Lua二维前缀和：容斥求和的矩形查询

local function buildPref(g)
    local m, n = #g, #g[1]
    local S = {}
    for i = 0, m do S[i] = {}; S[i][0] = 0 end
    for j = 0, n do S[0][j] = 0 end
    for i = 1, m do
        for j = 1, n do
            S[i][j] = S[i - 1][j] + S[i][j - 1]
                - S[i - 1][j - 1] + g[i][j]
        end
    end
    return S
end

local function rectSum(S, x1, y1, x2, y2)
    return S[x2][y2] - S[x1 - 1][y2]
        - S[x2][y1 - 1] + S[x1 - 1][y1 - 1]
end
local p = getplayerbyname("pref2d01")
local S = buildPref({{1, 2, 3}, {4, 5, 6}, {7, 8, 9}})
sendmsg(p, 1, "左上块合计 " .. rectSum(S, 1, 1, 2, 2))