{"id":75329,"date":"2026-02-12T01:26:16","date_gmt":"2026-02-11T17:26:16","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/75329.html"},"modified":"2026-02-12T01:26:16","modified_gmt":"2026-02-11T17:26:16","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e8%af%a6%e8%a7%a3%e3%80%91%e4%b8%89%e7%bb%b4%e5%89%8d%e7%bc%80%e5%92%8c%e4%b8%8e%e5%b7%ae%e5%88%86","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/75329.html","title":{"rendered":"\u3010\u7b97\u6cd5\u8be6\u89e3\u3011\u4e09\u7ef4\u524d\u7f00\u548c\u4e0e\u5dee\u5206"},"content":{"rendered":"

\u4e09\u7ef4\u524d\u7f00\u548c\u4e0e\u5dee\u5206<\/h2>\n

By Zhang_HangWei<\/p>\n

1. \u4e09\u7ef4\u524d\u7f00\u548c<\/h3>\n

1.1 \u516c\u5f0f<\/h4>\n

s[<\/span>x]<\/span>[<\/span>y]<\/span>[<\/span>z]<\/span> =<\/span> s[<\/span>x–<\/span>1<\/span>]<\/span>[<\/span>y]<\/span>[<\/span>z]<\/span> +<\/span> s[<\/span>x]<\/span>[<\/span>y–<\/span>1<\/span>]<\/span>[<\/span>z]<\/span> +<\/span> s[<\/span>x]<\/span>[<\/span>y]<\/span>[<\/span>z–<\/span>1<\/span>]<\/span> –<\/span> s[<\/span>x–<\/span>1<\/span>]<\/span>[<\/span>y–<\/span>1<\/span>]<\/span>[<\/span>z]<\/span> –<\/span> s[<\/span>x–<\/span>1<\/span>]<\/span>[<\/span>y]<\/span>[<\/span>z–<\/span>1<\/span>]<\/span> –<\/span> s[<\/span>x]<\/span>[<\/span>y–<\/span>1<\/span>]<\/span>[<\/span>z–<\/span>1<\/span>]<\/span> +<\/span> s[<\/span>x–<\/span>1<\/span>]<\/span>[<\/span>y–<\/span>1<\/span>]<\/span>[<\/span>z–<\/span>1<\/span>]<\/span> +<\/span> a[<\/span>x]<\/span>[<\/span>y]<\/span>[<\/span>z]<\/span><\/p>\n

1.2 \u516c\u5f0f\u7406\u89e3<\/h4>\n

s[x][y][z]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x-1][y][z]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x][y-1][z]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x][y][z-1]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x-1][y-1][z]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x-1][y][z-1]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x][y-1][z-1]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x-1][y-1][z-1]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

a[x][y][z]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

\u901a\u8fc7\u4ee5\u4e0a\u64cd\u4f5c\u6211\u4eec\u5f97\u5230\u524d\u7f00\u548cs[x][y][z]<\/p>\n

1.3 \u5e94\u7528：\u6c42\u5b50\u7acb\u65b9\u4f53\u548c<\/h4>\n

\u6211\u4eec\u8ba1\u7b97\u6574\u4e2a\u7ea2\u8272\u7acb\u65b9\u4f53\u4e2d\u84dd\u8272\u7acb\u65b9\u4f53\u91cc\u7684\u6570\u5b57\u548c（\u6bcf\u4e2a\u5c0f\u7acb\u65b9\u4f53\u5185\u5b58\u6709\u4e00\u4e2a\u6570\u5b57）<\/p>\n

\u6bd5\u7adf\u662f\u4e09\u7ef4\u6570\u7ec4\u561b！<\/p>\n

\u84dd\u8272\u7acb\u65b9\u4f53\u662f\u7ea2\u8272\u7acb\u65b9\u4f53\u7684\u5b50\u7acb\u65b9\u4f53<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

