动态规划

[CF] k-Tree

（考虑组合数做法？）

https://codeforces.com/group/GlRm4CeuZ9/contest/266331/problem/C

#include<bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
const int maxn = 1e5 + 5;
long long dp[maxn][3];
int main() {
int n, k, d;
scanf("%d%d%d", &n, &k, &d);
dp[0][0] = 1;
for (int i = 1; i <= n;i++) {
for (int j = 1; j <= k;j++) {
if(i>=j) {
if(j<d) {
dp[i][0] = (dp[i][0] + dp[i - j][0]) % mod;
dp[i][1] = (dp[i][1] + dp[i - j][1]) % mod;
}
else if(j>=d) {
dp[i][1] = (dp[i][1] + dp[i - j][0] + dp[i - j][1]) % mod;
}
}
}
}
cout << dp[n][1] << endl;
}


操作集锦

https://ac.nowcoder.com/acm/contest/4853/C

for (int i = 1; i <= n; i++) {
int v = s[i] - 'a';
pre[i] = pos[v];
pos[v] = i;
}
for (int i = 1; i <= k; i++) {
for (int j = 1; j <= n; j++) {
if (!pre[j])
dp[i][j] = (dp[i][j - 1] + dp[i - 1][j - 1] + (i > 1 ? 0 : 1)) % mod;

else
dp[i][j] = (dp[i][j-1]+dp[i-1][j-1]-dp[i-1][pre[j]-1]+mod) % mod;
}
}


[CF] LCIS

https://codeforces.com/group/GlRm4CeuZ9/contest/266331/problem/D

#include<bits/stdc++.h>
using namespace std;

const int maxn = 500 + 5;

int a[maxn],s[maxn];
int dp[maxn], pre[maxn];

int main() {
int n;
scanf("%d", &n);
for (int i = 1; i <= n;i++){
scanf("%d", &a[i]);
}
int m;
scanf("%d", &m);
for (int i = 1; i <= m;i++) {
scanf("%d", &s[i]);
}
//
for (int i = 1; i <= n;i++) {
int x = 0;
for (int j = 1; j <= m; j++) {
if(a[i]<s[j])
continue;
if(a[i]>s[j]) {
if(dp[j]>dp[x]){
x = j;
}
}
if(a[i] == s[j]) {
if(dp[j]<dp[x]+1) {
dp[j] = dp[x] + 1;
pre[j] = x;
}
}
}
}
//
int ans = 0;
int t = 0;

for (int i = 1; i <= m;i++) {
if(dp[i]>dp[t]){
ans = dp[i];
t = i;
}
}
printf("%d\n", ans);

vector<int> v;
while(t) {
v.push_back(s[t]);
t = pre[t];
}

int sz = v.size();
for (int i = sz - 1; i >= 0;i--) {
printf("%d", v[i]);
if(i == 0) printf("\n");
else printf(" ");
}
}


