(alls[mid] >= x) {
            r = mid;
        } else {
            l = mid + 1;
        }
    }
    return l + 1;
}

vector<int>::iterator unique(vector<int> &a) {
    int j = 0;
    for(int i = 0; i < a.size(); i ++) {
        if(!i || a[i] != a[i - 1]) {
            a[j ++] = a[i];
        }
    }
    return a.begin() + j;
}

int main() {
    
    cin >> n >> m;
    
    int x, c;
    for(int i = 1; i <= n; i ++) {
        cin >> x >> c;
        add.push_back({x, c});
        alls.push_back(x);
    }
    
    int l, r;
    for(int i = 1; i <= m; i ++) {
        cin >> l >> r;
        query.push_back({l, r});
        alls.push_back(l);
        alls.push_back(r);
    }
    
    sort(alls.begin(), alls.end());
    alls.erase(unique(alls), alls.end());
    
    for(auto item : add) {
        a[find(item.first)] += item.second;
    }
    
    for(int i = 1; i <= alls.size(); i ++) {
        s[i] = s[i - 1] + a[i];
    }
    
    for(auto item : query) {
        cout << s[find(item.second)] - s[find(item.first) - 1] << endl;
    }
    
    return 0;
}