\u5176\u4e2d (x1,y1,z1)(x_1,y_1,z_1)<\/span><\/span>(<\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>y<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e0e (x2,y2,z2)(x_2,y_2,z_2)<\/span><\/span>(<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>y<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>z<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u4e3a\u7acb\u65b9\u4f53\u7684\u5de6\u4e0a\u89d2\u4e0e\u53f3\u4e0b\u89d2<\/p>\n

\u516c\u5f0f<\/p>\n

sum =<\/span> s[<\/span>x2]<\/span>[<\/span>y2]<\/span>[<\/span>z2]<\/span> –<\/span> s[<\/span>x2]<\/span>[<\/span>y2]<\/span>[<\/span>z1–<\/span>1<\/span>]<\/span> –<\/span> s[<\/span>x2]<\/span>[<\/span>y1–<\/span>1<\/span>]<\/span>[<\/span>z2]<\/span> –<\/span> s[<\/span>x1–<\/span>1<\/span>]<\/span>[<\/span>y2]<\/span>[<\/span>z2]<\/span> +<\/span> s[<\/span>x1–<\/span>1<\/span>]<\/span>[<\/span>y1–<\/span>2<\/span>]<\/span>[<\/span>z2]<\/span> +<\/span> s[<\/span>x1–<\/span>1<\/span>]<\/span>[<\/span>y2]<\/span>[<\/span>z1–<\/span>1<\/span>]<\/span> +<\/span> s[<\/span>x2]<\/span>[<\/span>y1–<\/span>1<\/span>]<\/span>[<\/span>z1–<\/span>1<\/span>]<\/span> –<\/span> s[<\/span>x1–<\/span>1<\/span>]<\/span>[<\/span>y1–<\/span>1<\/span>]<\/span>[<\/span>z1–<\/span>1<\/span>]<\/span><\/p>\n

\u56fe\u793a<\/p>\n

s[x2][y2][z2]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

\u90fd\u662f\u4ee5 BB<\/span><\/span>B<\/span><\/span><\/span><\/span><\/span> \u4e3a\u539f\u70b9\u5411\u5de6\u5efa\u7acb xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u8f74，\u5411\u53f3\u5efa\u7acb yy<\/span><\/span>y<\/span><\/span><\/span><\/span><\/span> \u8f74，\u5411\u4e0b\u5efa\u7acb zz<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span> \u8f74<\/p>\n

s[x2][y2][z1-1]\u8fd9\u662f\u6700\u4e0a\u9762\u4e00\u5c42<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x2][y1-1][z2]\u8fd9\u662f y\u2212zy-z<\/span><\/span>y<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>z<\/span><\/span><\/span><\/span><\/span> \u90a3\u4e00\u9762<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x1-1][y2][z2]\u8fd9\u662f x\u2212zx-z<\/span><\/span>x<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>z<\/span><\/span><\/span><\/span><\/span> \u90a3\u4e00\u9762<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x1-1][y1-2][z2]\u8fd9\u662fzz<\/span><\/span>z<\/span><\/span><\/span><\/span><\/span> \u8f74\u4e0a\u7684<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x1-1][y2][z1-1] y\u2212zy-z<\/span><\/span>y<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>z<\/span><\/span><\/span><\/span><\/span> \u9762\u6700\u4e0a\u7684<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x2][y1-1][z1-1]<\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

s[x1-1][y1-1][z1-1]\u84dd\u8272\u7acb\u65b9\u4f53\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

2. \u4e09\u7ef4\u5dee\u5206<\/h3>\n

2.1 \u5b50\u7acb\u65b9\u4f53\u52a0\u6570<\/h4>\n

\u8fd9\u91cc\u5bf9\u5dee\u5206\u7684\u4ecb\u7ecd\u6211\u4eec\u4ecd\u7136\u662f\u5148\u4ecb\u7ecd\u5b50\u7acb\u65b9\u4f53\u52a0\u6570，\u7279\u6b8a\u7684\u5b50\u7acb\u65b9\u4f53\u52a0\u6570\u7684\u4e09\u7ef4\u5dee\u5206<\/p>\n

