【区间DP】CF39C，CF1025D，CF1312E，CF1178F1，CF1336C，CF49E，CF838E，CF1107E，CF1101F，CF888F

其他 2020-08-12 04:35:25 阅读次数: 0

题解等我有空再慢慢填坑

在这里插入图片描述

T1：CF39C Moon Craters

title

code

#include <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
#define MAXN 2002
vector < int > g[MAXN << 1];
int n, cnt, m;
int x[MAXN], y[MAXN], o[MAXN << 1];
int dp[MAXN << 1][MAXN << 1], exist[MAXN << 1][MAXN << 1], f[MAXN << 1][MAXN << 1];

void print( int l, int r ) {
	if( l > r || ! dp[l][r] ) return;
	if( f[l][r] ) print( l, f[l][r] ), print( f[l][r], r );
	else print( l + 1, r );
	if( exist[l][r] ) printf( "%d ", exist[l][r] );
}

int main() {
	scanf( "%d", &n );
	for( int i = 1, r, c;i <= n;i ++ ) {
		scanf( "%d %d", &c, &r );
		x[i] = o[++ cnt] = c - r;
		y[i] = o[++ cnt] = c + r;
	}
	sort( o + 1, o + cnt + 1 );
	m = unique( o + 1, o + cnt + 1 ) - o - 1;
	for( int i = 1;i <= n;i ++ ) {
		x[i] = lower_bound( o + 1, o + m + 1, x[i] ) - o;
		y[i] = lower_bound( o + 1, o + m + 1, y[i] ) - o;
		g[x[i]].push_back( y[i] );
		exist[x[i]][y[i]] = i;
	}
	for( int i = m;i;i -- )
		for( int j = i;j <= m;j ++ ) {
			dp[i][j] = dp[i + 1][j];
			for( int k = 0;k < g[i].size();k ++ ) {
				int v = g[i][k];
				if( v < j && dp[i][v] + dp[v][j] > dp[i][j] ) {
					dp[i][j] = dp[i][v] + dp[v][j];
					f[i][j] = v;
				}
			}
			dp[i][j] += ( exist[i][j] ? 1 : 0 );
		}
	printf( "%d\n", dp[1][m] );
	print( 1, m );
	return 0;
}

T2：CF1025D Recovering BST

title

code

#include <cstdio>
#define MAXN 705
int n;
int a[MAXN];
int left[MAXN][MAXN], right[MAXN][MAXN];
bool f[MAXN][MAXN];

int gcd( int x, int y ) {
	if( ! y ) return x;
	else return gcd( y, x % y );
}

int main() {
	scanf( "%d", &n );
	for( int i = 1;i <= n;i ++ ) {
		scanf( "%d", &a[i] );
		left[i][i] = right[i][i] = 1;
	}
	for( int i = 1;i <= n;i ++ )
		for( int j = 1;j <= n;j ++ )
			if( gcd( a[i], a[j] ) != 1 )
				f[i][j] = 1;
	for( int i = n;i;i -- )
		for( int j = i;j <= n;j ++ )
			for( int k = i;k <= j;k ++ )
				if( left[i][k] && right[k][j] ) {
					if( i == 1 && j == n ) return ! printf( "Yes" );
					if( f[i - 1][k] ) right[i - 1][j] = 1;
					if( f[k][j + 1] ) left[i][j + 1] = 1;
				}
	printf( "No" );
	return 0;
}

T3：CF1312E Array Shrinking

title

code

#include <cstdio>
#include <cstring>
#include <iostream>
using namespace std;
#define MAXN 501
int n;
int dp[MAXN][MAXN], w[MAXN][MAXN];

int main() {
	memset( dp, 0x3f, sizeof( dp ) );
	scanf( "%d", &n );
	for( int i = 1;i <= n;i ++ )
		scanf( "%d", &w[i][i] ), dp[i][i] = 1;
	for( int len = 2;len <= n;len ++ )
		for( int i = 1;i + len - 1 <= n;i ++ ) {
			int j = i + len - 1;
			for( int k = i;k < j;k ++ ) {
				dp[i][j] = min( dp[i][j], dp[i][k] + dp[k + 1][j] );
				if( dp[i][k] == dp[k + 1][j] && dp[i][k] == 1 && w[i][k] == w[k + 1][j] )
					dp[i][j] = 1, w[i][j] = w[i][k] + 1;
			}
		}
	printf( "%d", dp[1][n] );
	return 0;
}

T4：CF1178F1 Short Colorful Strip

title

code

#include <cstdio>
#define MAXN 505
#define lyx 998244353
int n, m;
int c[MAXN];
int dp[MAXN][MAXN];

int dfs( int l, int r ) {
	if( l > r ) return 1;
	if( dp[l][r] ) return dp[l][r];
	int p = l, temp = 0;
	for( int i = l;i <= r;i ++ )
		if( c[i] < c[p] ) p = i;
	for( int i = l;i <= p;i ++ )
		temp = ( 1ll * temp + 1ll * dfs( l, i - 1 ) * dfs( i, p - 1 ) % lyx ) % lyx;
	for( int i = p;i <= r;i ++ )
		dp[l][r] = ( 1ll * dp[l][r] + 1ll * temp * dfs( p + 1, i ) % lyx * dfs( i + 1, r ) % lyx ) % lyx;
	return dp[l][r];
}

int main() {
	scanf( "%d %d", &n, &m );
	for( int i = 1;i <= m;i ++ )
		scanf( "%d", &c[i] );
	printf( "%d", dfs( 1, n ) );
	return 0;
}

