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Educational Codeforces Round 41-E-Tufurama(樹狀數組)

Educational Codeforces Round 41-E-Tufurama(樹狀數組)
Educational Codeforces Round 41-E-Tufurama(樹狀數組)

題意:很扯的題意,翻譯過來就是給你一個長為n的數組,問你有多少對(i,j)滿足i<j && a[i]>=j && a[j]>=i?

題解:我們考慮先滿足後邊的條件,即找到最大的x使得x<j && a[j]>=x,然後q[x-1].push_back(i),我們所存的是a[i]對于答案的貢獻,其他類推,然後我們按原數組的順序一個個的加入樹狀數組中并查詢答案累加即可。注意答案會爆int

#include<vector>
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
#define maxn 200005
#define ll long long
int c[maxn],a[maxn],n;
vector<int>q[maxn];
void update(int x,int val)
{
	while(x<maxn)
		c[x]+=val,x+=x&-x;
}
int query(int x)
{
	int res=0;
	while(x)
		res+=c[x],x-=x&-x;
	return res;
}
int main(void)
{
	ll ans=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		a[i]=min(a[i],n);
		q[min(i-1,a[i])].push_back(i);
	}
	for(int i=1;i<=n;i++)
	{
		update(a[i],1);
		for(int j=0;j<q[i].size();j++)
			ans+=query(n)-query(q[i][j]-1);
	}
	printf("%lld\n",ans);
	return 0;
}