线段树专题
线段树：旨在自己看，题目来源与报告来自http://www.notonlysuccess.com/index.php/segment-tree-complete/是某位大牛写的，很犀利。。。
（1）：单点更新
HDU 1166敌兵布阵 http://acm.hdu.edu.cn/showproblem.php?pid=116
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 50005 int seg_tree[MAXN<<2]; void build_tree(int l,int r,int id); int query_tree(int left,int right,int l,int r,int id); void update_point_tree(int left,int right,int value,int l,int r,int id); void push_up_tree(int id); int main() { int tcase,n,i,left,right,value; char str[20]; while(scanf("%d",&tcase)==1) { for(i=1;i<=tcase;i++) { printf("Case %d:\n",i); scanf("%d",&n); build_tree(1,n,1); while(scanf("%s",str)!=EOF) { if(!strcmp(str,"Query")) { scanf("%d%d",&left,&right); printf("%d\n",query_tree(left,right,1,n,1)); } if(!strcmp(str,"Add")) { scanf("%d%d",&left,&value); update_point_tree(left,left,value,1,n,1); } if(!strcmp(str,"Sub")) { scanf("%d%d",&left,&value); update_point_tree(left,left,-value,1,n,1); } if(!strcmp(str,"End")) break; } } } } void build_tree(int l,int r,int id) { if(l==r) { scanf("%d",&seg_tree[id]); return ; } int mid=(l+r)/2; build_tree(l,mid,id<<1); build_tree(mid+1,r,id<<1|1); push_up_tree(id); } int query_tree(int left,int right,int l,int r,int id) { if(left<=l&&right>=r) return seg_tree[id]; int mid=(l+r)>>1,ret=0; if(left<=mid) ret+=query_tree(left,right,l,mid,id<<1); if(right>mid) ret+=query_tree(left,right,mid+1,r,id<<1|1); return ret; } void update_point_tree(int left,int right,int value,int l,int r,int id) { if(l==r) { seg_tree[id]+=value; return ;} int mid=(l+r)>>1; if(left<=mid) update_point_tree(left,right,value,l,mid,id<<1); else update_point_tree(left,right,value,mid+1,r,id<<1|1); push_up_tree(id); } void push_up_tree(int id) { seg_tree[id]=seg_tree[id<<1]+seg_tree[id<<1|1]; }
HDU 1754 I Hate it http://acm.hdu.edu.cn/showproblem.php?pid=1754
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 200005 int seg_tree[MAXN<<2]; void build_tree(int l,int r,int id); int query_tree(int left,int right,int l,int r,int id); void update_point_tree(int left,int right,int value,int l,int r,int id); void push_up_tree(int id); int main() { int tcase,n,i,left,right,value,m; char str[20]; while(scanf("%d%d",&n,&m)==2) { build_tree(1,n,1); while(m--) { scanf("%s",str); if(str[0]=='Q') { scanf("%d%d",&left,&right); printf("%d\n",query_tree(left,right,1,n,1)); } if(str[0]=='U') { scanf("%d%d",&left,&value); update_point_tree(left,right,value,1,n,1); } } } } void build_tree(int l,int r,int id) { if(l==r) { scanf("%d",&seg_tree[id]); return ; } int mid=(l+r)/2; build_tree(l,mid,id<<1); build_tree(mid+1,r,id<<1|1); push_up_tree(id); } int query_tree(int left,int right,int l,int r,int id) { if(left<=l&&right>=r) return seg_tree[id]; int mid=(l+r)>>1,ret0=0,ret1=0; if(left<=mid) ret0=query_tree(left,right,l,mid,id<<1); if(right>mid) ret1=query_tree(left,right,mid+1,r,id<<1|1); return ret0>=ret1?ret0:ret1; } void update_point_tree(int left,int right,int value,int l,int r,int id) { if(l==r) { seg_tree[id]=value; return ;} int mid=(l+r)>>1; if(left<=mid) update_point_tree(left,right,value,l,mid,id<<1); else update_point_tree(left,right,value,mid+1,r,id<<1|1); push_up_tree(id); } void push_up_tree(int id) { int temp1,temp2; temp1=seg_tree[id<<1]; temp2=seg_tree[id<<1|1]; seg_tree[id]=(temp1>=temp2?temp1:temp2); }