[CF] Elevator

https://codeforces.com/group/GlRm4CeuZ9/contest/266331/problem/E

#include<bits/stdc++.h>
using namespace std;
const int maxn = 2000 + 5;
const int inf = 0x3f3f3f3f;
int dp[maxn][10][10][10][10];
int x[maxn], y[maxn];
int n;
int dis(int x,int y) {
return abs(x - y);
}
int dfs(int i,int cur,int a,int b,int c) {
if(dp[i][cur][a][b][c])
return dp[i][cur][a][b][c];
int ans = inf;
if(i>n) {
if(!a&&!b&&!c)
return 0;
if(a)
ans = min(ans, dfs(i, a, 0, b, c) + dis(cur, a) + 1);
if(b)
ans = min(ans, dfs(i, b, a, 0, c) + dis(cur, b) + 1);
if(c)
ans = min(ans, dfs(i, c, a, b, 0) + dis(cur, c) + 1);
return dp[i][cur][a][b][c] = ans;
}
if(a)
ans = min(ans, dfs(i, a, 0, b, c) + dis(cur, a) + 1);
if(b)
ans = min(ans, dfs(i, b, a, 0, c) + dis(cur, b) + 1);
if(c)
ans = min(ans, dfs(i, c, a, b, 0) + dis(cur, c) + 1);
if(a&&b&&c) {
ans = min(ans, dfs(i + 1, y[i], a, b, c) + dis(cur, x[i]) + dis(x[i], y[i]) + 2);
ans = min(ans, dfs(i + 1, a, y[i], b, c) + dis(cur, x[i]) + dis(x[i], a) + 2);
ans = min(ans, dfs(i + 1, b, a, y[i], c) + dis(cur, x[i]) + dis(x[i], b) + 2);
ans = min(ans, dfs(i + 1, c, a, b, y[i]) + dis(cur, x[i]) + dis(x[i], c) + 2);
}
else {
if(!a)
ans = min(ans, dfs(i + 1, x[i], y[i], b, c) + dis(cur, x[i]) + 1);
else if(!b)
ans = min(ans, dfs(i + 1, x[i], a, y[i], c) + dis(cur, x[i]) + 1);
else if(!c)
ans = min(ans, dfs(i + 1, x[i], a, b, y[i]) + dis(cur, x[i]) + 1);
}
return dp[i][cur][a][b][c] = ans;
}
int main() {
scanf("%d", &n);
for (int i = 1;i<=n;i++)
scanf("%d%d", &x[i], &y[i]);
printf("%d\n", dfs(1, 1, 0, 0, 0));
}


[CF] 状压 Marbles

https://codeforces.com/contest/1215/problem/E

#include<bits/stdc++.h>
using namespace std;

const int inf = 0x3f3f3f3f;
const int maxn = 4e5 + 100;
int a[maxn];
int tot;

long long pre[30][30], cnt[30];
long long dp[1 << 21];

map<int, int> mp;
int main()
{
int n;
scanf("%d", &n);
for (int i = 1; i <= n;i++) {
scanf("%d", &a[i]);
if(!mp[a[i]]){
mp[a[i]] = tot++;
}
}
for (int i = 1; i <= n;i++) {
int x = mp[a[i]];
for (int j = 0; j < tot;j++) {
pre[x][j] += cnt[j];
}
cnt[x]++;
}
memset(dp, 0x3f, sizeof(dp));
dp[0] = 0;
for (int i = 1; i < (1 << tot); i++) {
for (int j = 0; j < tot;j++) {
if(i&(1<<j)) {
long long temp = 0;
for (int k = 0; k < tot;k++) {
if(j!=k&&!(i&(1<<k))) {
temp += pre[j][k];
}
}
dp[i] = min(dp[i], dp[i ^ (1 << j)] + temp);
}
}
}
printf("%lld\n", dp[(1 << tot) - 1]);
}


[CF1216F] Wi-Fi

https://codeforces.com/contest/1216/problem/F

#include<bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 100;
int a[maxn];
long long dp[maxn], tr[maxn << 2];

void update(int rt,int l,int r,int pos,long long v) {
if(l==pos&&r==pos) {
tr[rt] = v;
return;
}
int mid = (l + r) >> 1;
if(pos<=mid) {
update(rt << 1, l, mid, pos, v);
}
else {
update(rt << 1 | 1, mid + 1, r, pos, v);
}
tr[rt] = min(tr[rt << 1], tr[rt << 1 | 1]);
}

long long query(int rt,int l,int r,int L,int R){
if(L<=l&&r<=R) {
return tr[rt];
}
int mid = (l + r) >> 1;
long long ans = 1e18;
if(L<=mid)
ans = min(ans, query(rt << 1, l, mid, L, R));
if(R>mid)
ans = min(ans, query(rt << 1 | 1, mid + 1, r, L, R));
return ans;
}

int main() {
int n, k;
scanf("%d%d", &n, &k);
for (int i = 1; i <= n;i++) {
scanf("%1d", &a[i]);
}
memset(tr, 0x3f, sizeof(tr));
memset(dp, 0x3f, sizeof(dp));
dp[0] = 0;
update(1, 0, n, 0, 0);
for (int i = 1; i <= n;i++) {
if(a[i]==0)
dp[i] = min(dp[i], dp[i - 1] + i);
else {
int x = min(i + k, n);
int y = max(i - k - 1, 0);
dp[x] = min(dp[x], query(1, 0, n, y, n) + i);
update(1, 0, n, x, dp[x]);
}
dp[i] = min(dp[i], query(1, 0, n, i + 1, n));
update(1, 0, n, i, dp[i]);
}
printf("%lld\n", dp[n]);
}

