武林秘籍
头文件
#include<set>
#include<cmath>
#include<cstring>
#include<map>
#include<algorithm>
#include<map>
#include<sstream>
#include<iostream>
#include<functional>
const int inf = 0x3f3f3f3f;
#define inf 0x3f3f3f3f
素数筛选
int prime[MAXNUM];
bool isPrime[MAXNUM + 1];
int sieve(int n){
int p = 0;
fill(isPrime, isPrime + n + 1, true);
isPrime[0] = isPrime[1] = false;
for(int i = 2; i <= n; i++){
if(isPrime[i]){
prime[p++] = i;
for(int j = 2*i; j <= n; j += i)
isPrime[j] = false;
}
}
return p;
}
快速幂
typedef long long ll;
ll modPow(ll x, ll n, ll mod){
ll res = 1;
while(n > 0){
if(n & 1) res = res*x%mod;
x = x*x%mod;
n >>= 1;
}
return res;
}
GCD
int GCD(int a, int b){
return b == 0 ? a : GCD(b, a % b);
}
全排列
bool visit[MAXNUM];
int perm[MAXNUM];
void permutation(int pos, int n){
if(pos == n){
return ;
}
for(int i = 0; i < n; i++){
if(visit[i] == false){
visit[i] = true;
permutation(pos + 1, n);
visit[i] = false;
}
}
}
do{
} while(next_permutation(perm, perm + n));
二分查找
int bsearch(int *A, int left, int right, int x){
int m;
while (left < right){
m = left + (right - left) / 2;
if (A[m] >= x) right = m; else left = m + 1;
}
return left;
}
并查集
int findFather(int x){
return x == father[x] ? x : findFather(x);
}
}
int merge(int v, int u){
v = findFather(v);
u = findFather(u);
if(u != v){
father[u] = v;
return 1;
}
return 0;
}
Dijkstra(单源最短路径)
#include<iostream>
#include<algorithm>
using namespace std;
const int inf = 0x3f3f3f3f;
int e[510][510], dis[510];
bool visit[510];
int n, m;
int main(){
fill(e[0], e[0] + 510*510, inf);
fill(dis, dis + 510, inf);
scanf("%d%d", &n, &m);
int a, b, c;
for(int i = 0; i < m; i++){
scanf("%d%d%d", &a, &b, &c);
e[a][b] = e[b][a] = c;
}
dis[1] = 0;
for(int i = 0; i < n; i++){
int u = -1, minn = inf;
for(int j = 1; j <= n; j++)
if(visit[j] == false && dis[j] < minn){
minn = dis[j];
u = j;
}
if(u == -1) break;
visit[u] = true;
for(int v = 1; v <= n; v++)
if(visit[v] == false && e[u][v] != inf){
if(dis[v] > dis[u] + e[u][v])
dis[v] = dis[u] + e[u][v];
}
}
for(int i = 2; i <= n; i++)
printf("%d%c", dis[i], i == n ? '\n' : ' ');
return 0;
}
SPFA(单源最短路径解决负权)
写法一
#include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
const int inf = 0x3f3f3f3f;
int dis[510], head[510];
bool visit[510];
int n, m, cnt;
struct node{
int u, v, w;
int next;
}e[510];
void add(int u, int v, int w){
e[cnt].u = u;
e[cnt].v = v;
e[cnt].w = w;
e[cnt].next = head[u];
head[u] = cnt++;
}
int main(){
fill(dis, dis + 510, inf);
fill(head, head + 510, -1);
scanf("%d%d", &n, &m);
int u, v, w;
for(int i = 0; i < m; i++){
scanf("%d%d%d", &u, &v, &w);
add(u, v, w);
}
dis[1] = 0;
visit[1] = true;
queue<int> q;
q.push(1);
while(!q.empty()){
u = q.front();
q.pop();
visit[u] = false;
for(int i = head[u]; i != -1; i = e[i].next){
v = e[i].v;
w = e[i].w;
if(dis[v] > dis[u] + w){
dis[v] = dis[u] + w;
if(visit[v] == false)
visit[v] = true, q.push(v);
}
}
}
for(int i = 2; i <= n; i++)
printf("%d%c", dis[i], i == n ? '\n' : ' ');
}
写法二
#include<iostream>
#include<map>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
const int inf = 0x3f3f3f3f;
vector<pair<int, int> > e[510];
queue<int> q;
int dis[510];
bool visit[510];
int main(){
int n, m;
