杭电多校第二场 hdu 6315 Naive Operations 线段树变形

Naive Operations

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 502768/502768 K (Java/Others)
Total Submission(s): 2114    Accepted Submission(s): 915

Problem Description

In a galaxy far, far away, there are two integer sequence a and b of length n.
b is a static permutation of 1 to n. Initially a is filled with zeroes.
There are two kind of operations:
1. add l r: add one for al,al+1...ar
2. query l r: query ∑ri=l⌊ai/bi⌋

 

Input

There are multiple test cases, please read till the end of input file.
For each test case, in the first line, two integers n,q, representing the length of a,b and the number of queries.
In the second line, n integers separated by spaces, representing permutation b.
In the following q lines, each line is either in the form 'add l r' or 'query l r', representing an operation.
1≤n,q≤100000, 1≤l≤r≤n, there're no more than 5 test cases.

 

Output

Output the answer for each 'query', each one line.

 

Sample Input

5 12
1 5 2 4 3
add 1 4
query 1 4
add 2 5
query 2 5
add 3 5
query 1 5
add 2 4
query 1 4
add 2 5
query 2 5
add 2 2
query 1 5

 

Sample Output

1
1
2
4
4
6

 

Source

2018 Multi-University Training Contest 2

 

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题意：有个初始值为0的数组a，和一个数组b，每次可以对a数组所有数进行一次加一的操作，问每次查询时 a(l)/b(l) + a(l+1)/b(l+1) + ... + a(r)/b(r) 的和

分析：考虑我们要求的是[a1/b1] + [a2/b2] + ... + [an/bn]的和，看单独的项a1/b1，因为a1是从零开始的，所以只有当我们加的次数等于b1时（每次只加一），整体的和才会加一

a1每次加一一直加到b1相当于b1每次减一一直减到0（当bi的值减到一再重新赋值为bi这样可以一直进行加减操作），因为bi最开始的值是大于0的，所以我只需要用一个线段树来维护每次的最小值和区间和就行

#include <map>
#include <set>
#include <stack>
#include <cmath>
#include <queue>
#include <cstdio>
#include <vector>
#include <string>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <algorithm>
#define ls (r<<1)
#define rs (r<<1|1)
#define debug(a) cout << #a << " " << a << endl
using namespace std;
typedef long long ll;
const ll maxn = 1e5 + 1000;
const ll mod = 1e9 + 7;
struct node {
    ll fg;
    ll s;   //一段区间总和
    ll mv;  //记录最小值
}root[4*maxn];
ll b[maxn], n, m, le, ri;
char s[10];
void update( ll r ) {
    root[r].mv = min( root[ls].mv, root[rs].mv );
    root[r].s = root[ls].s + root[rs].s;
}
void setf( ll r, ll f ) {
    root[r].fg += f;
    root[r].mv += f;
}
void build( ll r, ll le, ll ri ) {
    root[r].fg = 0;
    if( le == ri ) {
        root[r].mv = b[le]-1;
        root[r].s = 0;
    } else {
        ll mid = ( le + ri ) >> 1;
        build( ls, le, mid );
        build( rs, mid+1, ri );
        update(r);
    }
}
void push( ll r ) {
    if( root[r].fg ) { //fg为-1进行操作，将左右子树最小值置为-1，同时将左右子树fg标记为-1
        setf( ls, root[r].fg );
        setf( rs, root[r].fg );
        root[r].fg = 0;
    }
}
ll query( ll r, ll le, ll ri, ll tl, ll tr ) {
    if( tl == le && tr == ri ) {
        return root[r].s;
    } else {
        push(r);
        ll mid = ( le + ri ) >> 1;
        if( tr <= mid ) {
            return query( ls, le, mid, tl, tr );
        } else if( tl > mid ) {
            return query( rs, mid+1, ri, tl, tr );
        } else {
            return query( ls, le, mid, tl, mid ) + query( rs, mid+1, ri, mid+1, tr );
        }
    }
}
void modify( ll r, ll le, ll ri, ll tl, ll tr ) {
    if( tl > tr ) {
        return;
    }
    if( tl == le && tr == ri ) {
        if( root[r].mv > 0 ) {
            root[r].mv --, root[r].fg --;
        } else {
            if( tl == tr ) {
                root[r].mv = b[le]-1;
                root[r].s ++;
            } else {
                push(r);
                ll mid = ( le + ri ) >> 1;
                if( root[ls].mv == 0 ) {
                    modify( ls, le, mid, tl, mid );
                } else {
                    setf( ls, -1 );
                }
                if( root[rs].mv == 0 ) {
                    modify( rs, mid+1, ri, mid+1, tr );
                } else {
                    setf( rs, -1 );
                }
                update(r);
            }
        }
    } else {
        push(r);
        ll mid = ( le + ri ) >> 1;
        if( tr <= mid ) {
            modify( ls, le, mid, tl, tr );
        } else if( tl > mid ) {
            modify( rs, mid+1, ri, tl, tr );
        } else {
            modify( ls, le, mid, tl, mid ), modify( rs, mid+1, ri, mid+1, tr );
        }
        update(r);
    }
}
int main() {
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    while( scanf("%lld%lld",&n,&m) != EOF ) {
        for( ll i = 1; i <= n; i ++ ) {
            scanf("%lld",&b[i]);
        }
        build(1,1,n);
        for( ll i = 1; i <= m; i ++ ) {
            scanf("%s%lld%lld",s,&le,&ri);
            if( s[0] == 'a' ) {
                modify( 1, 1, n, le, ri );
            } else {
                printf("%lld\n",query(1,1,n,le,ri));
            }
        }
    }
    return 0;
}