hdu Minimum Inversion Number http://acm.hdu.edu.cn/showproblem.php?pid=1394
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#include<cstdio> #include<cstdlib> #include<cstdlib> #include<cstring> #define MAXN 5010 int seg_tree[MAXN<<2]; void build_tree(int l,int r,int id); int query_tree(int left,int right,int l,int r,int id); void update_tree(int left,int right,int l,int r,int id); void push_up_tree(int id); int x[MAXN]; int main() { int n,i,j,k,sum; while(scanf("%d",&n)==1) { sum=0; build_tree(0,n-1,1); for(i=0;i<n;i++) { scanf("%d",x+i); } for(i=n-1;i>=0;i--) { sum+=query_tree(0,x[i],0,n-1,1); update_tree(x[i],x[i],0,n-1,1); } int ret=sum; for(i=0;i<n;i++) { sum+=n-1-x[i]-x[i]; if(ret>sum) ret=sum; } printf("%d\n",ret); } } void build_tree(int l,int r,int id) { if(l==r) {seg_tree[id]=0; return ; } int m=(l+r)>>1; build_tree(l,m,id<<1); build_tree(m+1,r,id<<1|1); push_up_tree(id); } int query_tree(int left,int right,int l,int r,int id) { if(left<=l&&right>=r) return seg_tree[id]; int m=(l+r)>>1,ret=0; if(left<=m) ret+=query_tree(left,right,l,m,id<<1); if(right>m) ret+=query_tree(left,right,m+1,r,id<<1|1); return ret; } void update_tree(int left,int right,int l,int r,int id) { if(l==r) {seg_tree[id]++; return ; } int m=(l+r)>>1; if(left<=m) update_tree(left,right,l,m,id<<1); else update_tree(left,right,m+1,r,id<<1|1); push_up_tree(id); } void push_up_tree(int id) { seg_tree[id]=seg_tree[id<<1]+seg_tree[id<<1|1]; }
HDU Billboard http://acm.hdu.edu.cn/showproblem.php?pid=2795
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 200002 void build_tree(int l,int r,int id); void push_up_tree(int id); void update_tree(int value,int *x,int l,int r,int id); int m_max(int a,int b); int seg_tree[MAXN<<2]; int h,w,n; int main() { int temp,value,x; while(scanf("%d%d%d",&h,&w,&n)==3) { h=(h>=n?n:h); build_tree(1,h,1); while(n--) { scanf("%d",&value); if(value>seg_tree[1]) { printf("-1\n"); } else { update_tree(value,&x,1,h,1); printf("%d\n",x); } } } } void build_tree(int l,int r,int id) { if(l==r) { seg_tree[id]=w; return ; } int m=(l+r)>>1; build_tree(l,m,id<<1); build_tree(m+1,r,id<<1|1); push_up_tree(id); } void push_up_tree(int id) { seg_tree[id]=m_max(seg_tree[id<<1],seg_tree[id<<1|1]); } int m_max(int a,int b) { return a>=b?a:b; } void update_tree(int value,int *x,int l,int r,int id) { if(l==r) { *x=l; seg_tree[id]-=value; return ; } int m=(l+r)>>1; if(seg_tree[id<<1]>=value) update_tree(value,x,l,m,id<<1); else update_tree(value,x,m+1,r,id<<1|1); push_up_tree(id); }
poj Buy Tickets http://poj.org/problem?id=2828
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 200005 int seg_tree[MAXN<<2]; void build_tree(int l,int r,int id); void push_up_tree(int id); void update_tree(int left,int right,int l,int r,int id); int ans[MAXN],cur; struct Node { int i; int num; }; Node temp[MAXN]; int main() { int n,i,j,k; while(scanf("%d",&n)==1) { build_tree(1,n,1); for(i=1;i<=n;i++) {scanf("%d%d",&temp[i].i,&temp[i].num);} for(i=n;i>0;i--) { cur=temp[i].num; update_tree(temp[i].i+1,n,1,n,1); } for(i=1;i<=n;i++) {if(i-1) printf(" "); printf("%d",ans[i]); } printf("\n"); } } void