fill(dis, dis + 510, inf);
scanf("%d%d", &n, &m);
int u, v, w;
for(int i = 0; i < m; i++){
scanf("%d%d%d", &u, &v, &w);
e[u].push_back(make_pair(v, w));
}
visit[1] = true;
dis[1] = 0;
q.push(1);
while(!q.empty()){
u = q.front();
q.pop();
visit[u] = false;
for(int i = 0; i < e[u].size(); i++){
v = e[u][i].first;
w = e[u][i].second;
if(dis[u] + w < dis[v]){
dis[v] = dis[u] + w;
if(visit[v] == false)
visit[v] = false, q.push(v);
}
}
}
for(int i = 2; i <= n; i++)
printf("%d%c", dis[i], i == n ? '\n' : ' ');
return 0;
}
Floyed
#include<iostream>
#include<algorithm>
using namespace std;
const int inf = 0x3f3f3f3f;
int e[510][510];
int n, m;
int main(){
fill(e[0], e[0] + 510*510, inf);
scanf("%d%d", &n, &m);
int u, v, w;
for(int i = 0; i < m; i++){
scanf("%d%d%d", &u, &v, &w);
e[u][v] = e[v][u] = w;
}
for(int k = 1; k <= n; k++)
for(int i = 1; i <= n; i++)
for(int j = 1; j <= n; j++)
if(e[i][j] > e[i][k] + e[k][j])
e[i][j] = e[i][k] + e[k][j];
for(int i = 1; i <= n; i++)
for(int j = 1; j <= n; j++)
printf("%d%c", e[i][j], j == n ? '\n' : ' ');
return 0;
}
Prim(最小生成树)
#include<iostream>
#include<algorithm>
using namespace std;
struct node{
int u, v, w;
bool friend operator < (const node &a, const node &b){
return a.w < b.w;
}
}e[510];
int n, m;
int father[510];
int findFather(int x){
return x == father[x] ? x : father[x] = findFather(father[x]);
}
int merge(int x, int y){
x = findFather(x);
y = findFather(y);
if(x != y){
father[x] = y;
return 1;
}
return 0;
}
int main(){
scanf("%d%d", &n, &m);
for(int i = 1; i <= n; i++)
father[i] = i;
for(int i = 0; i < m; i++)
scanf("%d%d%d", &e[i].u, &e[i].v, &e[i].w);
sort(e, e + m);
int sum = 0, cnt = 0;
for(int i = 0; i < m; i++){
if(merge(e[i].u, e[i].v)){
cnt++;
sum += e[i].w;
}
if(cnt == n - 1) break;
}
printf("%d\n", sum);
return 0;
}
kruskal(最小生成树)
#include<iostream>
#include<algorithm>
using namespace std;
const int inf = 0x3f3f3f3f;
int e[510][510], dis[510];
bool visit[510];
int main(){
int n ,m;
scanf("%d%d", &n, &m);
int a, b, c;
fill(dis, dis + 510, inf);
fill(e[0], e[0] + 510*510, inf);
for(int i = 0; i < m; i++){
scanf("%d%d%d", &a, &b, &c);
e[a][b] = e[b][a] = c;
}
dis[1] = 0;
int sum = 0;
for(int i = 0; i < n; i++){
int u = -1, minn = inf;
for(int j = 1; j <= n; j++){
if(visit[j] == false && dis[j] < minn){
minn = dis[j];
u = j;
}
}
if(u == -1) break;
sum += minn;
visit[u] = true;
for(int v = 1; v <= n; v++)
if(visit[v] == false && dis[v] > e[u][v]){
dis[v] = e[u][v];
}
}
printf("%d\n", sum);
return 0;
}
线段树(区间和,修改区间,区间最大最小)
#include<iostream>
#include<algorithm>
using namespace std;
struct node{
int l, r, max, sum;
int mild(){
return (l + r)>>1;
}
}T[510];
int n, m;
void up(int root){
T[root].sum = T[root<<1].sum + T[root<<1|1].sum;
T[root].max = max(T[root<<1].max, T[root<<1|1].max);
}
void build(int l, int r, int root){
T[root].l = l, T[root].r = r;
if(l == r){
int temp;
scanf("%d", &temp);
T[root].max = T[root].sum = temp;
}
int mild = T[root].mild();
build(l, mild, root<<1);
build(mild + 1, r, root<<1|1);
up(root);
}
void update(int root, int pos, int num){
if(T[root].l == T[root].r && T[root].r == pos){
T[root].max = T[root].sum = num;
return;
}
int mild = T[root].mild();
