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  • Solution -「JLOI 2015」「洛谷 P3262」战争调度

    (mathcal{Description})

      Link.

      给定一棵 (n) 层的完全二叉树,你把每个结点染成黑色或白色,满足黑色叶子个数不超过 (m)。对于一个叶子 (u),若其 (k) 级父亲与其同为黑色,则对答案贡献 (a_{uk});若同为白色,则对答案贡献 (b_{uk})。求最大贡献和。

      (nle10)

    (mathcal{Solution})

      想要 DP,比如令 (f(u,i)) 表示 (u) 子树内有 (i) 个叶子为黑色时的最大贡献和。但发现这根本没法转移 qwq。

      那……爆搜呢?

      从上往下搜索,直接钦定当前非叶结点是黑是白,搜到叶子时,在向上计算当前叶子是黑色/白色时的贡献,回溯时简单背包。复杂度 (mathcal O(n4^n)),可过欸!

    (mathcal{Code})

    /* Clearink */
    
    #include <cstdio>
    
    const int MAXN = 10;
    int n, m, a[1 << MAXN | 5][MAXN + 5], b[1 << MAXN | 5][MAXN + 5];
    int f[1 << MAXN | 5][1 << MAXN | 5];
    bool fight[1 << MAXN | 5];
    
    inline void chkmax ( int& a, const int b ) { a < b && ( a = b, 0 ); }
    
    inline void solve ( const int u, const int d ) {
    	for ( int i = 0; i <= 1 << d; ++ i ) f[u][i] = 0;
    	if ( !d ) {
    		for ( int i = 1; i <= n; ++ i ) {
    			if ( fight[u >> i] ) f[u][1] += a[u][i];
    			else f[u][0] += b[u][i];
    		}
    	} else {
    		for ( int k = 0; k <= 1; ++ k ) {
    			fight[u] = k;
    			solve ( u << 1, d - 1 ), solve ( u << 1 | 1, d - 1 );
    			for ( int i = 0; i <= 1 << d >> 1; ++ i ) {
    				for ( int j = 0; j <= 1 << d >> 1; ++ j ) {
    					chkmax ( f[u][i + j], f[u << 1][i] + f[u << 1 | 1][j] );
    				}
    			}
    		}
    	}
    }
    
    int main () {
    	scanf ( "%d %d", &n, &m ), -- n;
    	for ( int i = 0; i < 1 << n; ++ i ) {
    		for ( int j = 1; j <= n; ++ j ) {
    			scanf ( "%d", &a[( 1 << n ) + i][j] );
    		}
    	}
    	for ( int i = 0; i < 1 << n; ++ i ) {
    		for ( int j = 1; j <= n; ++ j ) {
    			scanf ( "%d", &b[( 1 << n ) + i][j] );
    		}
    	}
    	solve ( 1, n );
    	int ans = 0;
    	for ( int i = 0; i <= m; ++ i ) chkmax ( ans, f[1][i] );
    	printf ( "%d
    ", ans );
    	return 0;
    }
    
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  • 原文地址:https://www.cnblogs.com/rainybunny/p/14002563.html
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