Codeforces 961E - Tufurama

961E - Tufurama

思路：

线段树或者分块

遍历 1 - n - 1，求 区间[i + 1, min(a[i], n)]大于等于 i 的个数，累加起来

线段树：

#include<bits/stdc++.h>
using namespace std;
#define LL long long 
#define pb push_back
#define ls rt << 1, l, m
#define rs rt << 1 | 1, m + 1, r 
#define mem(a, b) memset(a, b, sizeof(a))

const int N = 2e5 + 5;
vector<int> vc[N<<2];
int a[N];
void build(int rt, int l, int r) {
    if (l == r) {
        vc[rt].pb(a[l]);
        return ;    
    }
    for (int i = l; i <= r; i++) vc[rt].pb(a[i]);
    sort(vc[rt].begin(), vc[rt].end());
    int m = l + r >> 1;
    build(ls);
    build(rs);
} 
int query(int L, int R, int rt, int l, int r) {
    if (L > R) return 0;
    if (L <= l && r <= R) {
        return vc[rt].size()-(lower_bound(vc[rt].begin(), vc[rt].end(), L - 1) - vc[rt].begin());
    }
    int ans = 0;
    int m = l + r >> 1;
    if (L <= m) ans += query(L, R, ls);
    if (R > m) ans += query(L, R, rs);
    return ans;
} 
int main() {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    build(1, 1, n);
    LL ans = 0;
    for (int  i = 1; i < n; i++) {
        ans += query(i + 1, min(a[i], n), 1, 1, n);
    }
    printf("%lld\n",ans);
    return 0;
}

分块：

#include<bits/stdc++.h>
using namespace std;
#define LL long long 
#define pb push_back
#define mem(a, b) memset(a, b, sizeof(a))

const int N = 2e5 + 5;
int a[N], block[1005], belong[N];
int blo;
vector<int> vc[1005];
int query(int L, int R){
    if (R < L) return 0;
    int ans = 0;
    if (belong[L] == belong[R]) {
        for (int i = L; i <= R; i++) {
            if (a[i] >= L - 1) ans++;
        }
        return ans;
    }
    for (int i = L; i <= belong[L] * blo; i++){
        if (a[i] >= L - 1) ans++;
    }
    for (int i = belong[L] + 1; i <= belong[R] - 1; i++) {
        ans += vc[i].size() - (lower_bound(vc[i].begin(), vc[i].end(), L - 1) - vc[i].begin());
    }
    for (int i = (belong[R] - 1) * blo + 1; i <= R; i++) {
        if (a[i] >= L - 1) ans++;
    }
    return ans;
}
int main() {
    int n;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
    blo = sqrt(n);
    for (int i = 1; i <= n; i++) {
        belong[i] = (i - 1) / blo + 1;        
    }
    for (int i = 1; i <= n; i++) {
        vc[belong[i]].pb(a[i]);
    } 
    for (int i = 1; i <= belong[n]; i++) {
        sort(vc[i].begin(), vc[i].end());
    }
    LL ans = 0;
    for (int i = 1; i <= n - 1; i++) {
        ans += query(i + 1, min(n, a[i]));
        //cout << ans << endl;
    }
    printf("%lld\n", ans);
    return 0;
}