数据结构总结

①并查集

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
#define e exit(0)
#define re register
const int M = 10005;
int n,m,fa[M];
inline int fd(){
    int s=1,t=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')s=-1;c=getchar();}
    while(c>='0'&&c<='9'){t=t*10+c-'0';c=getchar();}
    return s*t;
}
int find(int x){
    if(fa[x] == x) return x;
    else return fa[x] = find(fa[x]);
}
int main()
{
    freopen("P3367.in","r",stdin);
    freopen("P3367.out","w",stdout);
    n = fd(),m = fd();
    for(re int i=1;i<=n;++i)
        fa[i] = i;
    for(re int i=1;i<=m;++i){
        int c = fd(),x = fd(),y = fd();
        if(c == 1){
            int fa1 = find(x),fa2 = find(y);
            fa[fa1] = fa2;
        }
        else{
            int fa1 = find(x),fa2 = find(y);
            if(fa1 == fa2) printf("Y
");
            else printf("N
");
        }
    }
    return 0;
}

②一维树状数组.NO1.

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
#define e exit(0)
#define re register
#define LL long long
const int M = 500005;
int n,m,a[M],tree[M];
inline int fd(){
    int s=1,t=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')s=-1;c=getchar();}
    while(c>='0'&&c<='9'){t=t*10+c-'0';c=getchar();}
    return s*t;
}
int lowbit(int x){return x&(-x);}
void add(int x,int v){
    while(x<=n){
        tree[x] += v;
        x += lowbit(x);
    }
}
LL getsum(int x){
    LL sum = 0;
    while(x){
        sum += tree[x];
        x -= lowbit(x);
    }
    return sum;
}
int main()
{
    freopen("P3374.in","r",stdin);
    freopen("P3374.out","w",stdout);
    n = fd(),m = fd();
    for(re int i=1;i<=n;++i){
        a[i] = fd();
        add(i,a[i]);
    }
    while(m--){
        int c = fd(),x = fd(),y = fd();
        if(c == 1) add(x,y);
        else printf("%lld
",getsum(y)-getsum(x-1));
    }
    return 0;
}

③一维树状数组.NO2.

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
#define e exit(0)
#define re register
#define LL long long
const int M = 5e5+5;
int n,m,a[M],cf[M],tree[M];
inline int fd(){
    int s=1,t=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')s=-1;c=getchar();}
    while(c>='0'&&c<='9'){t=t*10+c-'0';c=getchar();}
    return s*t;
}
int lowbit(int x){
    return x&(-x);
}
void add(int x,int y){
    while(x<=n){
        tree[x] += y;
        x += lowbit(x);
    }
}
LL getsum(int x){
    LL s = 0;
    while(x){
        s += tree[x];
        x -= lowbit(x);
    }
    return s;
}
int main()
{
    freopen("P3368.in","r",stdin);
    freopen("P3368.out","w",stdout);
    n = fd(),m = fd();
    for(re int i=1;i<=n;++i){
        a[i] = fd();
        cf[i] = a[i] - a[i-1];
        add(i,cf[i]);
    }
    while(m--){
        int c = fd();
        if(c == 1){
            int x = fd(),y = fd(),k = fd();
            add(x,k),add(y+1,-k);
        }
        else{
            int x = fd();
            printf("%lld
",getsum(x));
        }
    }
    return 0;
}

④线段树.NO1.

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
using namespace std;
#define e exit(0)
#define re register
#define LL long long
const LL M = 1e5+5;
LL n,m,cnt,a[M];
struct shu{LL l,r,ls,rs,v,tag;}tree[M<<1];
inline LL fd(){
    LL s=1,t=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')s=-1;c=getchar();}
    while(c>='0'&&c<='9'){t=t*10+c-'0';c=getchar();}
    return s*t;
}
void build(LL l,LL r){
    LL sur = ++cnt;
    tree[sur].l = l,tree[sur].r = r;
    if(l != r){
        tree[sur].ls = cnt+1;
        build(l,(l+r)/2);
        tree[sur].rs = cnt+1;
        build((l+r)/2+1,r);
        LL lc = tree[sur].ls,rc = tree[sur].rs;
        tree[sur].v = tree[lc].v+tree[rc].v;
    }
    else tree[sur].v = a[l],tree[sur].tag = 0;
}
void pushdown(int x){
    LL ls = tree[x].ls,rs = tree[x].rs,d = tree[x].tag;
    tree[ls].v += (tree[ls].r-tree[ls].l+1)*d;
    tree[rs].v += (tree[rs].r-tree[rs].l+1)*d;
    tree[ls].tag += d,tree[rs].tag += d;
    tree[x].tag = 0;
}
void add(LL k,LL l,LL r,LL d){
    if(tree[k].l == l&&tree[k].r == r){
        tree[k].v += (tree[k].r-tree[k].l+1)*d;
        tree[k].tag += d;
        return;
    }
    if(tree[k].tag)
        pushdown(k);
    LL mid = (tree[k].l + tree[k].r)>>1;
    if(r<=mid) add(tree[k].ls,l,r,d);
    else if(mid<l) add(tree[k].rs,l,r,d);
    else add(tree[k].ls,l,mid,d),add(tree[k].rs,mid+1,r,d);
    tree[k].v = tree[tree[k].ls].v+tree[tree[k].rs].v;
}
LL ask(LL k,LL l,LL r){
    if(tree[k].l == l&&tree[k].r == r)
        return tree[k].v;
    if(tree[k].tag)
        pushdown(k);
    LL mid = (tree[k].l + tree[k].r)>>1;
    if(r<=mid) return ask(tree[k].ls,l,r);
    else if(mid<l) return ask(tree[k].rs,l,r);
    else return (ask(tree[k].ls,l,mid)+ask(tree[k].rs,mid+1,r));
}
int main()
{
    freopen("P3372.in","r",stdin);
    freopen("P3372.out","w",stdout);
    n = fd(),m = fd();
    for(re LL i=1;i<=n;++i)
        a[i] = fd();
    build(1,n);
    while(m--){
        LL c = fd();
        if(c == 1){
            LL x = fd(),y = fd(),k = fd();
            add(1,x,y,k);
        }
        else{
            LL x = fd(),y = fd();
            printf("%lld
",ask(1,x,y));
        }
    }
    return 0;
}

