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  • Problem B. Harvest of Apples HDU

    Problem Description
    There are n apples on a tree, numbered from 1 to n.
    Count the number of ways to pick at most m apples.
     
    Input
    The first line of the input contains an integer T (1T105) denoting the number of test cases.
    Each test case consists of one line with two integers n,m (1mn105).
     
    Output
    For each test case, print an integer representing the number of ways modulo 109+7.
     
    Sample Input
    2 5 2 1000 500
     
    Sample Output
    16 924129523
     
    Source
     

     解析:

       

      

    #include <iostream>
    #include <cstdio>
    #include <sstream>
    #include <cstring>
    #include <map>
    #include <cctype>
    #include <set>
    #include <vector>
    #include <stack>
    #include <queue>
    #include <algorithm>
    #include <cmath>
    #include <bitset>
    #define rap(i, a, n) for(int i=a; i<=n; i++)
    #define rep(i, a, n) for(int i=a; i<n; i++)
    #define lap(i, a, n) for(int i=n; i>=a; i--)
    #define lep(i, a, n) for(int i=n; i>a; i--)
    #define rd(a) scanf("%d", &a)
    #define rlld(a) scanf("%lld", &a)
    #define rc(a) scanf("%c", &a)
    #define rs(a) scanf("%s", a)
    #define pd(a) printf("%d
    ", a);
    #define plld(a) printf("%lld
    ", a);
    #define pc(a) printf("%c
    ", a);
    #define ps(a) printf("%s
    ", a);
    #define LL long long
    #define ULL unsigned long long
    #define Pair pair<int, int>
    #define mem(a, b) memset(a, b, sizeof(a))
    #define _  ios_base::sync_with_stdio(0),cin.tie(0)
    //freopen("1.txt", "r", stdin);
    using namespace std;
    const int maxn = 1e5 + 100, INF = 0x7fffffff, LL_INF = 0x7fffffffffffffff;
    const int MOD = 1e9+7;
    LL n, m, ans;
    LL up[maxn], down[maxn], pos[maxn], inc[maxn], inv[maxn];
    
    struct node
    {
        LL l, r;
        int id;
    }Node[maxn];
    
    bool cmp(node a, node b)
    {
        return pos[a.l] == pos[b.l] ? (a.r < b.r) : (a.l < b.l);
    }
    
    LL qp(LL a, LL b)
    {
        LL res = 1;
        while(b)
        {
            if(b & 1) res  = res * a % MOD;
            a = a * a % MOD;
            b >>= 1;
        }
        return res;
    }
    
    void init()
    {
        up[0] = 1;
        down[0] = 1;
        for(int i=1; i<maxn; i++)
        {
            up[i] = up[i-1] * i % MOD;
            down[i] = qp(up[i], MOD - 2) % MOD;
        }
    }
    
    LL C(LL n, LL m)
    {
        if(n < m) return 0;
        return up[n] * down[n-m] % MOD * down[m] % MOD;
    }
    
    int main()
    {
        init();
        int block = sqrt(100000);
        for(int i=1; i<=100000; i++)
            pos[i] = (i-1)/block + 1;
        int T;
        rd(T);
        for(int i=1; i<=T; i++)
        {
            rlld(Node[i].r), rlld(Node[i].l);
            Node[i].id = i;
        }
        sort(Node + 1, Node + T + 1, cmp);
        ans = 2;
        int tmp = qp(2, MOD - 2);
        for(int i=1, l=1, r=1; i<=T; i++)
        {
            for(; r < Node[i].r; r++)
                ans = (2 * ans - C(r, l) + MOD) % MOD;
            for(; r > Node[i].r; r--)
                ans = (ans + C(r-1, l)) * tmp % MOD;
            for(; l < Node[i].l; l++)
                ans = (ans + C(r, l+1)) % MOD;
            for(; l > Node[i].l; l--)
                ans = (ans - C(r, l) + MOD) % MOD;
            if(Node[i].l == Node[i].r)
            {
                inc[Node[i].id] = 1;
            }
    
            inc[Node[i].id] = ans;
        }
        for(int i=1; i<=T; i++)
            printf("%lld
    ", inc[i]);
    
    
        return 0;
    }
    自己选择的路,跪着也要走完。朋友们,虽然这个世界日益浮躁起来,只要能够为了当时纯粹的梦想和感动坚持努力下去,不管其它人怎么样,我们也能够保持自己的本色走下去。
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  • 原文地址:https://www.cnblogs.com/WTSRUVF/p/9695721.html
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