arithmetic_sum.hpp

[詳解]

#include"../../kyopro_library/template.hpp"
 
/// @brief 等差数列
struct ArithmeticProgression {
    ll start=INFL,goal=INFL,step=INFL,length=INFL;
 
    /// @brief 初項、公差、末項、項数のうち、足りない情報を計算する
    void normalize() {
        int undef_cnt=0;
        if(start==INFL) undef_cnt++;
        if(goal==INFL) undef_cnt++;
        if(step==INFL) undef_cnt++;
        if(length==INFL) undef_cnt++;
        assert(undef_cnt<=1);
        if(goal==INFL) goal=start+(length-1)*step;
        else if(start==INFL) start=goal-(length-1)*step;
        else if(step==INFL) step=(start==goal)?0:(goal-start)/(length-1);
        else if(length==INFL) {
            assert(step!=0);
            length=(goal-start)/step+1;
        }
    }
};
 
/// @brief 等差数列の和を返す
ll ArithmeticSum(ArithmeticProgression ap) {
    ap.normalize();
    return(ap.start+ap.goal)*ap.length/2;
}