題解 - HDU 6638 Snowy Smile （線段樹）

題目鏈接：http://acm.hdu.edu.cn/showproblem.php?pid=6638

題意

在二維平面上有2000個點，每個點的權值都在 $(?10^9,10^9)$ 之間，每個點的坐標也在 $(?10^9,10^9)$ 之間，現在要你畫出一個矩陣，獲取這個矩陣中所有點的權值，這個矩陣邊界必須與X軸Y軸平行。

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思路

線段樹維護最大子段和板題

線段樹維護前綴和，利用最大最小值查找當前枚舉的最大子段和（可優化，即當前的最大最小值已經小于ans就continue）

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代碼

//代碼一 最大子段和 #include <bits/stdc++.h> using namespace std; #define rep(i,j,k) for(ll i = (ll)j;i <= (ll)k;i ++) #define debug(x) cerr<<#x<<":"<<x<<endl #define max(a,b) (((a)>(b))?(a):(b)) #define min(a,b) (((a)<(b))?(a):(b)) #define pb push_back inline void test(){cerr<<"\n";} template<typename T,typename... Args>inline void test(T x,Args... args){cerr<<x<<" ";test(args...);}typedef long long ll; typedef pair<ll,ll> pi; const ll MAXN = (ll)1e6+7;struct Node{ll x,y,w;Node(ll x = 0,ll y = 0,ll w = 0):x(x),y(y),w(w){}bool operator < (const Node&a) const {if (x == a.x) return y < a.y;return x < a.x;} }e[MAXN];vector<ll> vpx,vpy; inline ll getX(ll x) {return lower_bound(vpx.begin(),vpx.end(),x)-vpx.begin()+1; } inline ll getY(ll y) {return lower_bound(vpy.begin(),vpy.end(),y)-vpy.begin()+1; }ll n,m;#define lson rt<<1 #define rson rt<<1|1ll val[2007<<2]; ll sum[2007<<2]; ll lsum[2007<<2]; ll rsum[2007<<2];inline void Build(ll l,ll r,ll rt) {if (l == r) {val[rt] = sum[rt] = lsum[rt] = rsum[rt] = 0;return ;}ll m = l+r>>1;Build(l,m,lson);Build(m+1,r,rson);val[rt] = sum[rt] = lsum[rt] = rsum[rt] = 0; } inline void PushUp(ll l,ll r,ll rt) {val[rt] = val[lson] + val[rson];sum[rt] = max(lsum[rson]+rsum[lson],max(sum[lson],sum[rson]));lsum[rt] = max(lsum[lson],val[lson]+lsum[rson]);rsum[rt] = max(rsum[rson],val[rson]+rsum[lson]); } inline void Update(ll L,ll C,ll l,ll r,ll rt) {if (l == r) {val[rt] += C;sum[rt] = max(0LL,val[rt]);rsum[rt] = lsum[rt] = sum[rt];return ;}b ll m = l+r>>1;if (L <= m) Update(L,C,l,m,lson);else Update(L,C,m+1,r,rson);PushUp(l,r,rt); }vector<ll> vxx[5007]; bool mark[5007];inline void init() {vpx.clear();vpy.clear(); }int main() {ll T;scanf("%lld",&T);while (T --) {ll N;init();scanf("%lld",&N);rep(i,1,N) {ll x,y,w;scanf("%lld %lld %lld",&x,&y,&w);e[i] = Node(x,y,w);vpx.pb(x);vpy.pb(y);}sort(vpx.begin(),vpx.end()); vpx.erase(unique(vpx.begin(),vpx.end()),vpx.end());sort(vpy.begin(),vpy.end()); vpy.erase(unique(vpy.begin(),vpy.end()),vpy.end());n = vpx.size();m = vpy.size();rep(i,0,n+3) vxx[i].clear();rep(i,1,N) {e[i].x = getX(e[i].x);e[i].y = getY(e[i].y);}sort(e+1,e+1+N);rep(i,1,N) {vxx[e[i].x].pb(i);}ll ans = 0;ll u,d;rep(i,1,N) {Build(1,m,1);memset(mark,0,sizeof(bool)*(n+2));rep(j,i,N) {if (mark[e[j].x] == 0) {mark[e[j].x] = 1;ll now = e[j].x;rep(kk,0,vxx[now].size()-1) {ll id = vxx[now][kk];Update(e[id].y,e[id].w,1,m,1);}}ans = max(ans,sum[1]);}}printf("%lld\n",ans);} } //代碼二 維護前綴和 #include <bits/stdc++.h> using namespace std; #define rep(i,j,k) for(ll i = (ll)j;i <= (ll)k;i ++) #define debug(x) cerr<<#x<<":"<<x<<endl#define pb push_back