inversion_number.hpp

[詳解]

#include "../../kyopro_library/template.hpp"
 
/// @brief 転倒数
/// @brief 配列 v の転倒数を求める
/// @note O(N log(N))
ll InversionNumber(const vector<int>& v) {
    ll ret=0;
    auto Merge=[&](const vector<int>& a, const vector<int>& b) {
        int n=a.size();
        int r=0;
        for(int l=0; l<n; l++) {
            while(r<n&&b[r]<a[l]) r++;
            ret+=r;
        }
        vector<int> c(2*n);
        merge(a.begin(),a.end(),b.begin(),b.end(),c.begin());
        return c;
    };
 
    int n=v.size(),n2=1;
    while(n2<n) n2<<=1;
    vector<vector<int>> node(n2<<1,vector<int>(1,INF));
    for(int i=0; i<n; i++) node[i+n2][0]=v[i];
    for(int i=n2-1; i>0; i--) node[i]=Merge(node[i<<1],node[i<<1|1]);
    return ret;
}