[SinGuLaRiTy] 复习模板-数据结构
【SinGuLaRiTy-1040】 Copyright (c) SinGuLaRiTy 2017. All Rights Reserved.
二维线段树 2D_Segment_Tree
//示例：单点修改，区间求和。 //注意内存限制 #include<cstdio> #include<iostream> #include<cstring> const int MAXN = 1025; #define L(x) ((x)<<1) #define R(x) ((x)<<1|1) #define M(x,y) (((x)+(y))>>1) using namespace std; int N, ans; struct Node { short l, r; int sum; } a[MAXN*4][MAXN*4]; int refer[MAXN]; void build_y(int &xid, int i, short l, short r) { a[xid][i].l = l; a[xid][i].r = r; if (l == r) return; build_y(xid, L(i), l, M(l,r)); build_y(xid, R(i), M(l,r)+1, r); } void build_x(int i, short l, short r) { a[0][i].l = l; a[0][i].r = r; build_y(i, 1, 0, N); if (l==r) { refer[l]=i; return; } build_x(L(i), l, M(l,r)); build_x(R(i), M(l,r)+1, r); } void update(int x, int y, int &dt) { int i = refer[x], j; while (i>0) { j = refer[y]; while (j>0) a[i][j].sum += dt, j >>= 1; i >>= 1; } } void sum_y(int& xid, int i, int& y1, int& y2) { if (a[xid][i].l > y2 || a[xid][i].r < y1) return; if (a[xid][i].l >= y1 && a[xid][i].r <= y2) { ans += a[xid][i].sum; return; } sum_y(xid, L(i), y1, y2); sum_y(xid, R(i), y1, y2); } void sum_x(int i, int& x1, int& y1, int& x2, int& y2) { if (a[0][i].l > x2 || a[0][i].r < x1) return; if (a[0][i].l >= x1 && a[0][i].r <= x2) { sum_y(i, 1, y1, y2); return; } sum_x(L(i), x1, y1, x2, y2); sum_x(R(i), x1, y1, x2, y2); } int main() { int op, x1, y1, x2, y2, t; scanf("%d%d", &N, &N); build_x(1, 0, N); while (scanf("%d", &op) && op!=3) { if (op == 1) { scanf("%d%d%d", &x1, &y1, &t); update(x1, y1, t); } else { scanf("%d%d%d%d", &x1, &y1, &x2, &y2); ans = 0; sum_x(1, x1, y1, x2, y2); printf("%d\n", ans); } } return 0; }
双向队列 deque
#include<iostream> #include<cstdio> #include<cstring> using namespace std; const int MAXN = 100010; struct Deque { int nxt[MAXN], prv[MAXN], stk[MAXN], tp; int val[MAXN]; int f, b, size, t; void clear() { f=b=size=0; tp=MAXN-2; for (int i=1; i<MAXN; ++i) nxt[i] = prv[i] = 0, stk[i] = i; } Deque() { clear(); } void push(bool d, int v) { if (!size) { f = b = stk[tp--]; val[f] = v; prv[f]=nxt[f]=0; } else { t = stk[tp--]; if (d) { nxt[b] = t; prv[t] = b; nxt[t] = 0; val[t] = v; b = t;} else { nxt[t] = f; prv[f] = t; prv[t] = 0; val[t] = v; f = t; } } ++size; } void pop(bool d) { --size; if (d) stk[++tp] = b, b = prv[b]; else stk[++tp] = f, f = nxt[f]; } int front() { return val[f]; } int back() { return val[b]; } } q; int main() { return 0; }
Splay平衡树 Splay_Tree
#include<iostream> #include<cstdio> #include<cstring> #define Max(a,b) ((a)>(b)?(a):(b)) #define L(x) x->ch[0] #define R(x) x->ch[1] using namespace std; const int MAXN = 100010; struct Node { int sz; Node *fa, *ch[2]; Node () { sz=0; } }nil, *NIL=&nil; struct SeqSplay //用来维护区间操作的splay { Node a[MAXN], *root; void init() { root=NIL; } inline void pushup(Node *x) { x->sz = L(x)->sz + R(x)->sz + 1;//size域一定要维护 } inline void pushdown(Node *x) { //标记下放或者左右交换 } void rotate(Node *x, int d) // 0左1右 { Node *y = x->fa; if (y==root) root = x; pushdown(y); pushdown(x); y->ch[!d] = x->ch[d]; if (x->ch[d] != NIL) x->ch[d]->fa = y; x->fa = y->fa; if (y->fa != NIL) y->fa->ch[ y->fa->ch[1]==y ] = x; x->ch[d] = y; y->fa = x; pushup(y); pushup(x); } void splay(Node*x, Node*target)//双旋至target以下 { Node *y, *z; while (x->fa != target) { y = x->fa; z = y->fa; pushdown(x); if (z == target) { rotate(x, x==y->ch[0]); return; } if (y == L(z)) if (x == L(y)) rotate(y, 1), rotate(x, 1); else rotate(x, 0), rotate(x, 1); else if (x == R(y)) rotate(y, 0), rotate(x, 0); else rotate(x, 1), rotate(x, 0); pushup(x); } } Node* build(int l, int r, Node* fa) { if (l>r) return NIL; int mid = (l+r)>>1; a[mid].ch[0] = build(l, mid-1, &a[mid]); a[mid].ch[1] = build(mid+1, r, &a[mid]); //此处根据题意具体录入节点内容 pushup(&a[mid]); return &a[mid]; } void init(int l, int r) { //伸展树的初始化，外部调用时一定要空置左右端点 root = build(l, r, NIL); } void getkth(int k, Node *&target)//将第k个元素旋转至target下面 { Node *t = root; while (1) { pushdown(t); if (k == (t->ch[0]->sz)+1) { splay(t, target); return; } if (k <= L(t)->sz) t = L(t); else k-=L(t)->sz+1, t = R(t); } } void form(int l, int r) //将区间[l,r]旋转至操作区域 { getkth(l, root); getkth(r+2, R(root)); } } tree; int main() { return 0; }
线段树
struct node { int l ,r ,sum ; }tre[MAXN<<2] ; void build(int code,int l,int r) { tre[code].l=l ,tre[code].r=r ; if(l==r)return; build(code*2,l,(l+r)/2); build(code*2+1,(l+r)/2+1,r); } void update(int code,int l,int r) { if(l<=tre[code].l&&tre[code].r<=r) { //修改 return; } //若有懒标记 pushdown(); int mid=(tre[code].l+tre[code].r)/2; if(l<=mid)update(code*2,l,r); if(mid<r)update(code*2+1,l,r); //更新 pushup(); tre[code].sum=tre[code*2].sum+tre[code*2+1].sum; } int query(int code,int l,int r) { if(l<=tre[code].l&&tre[code].r<=r) return tre[code].sum; int mid=(tre[code].l+tre[code].r)/2 ,ans=0 ; //pushdown(); if(l<=mid)ans+=query(code*2,l,r); if(mid<r)ans+=query(code*2+1,l,r); return ans; }
二维树状数组
#define LL long long int #define lowbit(a) ((a)&(-(a))) LL tre[MAXN+5][MAXN+5] ; void update(int a,int b,LL val) { val%=mod; for(;a<=n;a+=lowbit(a)) for(int j=y;j<=m;j+=lowbit(j)) { tre[i][j]+=val; if(tre[a][j]>=mod)tre[a][j]-=mod; } } LL getsum(int x,int y) { LL ans=0; for(;x>0;x-=lowbit(x)) for(int j=y;j>0;j-=lowbit(j)) { ans+=tre[x][j]; if(ans>=mod)ans-=mod; } return ans; }
树状数组
#define lowbit(a) ((a)&(-(a))) #define LL long long int LL tre[MAXN+5] ; void update(LL a,int pos) { a%=mod; while(pos<=n) { tre[pos]+=a; if(tre[pos]>=mod)tre[pos]-=mod; pos+=lowbit(pos); } } LL getsum(int pos) { LL ans=0 ; while(pos>0) { ans+=tre[pos]; if(ans>=mod)ans-=mod; pos-=lowbit(pos); } return ans; }
并查集
int getroot(int a) { if(fa[a]==a)return a; return fa[a]=getroot(fa[a]); } void Union(int a,int b) { fa[getroot(a)]=getroot(b); }
归并排序
///归并排序模板。记得和快排一块对着看。 #include<cstdio> #include<cstdlib> #include<iostream> #include<cstring> #include<cstring> #include<string> #include<cmath> #include<algorithm> #define LL long long #define inf 0x3f3f3f3f #define mod 1e9+7 const int maxn=1e5+5; using namespace std; int temp[maxn]; int num=0;///统计逆序对数的。 void Merge(int a[],int left ,int mid,int right) { int i=left,j=mid+1,n=0,length=right-left;///i开始为左半部分最左边，j为右半部分最左边。temp数组是从下标0开始存数。 while(i<=mid&&j<=right){ if(a[i]>a[j]){///左边比右边大。 temp[n++]=a[j++]; num+=mid-i+1;///从i到mid都是比a[j]大。 } else{ temp[n++]=a[i++]; } } if(i>mid){///这里说明的是左边全部填满了(因为前面的判断条件是i<=mid，那就是天右边了。 while(j<=right){ temp[n++]=a[j++]; } } else{ while(i<=mid){ temp[n++]=a[i++]; } } for(int k=0;k<=length;k++){///最后赋值到原数组必须要有的。 a[left+k]=temp[k]; } } void mergesort(int a[],int left,int right) { if(left<right){ int mid=(left+right)/2; mergesort(a,left,mid); mergesort(a,mid+1,right); Merge(a,left,mid,right); } } int main() { int number[30] = {}; mergesort(number,0,30-1);///初始化调用也要注意额。 for(int i=0;i<30;i++){ printf("%d ",number[i]); } }
堆排序
int adjust_heap(vector<int> &v, int length, int i){ int left = 2 * i; int right = 2 * i + 1; int largest = i; int temp; while(left < length || right < length){ if (left < length && v[largest] < v[left]){ largest = left; } if (right < length && v[largest] < v[right]){ largest = right; } if (i != largest){ temp = v[largest]; v[largest] = v[i]; v[i] = temp; i = largest; left = 2 * i; right = 2 * i + 1; } else{ break; } } } int build_heap(vector<int> &v, int length){ int i; int begin = length/2 - 1; //get the last parent node for (i = begin; i>=0; i--){ adjust_heap(v,length,i); } } int heap_sort(vector<int> &v){ int length = v.size(); int temp; printline("before sort:",v); build_heap(v,length); while(length > 1){ temp = v[length-1]; v[length-1] = v[0]; v[0] = temp; length--; adjust_heap(v,length,0); } printline("after sort:",v); }
线段树(update:单点增减; query:区间求和) - HDU1166 敌兵布阵
#include <cstdio> #define lson l , m , rt << 1 #define rson m + 1 , r , rt << 1 | 1 const int maxn = 55555; int sum[maxn<<2]; void PushUP(int rt) { sum[rt] = sum[rt<<1] + sum[rt<<1|1]; } void build(int l,int r,int rt) { if (l == r) { scanf("%d",&sum[rt]); return ; } int m = (l + r) >> 1; build(lson); build(rson); PushUP(rt); } void update(int p,int add,int l,int r,int rt) { if (l == r) { sum[rt] += add; return ; } int m = (l + r) >> 1; if (p <= m) update(p , add , lson); else update(p , add , rson); PushUP(rt); } int query(int L,int R,int l,int r,int rt) { if (L <= l && r <= R) { return sum[rt]; } int m = (l + r) >> 1; int ret = 0; if (L <= m) ret += query(L , R , lson); if (R > m) ret += query(L , R , rson); return ret; } int main() { int T , n; scanf("%d",&T); for (int cas = 1 ; cas <= T ; cas ++) { printf("Case %d:\n",cas); scanf("%d",&n); build(1 , n , 1); char op[10]; while (scanf("%s",op)) { if (op[0] == 'E') break; int a , b; scanf("%d%d",&a,&b); if (op[0] == 'Q') printf("%d\n",query(a , b , 1 , n , 1)); else if (op[0] == 'S') update(a , -b , 1 , n , 1); else update(a , b , 1 , n , 1); } } return 0; }
树的点分治-找出树中有多少点对,满足dis(u,k)<K
#include<iostream> #include<cstdio> #include<string> #include<cstring> #include<vector> #include<cmath> #include<queue> #include<stack> #include<map> #include<set> #include<algorithm> using namespace std; const int maxn=10010; int N,K; int ans,root,Max; struct node { int v,next,w; }edge[maxn*2]; int head[maxn],tot; int size[maxn];//树的大小 int maxv[maxn];//最大孩子节点的size int vis[maxn]; int dis[maxn]; int num; void init() { tot=0; ans=0; memset(head,-1,sizeof(head)); memset(vis,0,sizeof(vis)); } void add_edge(int u,int v,int w) { edge[tot].v=v; edge[tot].w=w; edge[tot].next=head[u]; head[u]=tot++; } //处理子树的大小 void dfssize(int u,int f) { size[u]=1; maxv[u]=0; for(int i=head[u];i!