HDU 6333 Problem B. Harvest of Apples——莫队

题意：

There are nn apples on a tree, numbered from 11 to nn. 
Count the number of ways to pick at most mm apples. 

思路：

sum(n, m) = 2sum(n-1, m) - c(n-1, m)

sum(n,m) = sum(n, m-1) + c(n, m)

可以发现若知道了sum(n, m)可以在O（1）时间内推出sum(n-1,m),sum(n,m-1),sum(n+1, m),sum(n,m+1)

可以用莫队

#include 
#include 
#include 
#include 
#include 

using namespace std;

typedef long long ll;
const int maxn = 1e5 + 10;
const int mod = 1e9 + 7;
const int block = 316;

int belong[maxn];
ll fac[maxn], inv[maxn];
struct Modui {
    int l, r, id;
    ll ans;
}modui[maxn];
bool cmp1(Modui &x, Modui &y) {
    if (belong[x.l] != belong[y.l]) return x.l < y.l;
    return x.r < y.r;
}
bool cmp2(Modui &x, Modui &y) {
    return x.id < y.id;
}

ll mpow(ll x, int y) {
    ll ans = 1;
    while (y) {
        if (y & 1) ans = ans * x % mod;
        x = x * x % mod;
        y >>= 1;
    }
    return ans;
}
ll C(int x, int y) {
    if (x < y) return 0;
    return fac[x] * inv[y] % mod * inv[x-y] % mod;
}
void init() {
    fac[0] = 1;
    for (int i = 1; i < maxn; i++) fac[i] = fac[i-1] * i % mod;
    inv[maxn-1] = mpow(fac[maxn-1], mod - 2);
    for (int i = maxn - 2; ~i; --i) inv[i] = inv[i + 1] * (i + 1) % mod;
    for (int i = 0; i < maxn; i++) belong[i] = i / block;
}

int main() {
    init();
    int T;
    scanf("%d", &T);
    for (int i = 1; i <= T; i++) {
        scanf("%d%d", &modui[i].l, &modui[i].r);
        modui[i].id = i;
    }
    sort(modui+1, modui+1+T, cmp1);
    int l = 1, r = 0;
    ll sum = 1;
    for (int i = 1; i <= T; i++) {
        while (l < modui[i].l) sum = ((sum*2%mod-C(l++, r))%mod+mod)%mod;
        while (l > modui[i].l) sum = (sum+C(--l, r))%mod*inv[2]%mod;
        while (r < modui[i].r) sum = (sum+C(l, ++r))%mod;
        while (r > modui[i].r) sum = ((sum-C(l, r--))%mod+mod)%mod;
        modui[i].ans = sum;
    }
    sort(modui+1, modui+1+T, cmp2);
    for (int i = 1; i <= T; i++) {
        printf("%lld\n", modui[i].ans);
    }
    return 0;
}