T5：CF1336C Kaavi and Magic Spell

title

code

#include <cstdio>
#include <cstring>
#define MAXN 3005
#define lyx 998244353
int n, m, ans;
char s[MAXN], t[MAXN];
int dp[MAXN][MAXN];

int main() {
	scanf( "%s %s", s + 1, t + 1 );
	int n = strlen( s + 1 ), m = strlen( t + 1 ); 
	for( int i = 1;i <= n;i ++ )
		dp[i][i] = ( i > m || s[1] == t[i] ) << 1;
	for( int len = 2;len <= n;len ++ )
		for( int i = 1;i + len - 1 <= n;i ++ ) {
			int j = i + len - 1;
			if( i > m || s[len] == t[i] ) dp[i][j] = ( dp[i][j] + dp[i + 1][j] ) % lyx;
			if( j > m || s[len] == t[j] ) dp[i][j] = ( dp[i][j] + dp[i][j - 1] ) % lyx;
		}
	for( int i = m;i <= n;i ++ )
		ans = ( ans + dp[1][i] ) % lyx;
	printf( "%d", ans );
	return 0;
}

T6：CF49E Common ancestor

title

code

#include <cstdio>
#include <vector>
#include <cstring>
using namespace std;
#define MAXN 55
vector < pair < int, int > > g[MAXN << 2];
int len1, len2, n;
char s1[MAXN], s2[MAXN], s[MAXN];
int dp[MAXN][MAXN], f1[MAXN][MAXN][MAXN << 2], f2[MAXN][MAXN][MAXN << 2];

int main() {
	scanf( "%s %s", s1 + 1, s2 + 1 );
	len1 = strlen( s1 + 1 ), len2 = strlen( s2 + 1 );
	scanf( "%d", &n );
	for( int i = 1;i <= n;i ++ ) {
		scanf( "%s", s );
		g[s[0]].push_back( make_pair( s[3], s[4] ) );
	}
	for( int i = 1;i <= len1;i ++ ) f1[i][i][s1[i]] = 1;
	for( int i = 1;i <= len2;i ++ ) f2[i][i][s2[i]] = 1;
	memset( dp, 0x3f, sizeof( dp ) ); dp[0][0] = 0;
	for( int len = 2;len <= len1;len ++ )
		for( int i = 1;i + len - 1 <= len1;i ++ ) {
			int j = i + len - 1;
			for( int ch = 'a';ch <= 'z';ch ++ )
				for( int k = i;k < j;k ++ )
					for( int u = 0;u < g[ch].size();u ++ )
						f1[i][j][ch] |= f1[i][k][g[ch][u].first] && f1[k + 1][j][g[ch][u].second];
		}
	for( int len = 2;len <= len2;len ++ )
		for( int i = 1;i + len - 1 <= len2;i ++ ) {	
			int j = i + len - 1;
			for( char ch = 'a';ch <= 'z';ch ++ )
				for( int k = i;k < j;k ++ )
					for( int u = 0;u < g[ch].size();u ++ )
						f2[i][j][ch] |= f2[i][k][g[ch][u].first] && f2[k + 1][j][g[ch][u].second];
		}
	for( int i = 1;i <= len1;i ++ )
		for( int j = 1;j <= len2;j ++ )
			for( int ii = 1;ii <= i;ii ++ )
				for( int jj = 1;jj <= j;jj ++ )
					for( char ch = 'a';ch <= 'z';ch ++ )
						if( f1[ii][i][ch] && f2[jj][j][ch] )
							dp[i][j] = min( dp[i][j], dp[ii - 1][jj - 1] + 1 );
	printf( "%d", ( dp[len1][len2] == 0x3f3f3f3f ) ? -1 : dp[len1][len2] );
	return 0;
}

T7：CF838E Convex Countour

title

code

#include <cmath>
#include <cstdio>
#include <iostream>
using namespace std;
#define MAXN 2505
struct node {
	int x, y;
	node() {}
	node( int X, int Y ) {
		x = X, y = Y;
	}
}s[MAXN];
int n;
double dp[MAXN][MAXN][2];

double dis( node u, node v ) {
	return sqrt( 1.0 * ( u.x - v.x ) * ( u.x - v.x ) + 1.0 * ( u.y - v.y ) * ( u.y - v.y ) );
}

int main() {
	scanf( "%d", &n );
	for( int i = 0;i < n;i ++ )
		scanf( "%d %d", &s[i].x, &s[i].y );
	for( int len = 2;len <= n;len ++ )
		for( int i = 0;i < n;i ++ ) {
			int j = ( i + len - 1 ) % n;
			dp[i][j][0] = max( dp[( i + 1 ) % n][j][0] + dis( s[i], s[( i + 1 ) % n] ), dp[( i + 1 ) % n][j][1] + dis( s[i], s[j] ) );
			dp[i][j][1] = max( dp[i][( j - 1 + n ) % n][0] + dis( s[i], s[j] ), dp[i][( j - 1 + n ) % n][1] + dis( s[( j - 1 + n ) % n], s[j] ) );
		}
	double ans = 0;
	for( int i = 0;i < n;i ++ )
		ans = max( ans, max( dp[i][( i - 1 + n ) % n][0], dp[i][( i - 1 + n ) % n][1] ) );
	printf( "%.10f", ans );
	return 0;
}