=-1;i=edge[i].next) { int v=edge[i].v; if(v==f||vis[v])continue; dfssize(v,u); size[u]+=size[v]; if(size[v]>maxv[u])maxv[u]=size[v]; } } //找重心 void dfsroot(int r,int u,int f) { if(size[r]-size[u]>maxv[u])//size[r]-size[u]是u上面部分的树的尺寸，跟u的最大孩子比，找到最大孩子的最小差值节点 maxv[u]=size[r]-size[u]; if(maxv[u]<Max)Max=maxv[u],root=u; for(int i=head[u];i!=-1;i=edge[i].next) { int v=edge[i].v; if(v==f||vis[v])continue; dfsroot(r,v,u); } } //求每个点离重心的距离 void dfsdis(int u,int d,int f) { dis[num++]=d; for(int i=head[u];i!=-1;i=edge[i].next) { int v=edge[i].v; if(v!=f&&!vis[v]) dfsdis(v,d+edge[i].w,u); } } //计算以u为根的子树中有多少点对的距离小于等于K int calc(int u,int d) { int ret=0; num=0; dfsdis(u,d,0); sort(dis,dis+num); int i=0,j=num-1; while(i<j) { while(dis[i]+dis[j]>K&&i<j)j--; ret+=j-i; i++; } return ret; } void dfs(int u) { Max=N; dfssize(u,0); dfsroot(u,u,0); ans+=calc(root,0); vis[root]=1; for(int i=head[root];i!=-1;i=edge[i].next) { int v=edge[i].v; if(!vis[v]) { ans-=calc(v,edge[i].w); dfs(v); } } } int main() { while(scanf("%d%d",&N,&K)!=EOF) { if(!N&&!K)break; int u,v,w; init(); for(int i=1;i<N;i++) { scanf("%d%d%d",&u,&v,&w); add_edge(u,v,w); add_edge(v,u,w); } dfs(1); printf("%d\n",ans); } return 0; }
Lower_bound & Upper_bound
ForwardIterator my_lower_bound(ForwardIterator beg, ForwardIterator end, T target) { ForwardIterator mid; typename iterator_traits<ForwardIterator>::difference_type count, step; count = distance(beg, end); while(count > 0) { mid = beg; step = count/2; advance(mid, step); if(*mid < target) //mid < target { beg = ++mid; count -= (step+1); //count表示当前数组中还有的元素个数 } else { count = step; } } return beg; }
template<class ForwardIterator, class T> ForwardIterator my_upper_bound(ForwardIterator beg, ForwardIterator end, T target) { ForwardIterator mid; typename iterator_traits<ForwardIterator>::difference_type count, step; count = distance(beg, end); while(count > 0) { mid = beg; step = count/2; advance(mid, step); if(target < *mid) //mid < target { count = step; } else { beg = ++mid; count -= (step+1); } } return beg; }
二分查找
//递归版本 int binarySearchRecusion(int* array,int len,int value){ if(len==0) return -1; int mid=(len-1)/2; if(array[mid]==value) return mid; if(array[mid]>value) //在右半区 binarySearchRecusion(array+mid+1,len-mid-1,value); else binarySearchRecusion(array,mid,value); //在左半区 }
//非递归版本 //有序数组递减排列 int binarySearch(int* array,int len,int value){ int mid=0; int low=0; int high=len-1; while(low<=high){ mid=(low+high)/2; if(array[mid]>value){ //在右半区 low=mid+1; continue; } else if(array[mid]<value){ //在左半区 high=mid-1; continue; }else return mid; //找到 } return -1; //查找失败 }
三分查找
double solve(double MIN,double MAX) { double Left, Right; double mid, midmid; double mid_value, midmid_value; Left = MIN; Right = MAX; while (Left +eps < Right) { mid = (Left + Right) / 2; midmid = (mid + Right) / 2; mid_value = Calc(mid); //Cal()为题意规定的计算内容 midmid_value = Calc(midmid); ///求最大值改成>= 最小值改成<= if (mid_value >= midmid_value) Right = midmid; else Left = mid; } return Left; }
Time: 2017-10-17
