分析
这个就比较简单了,转换问题就是:
求一段最长的连续序列,使得这段序列的前缀(+s) >= 0;
前缀的话我们可以考虑用前缀和快速计算;
暴力的想我们去枚举每个字段,然后判断字段的所有前缀是否都>=0就行;
显然这样是O(n^3)的;
考虑优化:
首先发现固定左端点后,我们的右端点是有单调性的;
(因为对于r只要出现一个前缀<0,则r’(>r)的都不满足)
所以我们可以枚举左端点,然后二分右端点;
其次,要使得[l,r]的所有前缀都>=0,即前缀的最小值都要>=0;
所以我们可以维护前缀的最小值(线段树/树状数组/RMQ),每次快速查询;
这样时间复杂度是:O(n*log(n)*log(n))
注意二分的写法…
代码
#include<iostream>
#include<queue>
#include<cstring>
#include<vector>
#include<stdio.h>
#include<map>
#include<algorithm>
#include<deque>
#include<stack>
#include<set>
// #include <unordered_map>
#include<math.h>
#include<string.h>
#define IOS ios::sync_with_stdio(false),cin.tie(0);
using namespace std;
#define pb push_back
#define coutl cout<<"------------"<<endl;
#define fi first
#define se second
#define ire(x) scanf("%d",&x)
#define iire(a,b) scanf("%d %d",&a,&b)
#define lre(x) scanf("%lld",&x)
#define llre(a,b) scanf("%lld %lld",&a,&b)
#define rep(i,a,b) for(int i=a;i<=b;i++)
#define endl "\n"
#define PI acos(-1.0)
//#define int long long
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> PII;
typedef pair<double, int> PDI;
typedef pair<ll, ll> PLL;
typedef pair<double, double> PDD;
typedef pair<double, pair<int, double> > PDID;
typedef pair<char, char> PCC;
typedef pair<char, pair<int, int> > PCII;
typedef pair<int, pair<int, int> > PIII;
typedef pair<int, pair<int, pair<int, int> > > PIIII;
typedef pair<ll, pair<int, int> > PLII;
const int maxn = 2e5 + 7;
const int N = 2e6 + 7;
const int M = 4e6 + 7;
const int mod = 998244353;
const int inv = mod - mod/2;
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const double pi = acos(-1);
const double eps = 1e-8;
ll gcd(ll a,ll b) {return b==0 ? a : gcd(b,a%b);}
ll lcm(ll a,ll b) {return a*b / gcd(a,b);}
ll qmi(ll a,ll b,ll p) {ll ans = 1; while(b) { if(b & 1) ans = ans * a % p; a = a * a % p; b >>= 1; } return ans;}
int lowbit(int x) {return x & (-x);}
ll a[maxn];
ll sum[maxn];
ll n,s;
struct node
{
int l,r;
ll v;
}tr[maxn*4];
void pushup(int u)
{
// tr[u].v = tr[u<<1].v + tr[u<<1|1].v;
tr[u].v = min(tr[u<<1].v, tr[u<<1|1].v);
}
void build(int u,int l,int r)
{
tr[u] = {l,r,INF};
if(l == r)
{
tr[u].v = sum[l];
return;
}
int mid = l + r >> 1;
build(u<<1,l,mid);
build(u<<1|1,mid+1,r);
pushup(u);
}
ll query(int u,int l,int r)
{
if(l <= tr[u].l && r >= tr[u].r) return tr[u].v;
int mid = tr[u].l + tr[u].r >> 1;
ll ans = INF;
if(l <= mid) ans = min(ans,query(u<<1, l, r));
if(r > mid) ans = min(ans,query(u<<1|1, l, r));
return ans;
}
void solve()
{
cin>>n>>s;
for(int i=1;i<=n;i++) cin>>a[i], sum[i] = 0;
for(int i=1;i<=n;i++) sum[i] = sum[i-1] + a[i];
build(1,1,n); //维护sum区间最小值
ll ans_len = -1;
ll ans_l,ans_r;
for(int i=1;i<=n;i++) //枚举左端点
{
//二分右端点
int l = i;
int r = n;
while(l < r)
{
int mid = l + r + 1 >> 1;
if(query(1,i,mid) + s >= sum[i-1]) l = mid;
else r = mid - 1;
}
// cout<<i<<' '<<l<<'\n';
if(query(1,i,l) + s >= sum[i-1] && l - i + 1 > ans_len)
{
ans_len = l-i+1;
ans_l = i;
ans_r = l;
}
}
if(ans_len == -1) cout<<ans_len<<'\n';
else cout<<ans_l<<' '<<ans_r<<'\n';
}
int main()
{
IOS;
int t;
// t = 1;
cin>>t;
// ire(t);
while(t--)
{
solve();
}
return 0;
}