#include<bits/stdc++.h>
using namespace std;

const int maxn = 2e5 + 100;

long long dp[maxn];
int f[maxn],a[maxn];

int main() {
int n, k;
scanf("%d%d", &n, &k);
for (int i = 1; i <= n;i++) {
scanf("%1d", &a[i]);
}
f[n + 1] = 2 * n + k;
for(int i = n;i>=1;i--) {
if(a[i]==1) {
f[i] = i;
}
else {
f[i] = f[i + 1];
}
}

for(int i=1;i<=n;i++) {
dp[i] = dp[i - 1] + i;
int t = f[max(1, i - k)];
if(t<=i+k) {
dp[i] = min(dp[i], dp[max(1, t - k) - 1] + t);
}
}
printf("%lld\n", dp[n]);
}


#include<bits/stdc++.h>
using namespace std;
const int maxn = 2e5 + 100;
int n, k;
int a[maxn];
long long dis[maxn];
int vis[maxn];
struct edge{
int to;
long long v;
};
vector<edge> G[maxn];
struct node{
int to;
long long dis;
bool operator<(const node& b)const
{
return dis>b.dis;
}
};
void dijkstra(int s) {
for (int i = 0; i <= n + 1;i++)
dis[i] = 1e18;

priority_queue<node> q;
q.push((node){s, 0});
dis[s] = 0;

while(!q.empty()) {
node t = q.top();
q.pop();
int u = t.to;
if(vis[u])
continue;
vis[u] = 1;
int sz = G[u].size();
for (int i = 0; i < sz; i++) {
int v = G[u][i].to;
long long d = G[u][i].v;
if(dis[u]+d<dis[v]) {
dis[v] = dis[u] + d;
q.push((node){v, dis[v]});
}
}
}
}
int main() {
scanf("%d%d", &n, &k);
for (int i = 1; i <= n;i++) {
scanf("%1d", &a[i]);
}
for (int i = 1; i <= n;i++) {
long long v = i;
G[i].push_back((edge){i + 1, v});
G[i].push_back((edge){i - 1, 0});
if(a[i]==1) {
int l = max(i - k, 1);
int r = min(i + k, n) + 1;
G[l].push_back((edge){r, v});
}
}
G[n+1].push_back((edge){n, 0});
dijkstra(1);
printf("%lld\n", dis[n + 1]);
}

#include<bits/stdc++.h>
using namespace std;
const int maxn = 4e5 + 100;

long long dp[maxn];
int a[maxn];

int main() {
int n, k;
scanf("%d%d", &n, &k);
for (int i = 1; i <= n;i++) {
scanf("%1d", &a[i]);
}

deque<int> d;
d.push_back(0);

for (int i = 1; i <= n + k;i++) {
dp[i] = dp[i - 1] + i;
if(i-k>0&&a[i-k]==1) {
while(!d.empty()&&d.front()<i-2*k-1)
d.pop_front();
dp[i] = min(dp[i], dp[d.front()] + i - k);
}
while(!d.empty()&&dp[d.back()]>=dp[i])
d.pop_back();
d.push_back(i);
}
long long ans = 1e18;
for (int i = n; i <= n + k;i++) {
ans = min(ans, dp[i]);
}
printf("%lld\n", ans);
}



[CF1324E] Sleeping Schedule

https://codeforces.com/contest/1324/problem/E

#include<bits/stdc++.h>
using namespace std;
const int maxn = 2000 + 5;
int a[maxn];
int dp[maxn][maxn];
int main() {
int n,h,l,r;
cin >> n >> h >> l >> r;
for (int i = 1; i <= n;i++) {
scanf("%d", &a[i]);
}
memset(dp,-0x3f,sizeof(dp));
dp[0][0] = 0;
for (int i = 1; i <= n;i++) {
for (int j = 0; j < h;j++) {
int x = (j + a[i] - 1) % h;
int f = 0;
if(l<=x&&x<=r)
f = 1;
dp[i][x] = max(dp[i-1][j] + f, dp[i][x]);
x = (j + a[i]) % h;
if(l<=x&&x<=r)
f = 1;
else
f = 0;
dp[i][x] = max(dp[i-1][j] + f, dp[i][x]);
}
}
int ans = 0;
for (int i = 0; i < h;i++) {
ans = max(ans, dp[n][i]);
}
cout << ans << endl;
}