build_tree(int l,int r,int id) { if(l==r) { seg_tree[id]=1; return ; } int m=(l+r)>>1; build_tree(l,m,id<<1); build_tree(m+1,r,id<<1|1); push_up_tree(id); } void push_up_tree(int id) { seg_tree[id]=seg_tree[id<<1]+seg_tree[id<<1|1]; } void update_tree(int left,int right,int l,int r,int id) { if(l==r) { seg_tree[id]--; ans[l]=cur; return ; } int m=(l+r)>>1; if(left<=seg_tree[id<<1]) update_tree(left,right,l,m,id<<1); else { left-=seg_tree[id<<1]; update_tree(left,right,m+1,r,id<<1|1); } push_up_tree(id); }
poj Who Gets the Most Candies? http://poj.org/problem?id=2886
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#include<cstdio> #include<cstdlib> #include<cmath> #include<memory.h> int seg_tree[500010<<2]; void build_tree(int l,int r,int id); void push_tree_up(int id); void update_tree(int value,int l,int r,int id); int f[500010]; void get_f(); int num[500010],h; char str[500010][10]; int cur_n,cur_i,next_i,ans,ans1; int main() { int n,k,i,j,cur,temp; //freopen("d:\\2.txt","r",stdin); //freopen("d:\\3.txt","w",stdout); memset(f,0,sizeof(f)); get_f(); while(scanf("%d%d%*c",&n,&k)!=EOF) { for(i=1;i<=n;i++) scanf("%s%d",str[i],num+i); cur_n=n; cur_i=n; next_i=k; build_tree(1,n,1); ans=0; ans1=1; h=1; for(i=1;i<=n;i++) { // printf("cur_i=%d next_i=%d",cur_i,next_i); if(next_i>=0) cur_i--; cur=(cur_i+next_i%cur_n+cur_n)%cur_n; // printf(" cur=%d\n",cur); update_tree(cur+1,1,n,1); cur_i=cur; h++; } printf("%s %d\n",str[ans1],ans); } } void build_tree(int l,int r,int id) { if(l==r) { seg_tree[id]=1; return ; } int mid=(l+r)>>1; build_tree(l,mid,id<<1); build_tree(mid+1,r,id<<1|1); push_tree_up(id); } void push_tree_up(int id) { seg_tree[id]=seg_tree[id<<1]+seg_tree[id<<1|1]; } void update_tree(int value,int l,int r,int id) { if(l==r) { seg_tree[id]--; // printf("tree[id]=%d",seg_tree[id]); // printf("l=%d\n",l); next_i=num[l]; cur_n--; if(ans<f[h]) { ans=f[h]; ans1=l; } return ; } int mid=l+r>>1; if(value<=seg_tree[id<<1]) { update_tree(value,l,mid,id<<1); } else { update_tree(value-seg_tree[id<<1],mid+1,r,id<<1|1); } push_tree_up(id); } void get_f() { int i,j; for(i=1;i<=500000;i++) for(j=1;i*j<=500000;j++) { f[i*j]++; } }
（2）：成段更新：
1：hdu 1698 just a hook http://acm.hdu.edu.cn/showproblem.php?pid=1698
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 200010 int color[MAXN<<2]; int tree[MAXN<<2]; void build_tree(int l,int r,int id); void up_date_tree(int left,int right,int l,int r,int id,int value); void push_down(int l,int r,int id); void push_up_tree(int id); int main() { int tcase,i,j,k,n,value,left,right,num; while(scanf("%d",&tcase)==1) { for(j=1;j<=tcase;j++) { scanf("%d",&n); build_tree(1,n,1); scanf("%d",&num); for(i=0;i<num;i++) { scanf("%d%d%d",&left,&right,&value); up_date_tree(left,right,1,n,1,value); } printf("Case %d: The total value of the hook is %d.\n",j,tree[1]); } } } void build_tree(int l,int r,int id) { color[id]=0; if(l==r) { tree[id]=1; return ; } tree[id]=r-l+1; int mid=l+r>>1; build_tree(l,mid,id<<1); build_tree(mid+1,r,id<<1|1); } void up_date_tree(int left,int right,int l,int r,int id,int value) { if(left<=l&&right>=r) { tree[id]=(r-l+1)*value; color[id]=value; return ; } push_down(l,r,id); int mid=l+r>>1; if(left<=mid) up_date_tree(left,right,l,mid,id<<1,value); if(right>mid) up_date_tree(left,right,mid+1,r,id<<1|1,value); push_up_tree(id); } void push_down(int l,int r,int id) { if(color[id]) { color[id<<1]=color[id]; color[id<<1|1]=color[id]; int mid=l+r>>1; tree[id<<1]=(mid-l+1)*color[id]; tree[id<<1|1]=(r-mid)*color[id]; } color[id]=0; } void push_up_tree(int id) { tree[id]=tree[id<<1]+tree[id<<1|1]; }
