結果

問題 No.2438 Double Least Square
ユーザー abap34
提出日時 2023-08-13 02:05:27
言語 Julia
(2.11.2)
結果
AC  
実行時間 1,997 ms / 2,000 ms
コード長 2,591 bytes
コンパイル時間 397 ms
コンパイル使用メモリ 6,944 KB
実行使用メモリ 339,792 KB
最終ジャッジ日時 2024-10-01 17:33:54
合計ジャッジ時間 65,234 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 30
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

using Printf
function score(xy, x², y²)
    if x² == 0
        return 0
    end
    coef = xy / x²
    return y² + (coef^2 * x²) - (2coef * xy)
end
function main()
    N = parse(Int, readline())
    H = parse(Int, readline())
    x = zeros(Int, N)
    y = zeros(Int, N)
    for i in 1:N
        x[i], y[i] = parse.(Int, split(readline()))
    end
    INF = 10^16
    slopes = zeros(Rational{Int}, N)
    for i in eachindex(x)
        if x[i] == 0
            slopes[i] = INF 
        else
            slopes[i] = (y[i] - (H // 2)) // x[i]
        end
    end
    slopes_perm = sortperm(slopes, rev=true)
    x_perm = sortperm(x, rev=true)
    # 全部lower
    xy = sum(x .* y)
    x² = sum(x .* x)
    y² = sum(y .* y)
    L_best = score(xy, x², y²)
    
    for i in eachindex(x)
        upper = slopes_perm[begin:i]    
        lower = slopes_perm[i+1:end]
        upper_set = Set(upper)
        upper_x = getindex.(Ref(x), upper)
        upper_y = getindex.(Ref(y .- H), upper)
        
        upper_xy = sum(upper_x .* upper_y)
        upper_x² = sum(upper_x .* upper_x)
        upper_y² = sum(upper_y .* upper_y)
        
        lower_x = getindex.(Ref(x), lower)
        lower_y = getindex.(Ref(y), lower)
        
        lower_xy = sum(lower_x .* lower_y)
        lower_x² = sum(lower_x .* lower_x)
        lower_y² = sum(lower_y .* lower_y)
        L_u = score(upper_xy, upper_x², upper_y²)
        L_b = score(lower_xy, lower_x², lower_y²)
        L = L_u + L_b
        if L < L_best
            L_best = L
        end
        
        for j in eachindex(x)
            new_idx = x_perm[j]     
            if new_idx in upper_set
                upper_xy -= x[new_idx] * (y[new_idx] - H)
                upper_x² -= x[new_idx]^2
                upper_y² -= (y[new_idx] - H)^2
                
                lower_xy += x[new_idx] * y[new_idx]
                lower_x² += x[new_idx]^2
                lower_y² += y[new_idx]^2
            else
                upper_xy += x[new_idx] * (y[new_idx] - H)
                upper_x² += x[new_idx]^2
                upper_y² += (y[new_idx] - H)^2
                lower_xy -= x[new_idx] * y[new_idx]
                lower_x² -= x[new_idx]^2
                lower_y² -= y[new_idx]^2
            end
            L_u = score(upper_xy, upper_x², upper_y²)
            L_b = score(lower_xy, lower_x², lower_y²)
    
            L = L_u + L_b
            if L < L_best
                L_best = L
            end
            
        end        
    end 
    @printf "%0.20f\n" L_best
end
main()
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