if(pos <= mild)
update(root<<1, pos, num);
else
update(root<<1|1, pos, num);
up(root);
}
int getSum(int l, int r, int root){
if(l == T[root].l && r == T[root].r)
return T[root].sum;
int mild = T[root].mild();
if(r <= mild)
return getSum(l, r, root<<1);
else if(l > mild)
return getSum(l, r, root<<1|1);
else
return getSum(l, mild, root<<1) + getSum(mild + 1, r, root<<1|1);
}
int getMax(int l, int r, int root){
if(l == T[root].l && r == T[root].r)
return T[root].max;
int mild = T[root].mild();
if(r <= mild)
return getMax(l, r, root<<1);
else if(l > mild)
return getSum(l, r, root<<1|1);
else
return max(getMax(l, mild, root<<1), getMax(mild + 1, r, root<<1|1))
}
int main(){
scanf("%d%d", &n, &m);
build(1, n, 1);
while(m--){
int x, y, p;
scanf("%d%d%d", &p, &x, &y);
if(p == 1)
update(x, 1, y);
else if(p == 2)
printf("%d\n", getSum(x,y,1));
else
printf("%d\n", getMax(x,y,1));
}
return 0;
}
主席树(区间第K大问题)
#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;
const int N = 1e5 + 7;
int root[N], a[N], cnt, x, y, k, n, m;
struct node{
int l, r, sum;
}T[40*N];
vector<int> v;
int getid(int x){
return lower_bound(v.begin(), v.end(), x) - v.begin() + 1;
}
void update(int l, int r, int &x, int y, int pos){
T[++cnt] = T[y], T[cnt].sum++, x = cnt;
if(l == r) return;
int mild = (l + r)>>1;
if(pos <= mild)
update(l, mild, T[x].l, T[y].l, pos);
else
update(mild + 1, r, T[x].r, T[y].r, pos);
}
int query(int l, int r, int x, int y, int k){
if(l == r)
return l;
int sum = T[T[y].l].sum - T[T[x].l].sum;
int mild = (l + r)>>1;
if(k <= sum)
return query(l, mild, T[x].l, T[y].l, k);
else
return query(mild + 1, r, T[x].r, T[y].r, k - sum)
}
int main(){
scanf("%d%d", &n, &m);
for(int i = 1; i <= n; i++)
scanf("%d", &a[i]), v.push_back(a[i]);
sort(v.begin(), v.end()), v.erase(unique(v.begin(), v.end()), v.end());
for(int i = 1; i <= n; i++)
update(1, n, root[i], root[i - 1], getid(a[i]));
for(int i = 0; i < m; i++){
scanf("%d%d%d", &x, &y, &k);
printf("%d\n", v[query(1, n, root[x - 1], root[y], k) - 1]);
}
return 0;
}
树状数组(区间第K大问题)
#include<iostream>
#include<vector>
#include<algorithm>
#include<cstring>
#include<queue>
using namespace std;
const int N =
1e5 +
10;
#define lowbit(x) (x & -x)
int c[N], a[N];
char str[N][
10];
vector<
int> v;
int n, m;
int getid(int x){
return lower_bound(v.begin(), v.end(), x) - v.begin() +
1;
}
void update(int x, int val){
for(
int i = x; i <= n; i += lowbit(i))
c[i] += val;
}
int getsum(int x){
int sum =
0;
for(
int i = x; i >=
1; i -= lowbit(i))
sum += c[i];
return sum;
}
int solve(int x){
int left =
1, right = n, mid;
int k = x /
2 +
1;
while(left < right) {
mid = (left + right) /
2;
if(getsum(mid) >= k)
right = mid;
else
left = mid +
1;
}
return left;
}
int main(){
int T =
1, x;
while(~
scanf(
"%d", &m)){
queue<
int> q;
memset(c,
0,
sizeof(c)), v.clear();
for(
int i =
1; i <= m; ++i){
scanf(
"%s", str[i]);
if(str[i][
0] ==
'i'){
scanf(
"%d", &a[i]);
v.push_back(a[i]);
}
}
sort(v.begin(), v.end()), v.erase(unique(v.begin(), v.end()), v.end());
n = v.size();
printf(
"Case #%d:\n",T++);
for(
int i =
1; i <= m; ++i){
if(str[i][
0] ==
'i'){
x = getid(a[i]);
update(x,
1);
q.push(x);
}
else if(str[i][
0] ==
'o'){