void test(){cerr<<"\n";} template<typename T,typename... Args>void test(T x,Args... args){cerr<<x<<" ";test(args...);}typedef long long ll; typedef pair<ll,ll> pi; const ll MAXN = (ll)1e6+7;struct Node{ll x,y,w;Node(ll x = 0,ll y = 0,ll w = 0):x(x),y(y),w(w){}bool operator < (const Node&a) const {if (x == a.x) return y < a.y;return x < a.x;} }e[MAXN];vector<ll> vpx,vpy; inline ll getX(ll x) {return lower_bound(vpx.begin(),vpx.end(),x)-vpx.begin()+1; } inline ll getY(ll y) {return lower_bound(vpy.begin(),vpy.end(),y)-vpy.begin()+1; }ll n,m;inline void cal(ll i,ll j,ll& u,ll& d) {u = e[i].y ,d = e[j].y;if (u > d) swap(u,d); }#define lson rt<<1 #define rson rt<<1|1ll mn[5007<<2]; ll mx[5007<<2]; ll add[5007<<2];inline void PushUp(ll rt){mx[rt] = max(mx[lson] , mx[rson]);mn[rt] = min(mn[lson] , mn[rson]); }inline void Build(ll l,ll r,ll rt){if (l == r){mx[rt] = 0;mn[rt] = 0;add[rt] = 0;return ;}ll m = (l+r)>>1;Build(l,m,lson);Build(m+1,r,rson);mx[rt] = 0;mn[rt] = 0;add[rt] = 0; }inline void PushDown(ll rt){if (add[rt]){mx[lson] += add[rt];mx[rson] += add[rt];mn[lson] += add[rt];mn[rson] += add[rt];add[lson] += add[rt];add[rson] += add[rt];add[rt] = 0;} }inline void Update(ll L,ll R,ll C,ll l,ll r,ll rt){if (L <= l && r <= R){mx[rt] += C;mn[rt] += C;add[rt] += C;return ;}ll m = (l+r)>>1;PushDown(rt);if (L <= m) Update(L,R,C,l,m,lson);if (R > m) Update(L,R,C,m+1,r,rson);PushUp(rt); }ll ansMx = 0,ansMn = 0; inline void QueryMaxz(ll L,ll R,ll l,ll r,ll rt){if (L <= l && r <= R){ansMx = max(ansMx,mx[rt]);return ;}ll m = (l+r)>>1;PushDown(rt);if (L <= m) QueryMaxz(L,R,l,m,lson);if (R > m) QueryMaxz(L,R,m+1,r,rson); } inline void QueryMin(ll L,ll R,ll l,ll r,ll rt){if (R < L) return ;if (L <= l && r <= R){ansMn = min(ansMn,mn[rt]);return;}ll m = (l+r)>>1;PushDown(rt);if (L <= m) QueryMin(L,R,l,m,lson);if (R > m) QueryMin(L,R,m+1,r,rson);return ; }vector<ll> vxx[5007]; bool mark[5007];void init() {vpx.clear();vpy.clear(); }int main() {ll T;scanf("%lld",&T);while (T --) {ll N;init();scanf("%lld",&N);rep(i,1,N) {ll x,y,w;scanf("%lld %lld %lld",&x,&y,&w);e[i] = Node(x,y,w);vpx.pb(x);vpy.pb(y);}sort(vpx.begin(),vpx.end()); vpx.erase(unique(vpx.begin(),vpx.end()),vpx.end());sort(vpy.begin(),vpy.end()); vpy.erase(unique(vpy.begin(),vpy.end()),vpy.end());n = vpx.size();m = vpy.size();rep(i,0,n+3) vxx[i].clear();rep(i,1,N) {e[i].x = getX(e[i].x);e[i].y = getY(e[i].y);}sort(e+1,e+1+N);rep(i,1,N) {vxx[e[i].x].pb(i);}ll ans = 0;ll u,d;rep(i,1,N) {Build(1,m,1);memset(mark,0,sizeof(bool)*(n+2));rep(j,i,N) {if (mark[e[j].x] == 0) {mark[e[j].x] = 1;ll now = e[j].x;rep(kk,0,vxx[now].size()-1) {ll id = vxx[now][kk];Update(e[id].y,N,e[id].w,1,m,1);}}cal(i,j,u,d);ansMx = -1e18;ansMn = 1e18;if (mx[1] - min(mn[1],0LL) <= ans) continue; //剪枝QueryMaxz(d,N,1,m,1);QueryMin(1,u-1,1,m,1);ll resMX = ansMx;ll resMN = ansMn;resMN = min(resMN,0LL);ll nowAns = resMX-resMN;ans = max(ans,nowAns);}}printf("%lld\n",ans);} }

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