016.递归枚举
今日做luogu枚举题单，发现很多题目共性很强
类似题目在leetcode上也有不少
共性
- 从一个序列中按规定选取若干元素
- “ 做选择 ” 产生了一颗选择二叉树
- 题目数据不强，暴力遍历即可找出答案
细节差异
- 选取元素的限制：数量，顺序，大小（子集，组合，排列的区别）
- 子集：不限制数量，顺序
- 组合：元素数量一定的子集
- 排列：数量最大，对顺序敏感的子集
- 根据题目情境遍历二叉树，在特定的位置进行比较，修改
注：还有原序列是否含重复元素，同一元素是否可以重选等问题
习题
以下题目框架几乎完全一样，主要关注细节差异
#include<bits/stdc++.h>
using namespace std;
namespace IO{template<typename T>void read(T&x){x=0;bool f=0;char ch=getchar();while(ch<'0'||ch>'9'){if(ch=='-')f=1;ch=getchar();}while(ch>='0'&&ch<='9'){x=(x<<3)+(x<<1)+(ch^48);ch=getchar();}if(f)x=-x;}void read(char&c){c=getchar();while(isspace(c))c=getchar();}void read(string&s){s.clear();char ch=getchar();while(isspace(ch))ch=getchar();while(!isspace(ch)&&ch!=EOF){s+=ch;ch=getchar();}}template<typename T,typename...Args>void read(T&first,Args&...rest){read(first);read(rest...);}template<typename T>void wr(T x){if(x==0){putchar('0');return;}if(x<0){putchar('-');x=-x;}char stk[20];int top=0;while(x){stk[++top]=x%10+'0';x/=10;}while(top){putchar(stk[top--]);}}void wr(const char c){putchar(c);}void wr(const string&s){for(char c:s)putchar(c);}void wr(const char*s){while(*s)putchar(*s++);}template<typename T>void wr(const T&x,char sep){wr(x);putchar(sep);}template<typename T,typename...Args>void wr(const T&first,const Args&...rest){wr(first);((putchar(' '),wr(rest)),...);}}using namespace IO;
typedef long long ll;
typedef pair<int,int> pii;
vector<vector<int>>ans;
vector<int>path;
void dfs(int x,int n,int k){
if((int)path.size()==k){
ans.push_back(path);
return;
}
for(int i=x;i<=n;i++){
path.push_back(i);
dfs(i+1,n,k);
path.pop_back();
}
}
void solve(){
int n,r;
read(n,r);
dfs(1,n,r);
for(auto x:ans){
for(int i=0;i<r;i++){
cout<<setw(3)<<x[i];
}
wr('\n');
}
}
int main(){
int T=1;
//read(T);
while(T--){
solve();
}
}
bitset<100000000>isp;//埃氏筛，预处理素数
vector<int>x(25);
int n,k,ans=0;
void init(){
for(int i=0;i<n;++i)read(x[i]);
isp.set();
isp[0]=isp[1]=0;
for(int i=2;i*i<=100000000;++i){
if(isp[i]){
for(int j=i*i;j<=100000000;j+=i)
isp[j]=0;
}
}
}
void dfs(int indx,int cnt,int sum){
if(cnt==k){
if(isp[sum])ans++;
return ;
}
for(int i=indx;i<n;i++){
dfs(i+1,cnt+1,sum+x[i]);
}
}
void solve(){
read(n,k);
init();
dfs(0,0,0);
wr(ans);
}
vector<vector<int>>ans;
vector<int>path;
void dfs(int sum,int tar){
if(path.size()==10){
if(sum==tar)ans.push_back(path);
return;
}
for(int i=1;i<=3;i++){
path.push_back(i);
dfs(sum+i,tar);
path.pop_back();
}
}
void solve(){
int n;
read(n);
if(n>30||n<10){
wr(0);
return;
}
dfs(0,n);
wr(ans.size(),'\n');
for(auto x:ans){
for(int i=0;i<10;i++)wr(x[i],i==9?'\n':' ');
}
}
void dfs(int& ans,vector<int>&a,int indx,int A,int B){
if(indx==(int)a.size()){
ans=min(ans,max(A,B));
return;
}
dfs(ans,a,indx+1,A+a[indx],B);
dfs(ans,a,indx+1,A,B+a[indx]);
}
void solve(){
vector<int>s(4);
for(int i=0;i<4;i++)read(s[i]);
int ans=0;
for(int i=0;i<4;++i){
vector<int>a(s[i]);
for(int j=0;j<s[i];++j)read(a[j]);
int t=1200;
dfs(t,a,0,0,0);
ans+=t;
}
wr(ans);
}
int n,a[10],b[10];
int ans=INT_MAX;
void dfs(int indx,int A,int B){
if(indx!=0)ans=min(ans,abs(A-B));
for(int i=indx;i<n;++i){
dfs(i+1,A*a[i],B+b[i]);
}
}
void solve(){
read(n);
for(int i=0;i<n;++i)read(a[i],b[i]);
dfs(0,1,0);
wr(ans);
}
class Solution {
vector<vector<int>>ans;
vector<int>path;
public:
vector<vector<int>> subsetsWithDup(vector<int>& nums) {
sort(nums.begin(),nums.end());
dfs(0,nums);
return ans;
}
void dfs(int indx,vector<int>nums){
ans.push_back(path);
for(int i=indx;i<(int)nums.size();++i){
if(i>indx&&nums[i]==nums[i-1])continue;
path.push_back(nums[i]);
dfs(i+1,nums);
path.pop_back();
}
}
};
class Solution {
vector<vector<int>>ans;
vector<int>path;
public:
vector<vector<int>> permuteUnique(vector<int>& nums) {
vector<bool>vis(nums.size(),0);
sort(nums.begin(),nums.end());
dfs(nums,vis);
return ans;
}
void dfs(vector<int>&nums,vector<bool>&vis){
if(path.size()==nums.size()){
ans.push_back(path);
return;
}
for(int i=0;i<(int)nums.size();++i){
if(i>0&&nums[i]==nums[i-1]&&!vis[i-1])continue;
if(!vis[i]){
vis[i]=1;
path.push_back(nums[i]);
dfs(nums,vis);
vis[i]=0;
path.pop_back();
}
}
}
};
class Solution {
vector<vector<int>>ans;
vector<int>path;
public:
vector<vector<int>> combinationSum2(vector<int>& candidates, int target) {
sort(candidates.begin(),candidates.end());
dfs(0,0,candidates,target);
return ans;
}
void dfs(int indx,int sum,vector<int>& candidates, int target){
if(sum==target){
ans.push_back(path);
return ;
}
if(sum>target)return;
for(int i=indx;i<(int)candidates.size();i++){
if(i>indx&&candidates[i]==candidates[i-1])continue;
path.push_back(candidates[i]);
dfs(i+1,sum+candidates[i],candidates,target);
path.pop_back();
}
}
};
class Solution {
vector<vector<int>>ans;
vector<int>path;
public:
vector<vector<int>> combinationSum(vector<int>& candidates, int target) {
dfs(0,0,candidates,target);
return ans;
}
void dfs(int indx,int sum,vector<int>& candidates, int target){
if(sum==target){
ans.push_back(path);
return ;
}
if(sum>target)return;
for(int i=indx;i<(int)candidates.size();i++){
path.push_back(candidates[i]);
dfs(i,sum+candidates[i],candidates,target);
path.pop_back();
}
}
};
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