T8：CF1107E Vasya and Binary String

title

code

#include <cstdio>
#include <iostream>
using namespace std;
#define ll long long
#define MAXN 105
int n;
char s[MAXN];
ll a[MAXN];
ll dp[MAXN][MAXN][MAXN];

int main() {
	scanf( "%d %s", &n, s + 1 );
	for( int i = 1;i <= n;i ++ )
		scanf( "%lld", &a[i] );
	for( int i = 1;i <= n;i ++ )
		for( int j = 1;j < i;j ++ )
			a[i] = max( a[i], a[j] + a[i - j] );
	for( int len = 1;len <= n;len ++ )
		for( int i = 1;i + len - 1 <= n;i ++ ) {
			int j = i + len - 1;
			for( int k = 0;k <= n;k ++ ) {
				dp[i][j][k] = max( dp[i][j][k], dp[i + 1][j][0] + a[k + 1] );
				for( int p = i + 1;p <= j;p ++ )
					if( s[i] == s[p] )
						dp[i][j][k] = max( dp[i][j][k], dp[i + 1][p - 1][0] + dp[p][j][k + 1] );
			}
		}
	printf( "%lld", dp[1][n][0] );
	return 0;
}

T9：CF1101F Trucks and Cities

title

code

#include <cstdio>
#include <vector>
#include <cstring>
#include <iostream>
using namespace std;
#define ll long long
#define MAXN 405
#define MAXM 250005
vector < int > g[MAXN];
int n, m;
ll ans;
ll a[MAXN], s[MAXM], t[MAXM], c[MAXM], r[MAXM];
ll dp[MAXN][MAXN][2];

int main() {
	scanf( "%d %d", &n, &m );
	for( int i = 1;i <= n;i ++ )
		scanf( "%lld", &a[i] );
	for( int i = 1;i <= m;i ++ ) {
		scanf( "%lld %lld %lld %lld", &s[i], &t[i], &c[i], &r[i] );
		r[i] = min( r[i] + 1, t[i] - s[i] );
		g[r[i]].push_back( i );
	}
	memset( dp, 0x7f, sizeof( dp ) );
	for( int i = 1;i <= n;i ++ ) 
		for( int j = i;j <= n;j ++ )
			dp[i][j][1] = a[j] - a[i];
	for( int k = 1;k < n;k ++ ) {
		for( int i = 0;i < g[k].size();i ++ )
			ans = max( ans, dp[s[g[k][i]]][t[g[k][i]]][k & 1] * c[g[k][i]] );
		for( int i = 1;i <= n;i ++ ) {
			dp[i][i][k & 1] = 0;
			int last = i;
			for( int j = i + 1;j <= n;j ++ ) {
				while( dp[i][last][k & 1] < a[j] - a[last] ) last ++;
				dp[i][j][( k + 1 ) & 1] = min( dp[i][last][k & 1], a[j] - a[last - 1] );
			}
		}
	}
	printf( "%lld", ans );
	return 0;
}

T10：CF888F Connecting Vertices

title

code

#include <cstdio>
#define lyx 1000000007
#define ll long long
#define MAXN 505
int n;
int a[MAXN][MAXN];
ll dp[MAXN][MAXN][2];

int main() {
	scanf( "%d", &n );
	for( int i = 1;i <= n;i ++ ) {
		for( int j = 1;j <= n;j ++ )
			scanf( "%d", &a[i][j] );
		dp[i][i][0] = 1;
	}
	for( int len = 2;len <= n;len ++ )
		for( int i = 1;i + len - 1 <= n;i ++ ) {
			int j = i + len - 1;
			if( a[i][j] )			
				for( int k = i;k < j;k ++ )
					dp[i][j][0] = ( dp[i][j][0] + ( ( dp[i][k][0] + dp[i][k][1] ) % lyx ) * ( ( dp[k + 1][j][1] + dp[k + 1][j][0] ) % lyx ) % lyx ) % lyx; 
			for( int k = i + 1;k < j;k ++ )
				if( a[i][k] )
					dp[i][j][1] = ( dp[i][j][1] + dp[i][k][0] * ( ( dp[k][j][0] + dp[k][j][1] ) % lyx ) % lyx ) % lyx;
		}
	printf( "%lld", ( dp[1][n][0] + dp[1][n][1] ) % lyx );
	return 0;
}

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