⑤线段树.NO2.

#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
#define e exit(0)
#define re register
#define LL long long
const int N = 1e5+5;
int n,m,cnt,M,a[N];
struct shu{LL l,r,ls,rs,v,tag1,tag2;}tree[N<<1];
inline LL fd(){
    LL s=1,t=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')s=-1;c=getchar();}
    while(c>='0'&&c<='9'){t=t*10+c-'0';c=getchar();}
    return s*t;
}
void build(LL l,LL r){
    LL sur = ++cnt;
    tree[sur].l = l,tree[sur].r = r,tree[sur].tag2 = 1;
    if(l != r){
        tree[sur].ls = cnt+1;
        build(l,(l+r)/2);
        tree[sur].rs = cnt+1;
        build((l+r)/2+1,r);
        LL ls = tree[sur].ls,rs = tree[sur].rs;
        tree[sur].v = tree[ls].v+tree[rs].v; 
    }
    else tree[sur].v = a[l];
}
void pushdown(LL x){
    if(tree[x].tag1||tree[x].tag2 != 1){
        LL ls = tree[x].ls,rs = tree[x].rs,d1 = tree[x].tag1,d2 = tree[x].tag2;
        tree[ls].v = (tree[ls].v*d2%M+(tree[ls].r-tree[ls].l+1)*d1%M)%M;
        tree[rs].v = (tree[rs].v*d2%M+(tree[rs].r-tree[rs].l+1)*d1%M)%M;
        tree[ls].tag1 = (tree[ls].tag1*d2%M+d1%M)%M;
        tree[rs].tag1 = (tree[rs].tag1*d2%M+d1%M)%M;
        tree[ls].tag2 = (tree[ls].tag2%M*d2%M)%M;
        tree[rs].tag2 = (tree[rs].tag2%M*d2%M)%M;
        tree[x].tag1 = 0,tree[x].tag2 = 1;
    }
}
void Mul(LL k,LL l,LL r,LL d){
    if(tree[k].l == l&&tree[k].r == r){
        tree[k].v = (tree[k].v%M*d%M)%M;
        tree[k].tag1 = (tree[k].tag1%M*d%M)%M;
        tree[k].tag2 = (tree[k].tag2%M*d%M)%M;
        return;
    }
    pushdown(k);
    LL mid = (tree[k].l + tree[k].r)>>1;
    if(r<=mid) Mul(tree[k].ls,l,r,d);
    else if(mid<l) Mul(tree[k].rs,l,r,d);
    else Mul(tree[k].ls,l,mid,d),Mul(tree[k].rs,mid+1,r,d);
    tree[k].v = (tree[tree[k].ls].v%M+tree[tree[k].rs].v%M)%M;
}
void add(LL k,LL l,LL r,LL d){
    if(tree[k].l == l&&tree[k].r == r){
        tree[k].v = (tree[k].v%M+(tree[k].r-tree[k].l+1)*d%M)%M;
        tree[k].tag1 = (tree[k].tag1%M+d%M)%M;
        return;
    }
    pushdown(k);
    LL mid = (tree[k].l + tree[k].r)>>1;
    if(r<=mid) add(tree[k].ls,l,r,d);
    else if(mid<l) add(tree[k].rs,l,r,d);
    else add(tree[k].ls,l,mid,d),add(tree[k].rs,mid+1,r,d);
    tree[k].v = (tree[tree[k].ls].v%M+tree[tree[k].rs].v%M)%M;
}
LL ask(LL k,LL l,LL r){
    if(tree[k].l == l&&tree[k].r == r)
        return tree[k].v%M;
    pushdown(k);
    LL mid = (tree[k].l + tree[k].r)>>1;
    if(r<=mid) return ask(tree[k].ls,l,r)%M;
    else if(mid<l) return ask(tree[k].rs,l,r)%M;
    else return (ask(tree[k].ls,l,mid)%M+ask(tree[k].rs,mid+1,r)%M)%M;
}
int main()
{
    freopen("P3373.in","r",stdin);
    freopen("P3373.out","w",stdout);
    n = fd(),m = fd(),M = fd();
    for(re LL i=1;i<=n;++i)
        a[i] = fd();
    build(1,n);
    while(m--){
        LL c = fd();
        if(c == 1){
            LL x = fd(),y = fd(),k = fd();
            Mul(1,x,y,k);
        }
        else if(c == 2){
            LL x = fd(),y = fd(),k = fd();
            add(1,x,y,k);
        }
        else{
            LL x = fd(),y = fd();
            printf("%lld
",ask(1,x,y)%M);
        }
    }
    return 0;
}