(3): poj 3468 A Simple Problem with Integers http://poj.org/problem?id=3468
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 100010 __int64 color[MAXN<<2]; __int64 tree[MAXN<<2]; int n,num; void build_tree(int l,int r,int id); void push_up_tree(int id); __int64 query_tree(int left,int right,int l,int r,int id); void update_tree(int left,int right,int l,int r,int id,__int64 value); void push_down(int l,int r,int id); int main() { int i,left,right; __int64 value; char str[10]; while(scanf("%d%d",&n,&num)==2) { build_tree(1,n,1); //printf("%I64d\n",tree[4]); for(i=1;i<=num;i++) { scanf("%s",str); if(str[0]=='Q') { scanf("%d%d",&left,&right); // printf("%s %d %d\n",str,left,right); printf("%I64d\n",query_tree(left,right,1,n,1)); } if(str[0]=='C') { scanf("%d%d%I64d",&left,&right,&value); update_tree(left,right,1,n,1,value); } } } } void build_tree(int l,int r,int id) { color[id]=0; if(l==r) { scanf("%I64d",&tree[id]); return ; } int mid=l+r>>1; build_tree(l,mid,id<<1); build_tree(mid+1,r,id<<1|1); push_up_tree(id); } void push_up_tree(int id) { tree[id]=tree[id<<1]+tree[id<<1|1]; } __int64 query_tree(int left,int right,int l,int r,int id) { if(left<=l&&right>=r) return tree[id]; push_down(l,r,id); int mid=l+r>>1;__int64 ret0=0; if(left<=mid) ret0+=query_tree(left,right,l,mid,id<<1); if(right>mid) ret0+=query_tree(left,right,mid+1,r,id<<1|1); return ret0; } void push_down(int l,int r,int id) { if(color[id]) { int mid=l+r>>1; color[id<<1]+=color[id]; color[id<<1|1]+=color[id]; tree[id<<1]+=(mid-l+1)*color[id]; tree[id<<1|1]+=(r-mid)*color[id]; color[id]=0; } } void update_tree(int left,int right,int l,int r,int id, __int64 value) { if(left<=l&&right>=r) { color[id]+=value; tree[id]+=(r-l+1)*value; return ; } push_down(l,r,id); int mid=l+r>>1; if(left<=mid) { update_tree(left,right,l,mid,id<<1,value); } if(right>mid) update_tree(left,right,mid+1,r,id<<1|1,value); push_up_tree(id); }
（4）：poj 3255 Help with Intervals http://poj.org/problem?id=3225
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 131072 int c_cover[MAXN<<2],c_xor[MAXN<<2]; bool hash[MAXN+10]; void update(char op,int left,int right,int l,int r,int id); void f_xor(int id); void push_down(int id); void push_down(int id); void query(int l,int r,int id); int main() { char op,c_left,c_right; int i,left,right; c_xor[1]=0; c_cover[1]=0; while(~scanf("%c %c%d,%d%c\n",&op,&c_left,&left,&right,&c_right)) { left<<=1; right<<=1; if(c_left=='(') left++; if(c_right==')') right--; if(left>right) { if(op=='C'||op=='I') c_cover[1]=c_xor[1]=0; } else update(op,left,right,0,MAXN,1); } query(0,MAXN,1); int a=-1,b; bool flag=false; for(i=0;i<=MAXN;i++) { if(hash[i]) { b=i; if(a==-1)a=i; } else if(a!=-1) { if(flag) printf(" "); printf("%c%d,%d%c",a&1?'