x = q.front();
update(x, -
1);
q.pop();
}
else{
printf(
"%d\n", v[solve(q.size()) -
1]);
}
}
}
return 0;
}
树状数组(区间和)
#include<iostream>
using namespace std;
int tree[510];
int n;
int lowbit(int x){
return x & (-x);
}
void update(int x, int num){
while(x <= n){
tree[x] += num;
x = lowbit(x);
}
}
int getSum(int x){
int sum = 0;
while(x > 0){
sum += tree[x];
x -= lowbit(x);
}
return sum;
}
int main(){
scanf("%d", &n);
int temp;
for(int i = 1; i <= n; i++){
scanf("%d", &temp);
update(i, temp);
}
return 0;
}
凸包
#include<iostream>
#include<algorithm>
#include<cmath>
#include<vector>
#define N 105
using namespace std;
struct node{
int x, y;
bool friend operator < (const node &a, const node &b){
if(a.y == b.y)
return a.x < b.x;
return a.y < b.y;
}
}point[N];
double calcurateDis(node a, node b){
return sqrt((a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y));
}
bool judge(node a, node b, node c){
return (a.x - c.x)*(b.y - c.y) >= (b.x - c.x)*(a.y - c.y);
}
double solve(int n){
vector<node> tempPoint(n*2);
sort(point, point + n);
if(n == 1){
return 0;
}
if(n == 2){
return calcurateDis(point[0], point[1]);
}
tempPoint[0] = point[0];
tempPoint[1] = point[1];
tempPoint[2] = point[2];
int top = 1;
for(int i = 2; i < n; i++){
while(top != 0 && judge(point[i], tempPoint[top], tempPoint[top - 1])) top--;
tempPoint[++top] = point[i];
}
int len = top;
tempPoint[++top] = point[n - 2];
for(int i = n - 3; i >= 0; i--){
while(top != len && judge(point[i], tempPoint[top], tempPoint[top - 1])) top--;
tempPoint[++top] = point[i];
}
double result = 0.0;
for(int i = 0; i < top; i++){
result += calcurateDis(tempPoint[i], tempPoint[i + 1]);
}
return result;
}
int main(){
int n;
while(~scanf("%d", &n), n){
for(int i = 0; i < n; i++)
scanf("%d %d", &point[i].x, &point[i].y);
printf("%.2lf\n", solve(n));
}
return 0;
}
二分图(最佳完备匹配)
#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
const int inf = 0x3f3f3f3f;
const int N = 105;
int e[N][N], line[N], cx[N], cy[N];
bool usex[N], usey[N];
int n, m;
int find(int x){
usex[x] = true;
for(int i = 1; i <= m; i++)
if(usey[i] == false && cx[x] + cy[i] == e[u][i]){
usey[i] = true;
if(line[i] == 0 || find(line[i])){
line[i] = x;
return 1;
}
}
return 0;
}
int KM(){
for(int i = 1; i <= n; i++){
while(true){
memset(usex, 0, sizeof(usex));
memset(usey, 0, sizeof(usey));
if(find(i)) break;
int d = inf;
for(int j = 1; j <= n; j++){
if(usex[j])
for(int k = 1; k <= m; k++){
if(usey[k] == false)
d = min(d, cx[j] + cy[k] - e[j][k]);
}
}
if(d == inf) return -1;
for(int j = 1; j <= n; j++)
if(usex[j]) cx[j] -= d;
for(int j = 1; j <= m; j++)
if(usey[j]) cy[j] += d;
}
}
int sum = 0;
for(int i = 1; i <= m; i++)
sum += e[line[i]][i];
return sum;
}
int main(){
while(~scanf("%d%d", &n, &m)){
memset(cy, 0, sizeof(cy));
memset(e, 0, sizeof(e));
memset(cx, 0, sizeof(cx));
for(int i = 1; i <= n; i++){
int d = 0;
for(int j = 1; j <= n; j++){
scanf("%d", &e[i][j]);
d = max(d, e[i][j]);
}
cx[i] = d;
}
memset(line, 0, sizeof);
peintf("%d\n", KM());
}
return 0;
}
最大流Dinic
#include <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <algorithm>
#include <map>
#include <queue>
#include <vector>
using namespace std;
const int N =
1100;