状压DP

找朋友

#include <bits/stdc++.h>
#include<stdint.h>
using namespace std;
#define int long long
#define scan(n) scanf("%lld", &(n))
#define scann(n, m) scanf("%lld%lld", &(n), &(m))
#define scannn(a, b, c) scanf("%lld%lld%lld", &(a), &(b), &(c))
#define prin(n) printf("%lld", (n))
#define pb push_back
#define mp make_pair
#define ms(a) memset(a, 0, sizeof(a))
#define fo(i, a, b) for (int i = (a); i <= (b); i++)
#define ro(i, a, b) for (int i = (a); i >= (b); i--)
#define dbg(args...) do {cout << #args << " : "<< args << endl;}
const int inf = 0x3f3f3f3f;
const int maxn = (1<<21);
int x[25],y[25];
int n,f;
double dp[maxn];
bool check(int s,int t){
for(int i=1;i<=n;i++){
int x=(1<<i);
if((!(s&x))&&(t&x))return false;
}
return true;
}
double dis(int i,int j){
return sqrt((x[i]-x[j])*(x[i]-x[j])+(y[i]-y[j])*(y[i]-y[j]));
}
double min_dis(int t,int j){
vector<double>v;
for(int i=1;i<=n;i++){
int x=(1<<i);
if(t&x){
v.pb(dis(i,j));
}
}
sort(v.begin(),v.end());
if(v.size()<=1)return inf;
return v[0]+v[1];
}
int32_t main() {
int T;scan(T);
while(T--){
scan(n);
int s=0;
int xx=((1<<(n+1))-1)^1;
for(int i=0;i<=maxn-1;i++)dp[i]=inf;
fo(i,1,n){
scannn(x[i],y[i],f);
if(f)s^=(1<<i);
}
dp[s]=0;
for(int i=s;i<=xx;i++){
if(!check(i,s))continue;
fo(j,1,n){
int t=(1<<j);
if((i&t)&&(!(s&t))){
int x=i^t;
dp[i]=min(dp[x]+min_dis(x,j),dp[i]);
}
else continue;
}
}
if(dp[xx]==inf){
cout<<"No Solution\n";
continue;
}
printf("%.6lf\n",dp[xx]);
}
return 0;
}


区间DP

[CF1199F] Rectangle Painting

https://codeforces.com/contest/1199/problem/F

#include<bits/stdc++.h>
#define fo(i,a,b) for(int i=a;i<=b;i++)
using namespace std;
char a[55][55];
int f[55][55][55][55];
int dp(int x,int y,int xx,int yy){
if(f[x][y][xx][yy]!=-1)return f[x][y][xx][yy];
int ans=max(xx-x+1,yy-y+1);
fo(i,x,xx-1)ans=min(ans,dp(x,y,i,yy)+dp(i+1,y,xx,yy));
fo(i,y,yy-1)ans=min(ans,dp(x,y,xx,i)+dp(x,i+1,xx,yy));
return f[x][y][xx][yy]=ans;
}
int main(){
int n;scanf("%lld",&n);
fo(i,1,n)scanf("%s",a[i]+1);
memset(f,-1,sizeof(f));
fo(x,1,n){
fo(y,1,n){
fo(xx,1,n){
fo(yy,1,n){
if(x>xx||y>yy)f[x][y][xx][yy]=0;
if(x==xx&&y==yy)f[x][y][xx][yy]=(a[x][y]=='#'?1:0);
}
}
}
}
cout<<dp(1,1,n,n)<<endl;

}

posted @ 2020-03-27 23:39  瓜瓜站起来  阅读(153)  评论(0编辑  收藏  举报