(':'[',a>>1,(b+1)>>1,b&1?')':']'); flag=true; a=-1; } } if(!flag) printf("empty set"); puts(""); } void update(char op,int left,int right,int l,int r,int id) { if(left<=l&&right>=r) { if(op=='U') { c_cover[id]=1; c_xor[id]=0; } else if(op=='D') { c_cover[id]=0; c_xor[id]=0; } else if(op=='S'||op=='C') { f_xor(id); } return ; } push_down(id); int mid=(l+r)>>1; if(left<=mid) update(op,left,right,l,mid,id<<1); else if(op=='I'||op=='C') { c_cover[id<<1]=0; c_xor[id<<1]=0; } if(right>mid) { update(op,left,right,mid+1,r,id<<1|1); } else if(op=='I'||op=='C') { c_cover[id<<1|1]=0; c_xor[id<<1|1]=0; } } void f_xor(int id) { if(c_cover[id]!=-1) c_cover[id]^=1; else c_xor[id]^=1; } void push_down(int id) { if(c_cover[id]!=-1) { c_cover[id<<1]=c_cover[id<<1|1]=c_cover[id]; c_xor[id<<1]=c_xor[id<<1|1]=0; c_cover[id]=-1; } if(c_xor[id]) { f_xor(id<<1); f_xor(id<<1|1); c_xor[id]=0; } } void query(int l,int r,int id) { if(c_cover[id]==1) { int i; for(i=l;i<=r;i++) { hash[i]=1; } return ; } else if(c_cover[id]==0) return ; if(l==r) return ; push_down(id); int mid=(l+r)>>1; query(l,mid,id<<1); query(mid+1,r,id<<1|1); }
（5）：poj 3667 Hotel http://poj.org/problem?id=3667
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#include<cstdio> #include<cstdlib> #include<cmath> #include<cstring> #define MAXN 55555 int lmax[MAXN<<2],rmax[MAXN<<2],mmax[MAXN<<2],cover[MAXN<<2]; void build(int l,int r,int id); void update(int left,int right,int l,int r,int id,int value); int query(int value,int l,int r,int id); void pushdown(int id,int l,int r); void pushup(int id,int l,int r); int max(int a,int b); int main() { int n,m,op,value,left,right,i; while(scanf("%d%d",&n,&m)==2) { build(1,n,1); while(m--) { scanf("%d",&op); if(op==1) { scanf("%d",&value); if(value>mmax[1]) printf("0\n"); else { left=query(value,1,n,1); printf("%d\n",left); update(left,left+value-1,1,n,1,0); } } else { scanf("%d%d",&left,&right); update(left,left+right-1,1,n,1,1); } } } } void build(int l,int r,int id) { lmax[id]=rmax[id]=mmax[id]=(r-l+1); cover[id]=-1; if(l==r) return; int mid=l+r>>1; build(l,mid,id<<1); build(mid+1,r,id<<1|1); } void update(int left,int right,int l,int r,int id,int value) { if(left<=l&&right>=r) { cover[id]=value; rmax[id]=mmax[id]=lmax[id]=(r-l+1)*value; return ; } if(l==r) return ; int mid=l+r>>1; pushdown(id,l,r); if(left<=mid) update(left,right,l,mid,id<<1,value); if(right>mid) update(left,right,mid+1,r,id<<1|1,value); pushup(id,l,r); } int query(int value,int l,int r ,int id) { if(l==r) return l; pushdown(id,l,r); int mid=l+r>>1; if(mmax[id<<1]>=value) return query(value,l,mid,id<<1); else if(rmax[id<<1]+lmax[id<<1|1]>=value) return mid-rmax[id<<1]+1; else return query(value,mid+1,r,id<<1|1); //pushup(id,l,r); } void pushdown(int id,int l,int r) { if(cover[id]!=-1) { int mid=l+r>>1; cover[id<<1]=cover[id<<1|1]=cover[id]; lmax[id<<1]=mmax[id<<1]=rmax[id<<1]=(mid-l+1)*cover[id]; lmax[id<<1|1]=rmax[id<<1|1]=mmax[id<<1|1]=(r-mid)*cover[id]; cover[id]=-1; } } void pushup(int id,int l,int r) { int mid=r+l>>1; rmax[id]=rmax[id<<1|1]+((rmax[id<<1|1]==r-mid)?rmax[id<<1]:0); lmax[id]=lmax[id<<1]+((lmax[id<<1]==mid-l+1)?lmax[id<<1|1]:0); mmax[id]=max(max(mmax[id<<1],mmax[id<<1|1]),rmax[id<<1]+lmax[id<<1|1]); } int max(int a,int b) { return a>=b?a:b; }