const int INF =
0x3f3f3f3f;
struct Node
{
int to;
int cap;
int rev;
};
vector<Node> v[N];
int level[N];
int iter[N];
void add_Node(int from,int to,int cap)
{
v[from].push_back((Node){to,cap,v[to].size()});
v[to].push_back((Node){from,
0,v[from].size()-
1});
}
void bfs(int s){
memset(level, -
1,
sizeof(level));
queue<
int> que;
level[s] =
0;
que.push(s);
while(!que.empty()){
int t = que.front();
que.pop();
for(
int i =
0; i < v[t].size(); i++){
Node &e = v[t][i];
if(e.cap >
0 && level[e.to] <
0){
level[e.to] = level[t] +
1;
que.push(e.to);
}
}
}
}
int dfs(int s, int t, int f)
{
if(s==t)
return f;
for(
int &i= iter[s]; i<v[s].size() ; i++)
{
Node &e = v[s][i];
if(level[s] < level[e.to] && e.cap>
0)
{
int d=dfs(e.to, t, min(f,e.cap));
if(d>
0)
{
e.cap -= d;
v[e.to][e.rev].cap += d;
return d;
}
}
}
return 0;
}
int max_flow(int s, int t)
{
int flow=
0;
for(;;){
bfs(s);
if(level[t] <
0)
return flow;
memset(iter,
0,
sizeof(iter));
int f;
while((f = dfs(s, t, INF)) >
0)
flow+=f;
}
}
int main()
{
int n,m;
while(~
scanf(
"%d%d",&n,&m))
{
memset(v,
0,
sizeof(v));
for(
int i=
0;i<n;i++)
{
int x,y,z;
scanf(
"%d%d%d",&x,&y,&z);
add_Node(x,y,z);
}
printf(
"%d\n",max_flow(
1,m));
}
}
最小费用
#include<iostream>
#include<cstring>
#include<cstdio>
#include<vector>
#include<queue>
#include<algorithm>
using namespace std;
const int INF =
0x3f3f3f3f;
const int N =
100;
typedef pair<
int,
int> P;
struct node{
int to;
int cap;
int cost;
int rev;
};
vector<node> G[N];
int dis[N];
int prevv[N];
int preve[N];
int addNOde(int from, int to, int cap, int cost){
G[from].push_back((node){to, cap, cost, G[to].size()});
G[to].push_back((node){from,
0, - cost, G[from].size() -
1});
}
int V;
int min_cost_flow(int s, int t, int f){
int ret =
0;
while(f >
0){
fill(dis, dis + N, INF);
dis[s] =
0;
bool update =
true;
while(update){
update =
false;
for(
int i =
0; i < V; ++i){
if(dis[i] == INF)
continue;
for(
int j =
0; j < G[i].size(); ++j){
node &e = G[i][j];
if(e.cap >
0 && dis[e.to] > dis[i] + e.cost){
dis[e.to] = dis[i] + e.cost;
prevv[e.to] = i;
preve[e.to] = j;
}
}
}
}
if(dis[t] == INF)
return -
1;
int d = f;
for(
int v = t; v != s; v = prevv[v]) d = min(d, G[prevv[v]][preve[v]].cap);
ret += d * dis[t];
f -= d;
for(
int v = t; v != s; v = prevv[v]){
node &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[e.to][e.rev] += d;
}
}
return ret;
}
int min_cost_flow(int s, int t, int f){
int ret =
0;
memset(h,
0,
sizeof(h));
while(f >
0){
priority_queue<P,
vector<P>, greater<P> > q;
fill(dis, dis + N, INF);
dis[s] =
0;
q.push(P(
0, s));
while(!q.empty()){
P p = q.top(); q.pop();
int v = p.second;
if(dis[v] < p.second)
continue;
for(
int i =
0; i < G[v].size(); ++i){
node &e = G[v][i];
if(e.cap >
0 && dis[e.to] > dis[v] + e.cost + h[v] - h[e.to]){
dis[e.to] = dis[v] + e.cost + h[v] - h[e.to];
prevv[e.to] = v;
preve[e.to] = i;
q.push(P(dis[e.to], e.to));
}
}
}
if(dis[t] == INF)
return -
1;
for(
int v =
0; v < V; ++v) h[v] += dis[v];
int d = f;
for(
int v = t; v != s; v = prevv[v]) d = min(d, G[prevv[v]][preve[v]].cap);
ret += h[t] * d;
f -= d;
for(
int v = t; v != s; v = prevv[v]){
node &e = G[prevv[v]][preve[v]];
e.cap -= d;
G[e.to][e.rev] += d;
}
}
return ret;
}