\u9996\u5148\u6211\u4eec\u5bf9a[x][y][z]\u52a0\u4e0a CC<\/span><\/span>C<\/span><\/span><\/span><\/span><\/span> \u5c31\u662f\u5bf9s[x][y][z]\u53f3\u4e0b\u89d2\u7684\u6bcf\u4e2as[][][]\u6570\u7ec4\u52a0 CC<\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u8fd9\u91cc\u6211\u4eec\u5bf9\u5b50\u7acb\u65b9\u4f53 (x1,y1,z1)(x_1,y_1,z_1)<\/span><\/span>(<\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>y<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span>, (x2,y2,z2)(x_2,y_2,z_2)<\/span><\/span>(<\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>y<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>z<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u52a0\u4e0a CC<\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u84dd\u8272\u90e8\u5206\u52a0\u4e0a CC<\/span><\/span>C<\/span><\/span><\/span><\/span><\/span><\/p>\n

\"\u5916\u94fe\u56fe\u7247\u8f6c\u5b58\u5931\u8d25,\u6e90\u7ad9\u53ef\u80fd\u6709\u9632\u76d7\u94fe\u673a\u5236,\u5efa\u8bae\u5c06\u56fe\u7247\u4fdd\u5b58\u4e0b\u6765\u76f4\u63a5\u4e0a\u4f20\"<\/p>\n

\u516c\u5f0f<\/p>\n

a[<\/span>x1]<\/span>[<\/span>y1]<\/span>[<\/span>z1]<\/span> +=<\/span> c;<\/span>
\na[<\/span>x1]<\/span>[<\/span>y1]<\/span>[<\/span>x2 +<\/span> 1<\/span>]<\/span> -=<\/span> c;<\/span>
\na[<\/span>x1]<\/span>[<\/span>y2 +<\/span> 1<\/span>]<\/span>[<\/span>z1]<\/span> -=<\/span> c;<\/span>
\na[<\/span>x2 +<\/span> 1<\/span>]<\/span>[<\/span>y1]<\/span>[<\/span>z1]<\/span> -=<\/span> c;<\/span>
\na[<\/span>x1]<\/span>[<\/span>y2 +<\/span> 1<\/span>]<\/span>[<\/span>z2 +<\/span> 1<\/span>]<\/span> +=<\/span> c;<\/span>
\na[<\/span>x2 +<\/span> 1<\/span>]<\/span>[<\/span>y1]<\/span>[<\/span>z2 +<\/span> 1<\/span>]<\/span> +=<\/span> c;<\/span>
\na[<\/span>x2 +<\/span> 1<\/span>]<\/span>[<\/span>y2 +<\/span> 1<\/span>]<\/span>[<\/span>z1]<\/span> +=<\/span> c;<\/span>
\na[<\/span>x2 +<\/span> 1<\/span>]<\/span>[<\/span>y2 +<\/span> 1<\/span>]<\/span>[<\/span>z2 +<\/span> 1<\/span>]<\/span> -=<\/span> c;<\/span><\/p>\n

2.2 \u5dee\u5206<\/h4>\n

\u5f53 x1=x2,y1=y2,z1=z2x_1 = x_2,y_1 = y_2, z_1= z_2<\/span><\/span>x<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>x<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>y<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>y<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>,<\/span><\/span>z<\/span><\/span>1<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>z<\/span><\/span>2<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u662f\u7528\u4ee5\u4e0a\u516c\u5f0f\u5c31\u662f\u5dee\u5206<\/p>\n","protected":false},"excerpt":{"rendered":"

\u4e09\u7ef4\u524d\u7f00\u548c\u4e0e\u5dee\u5206
\nBy Zhang_HangWei
\n1. \u4e09\u7ef4\u524d\u7f00\u548c
\n1.1 \u516c\u5f0f
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