➕ 把整数改写成若干数之和Rewrite Integer as Sum

使用说明与常见问题How-to & FAQ

「把整数改写成若干数之和」是什么？What is the Rewrite Integer as Sum tool?

把每个正整数改写成若干正整数之和：按固定加数（如全是 1）、按十进制位权展开，或随机拆分（可设种子）。本地处理。Rewrite each positive integer as a sum of positive integers: fixed addends (e.g. all 1s), decimal place-value expansion, or a random split (optional seed). Processed locally.

如何使用「把整数改写成若干数之和」？How do I use the Rewrite Integer as Sum tool?

在「把整数改写成若干数之和」中，把内容粘贴或输入到上方输入框，按需设置「方式」、「随机块上限（可选）」、「种子（随机拆分）」，结果会实时显示在下方，点击「复制结果」即可复制。例如输入「123」，得到「123 = 100 + 20 + 3」。Paste positive integers and choose a "Mode": Place values (123 = 100 + 20 + 3), All ones, or Random split, which can use "Random chunk max (optional)" and a "Seed" to repeat the same split. Click "Copy result" to copy the output.

怎样输入多个整数？How do I enter several integers?

每行一个，或用空格、逗号、分号分隔。像 1,234,567 这样每 3 位一个逗号的写法按千位分隔读作一个数（所以 10,100 是 10100，要表示两个数请写 10 100）；也可以用下划线分组（1_000）。负号可用 -、−（U+2212）或全角 －，全角数字也能识别。小数、科学计数法（1e3）或夹杂文字会报错并指出是第几个、完整显示那个值。One per line, or separated by spaces, commas or semicolons. A value with a comma every three digits, like 1,234,567, is read as one number with thousands separators (so 10,100 is 10100; write 10 100 for two values); underscores also group digits (1_000). Minus can be a hyphen, the Unicode minus (U+2212) or the fullwidth minus, and fullwidth digits work. Decimals, scientific notation (1e3) or stray text give an error naming the position and showing the whole value.

结果精确吗？Are the results exact?

精确。所有整数都按大整数（BigInt）逐位处理，不经过浮点，超过 2^53 的数（例如 9007199254740993）也不会被舍入。粘贴几千上万行也是线性处理，通常在几十毫秒内完成。Yes. Every value is handled as a big integer (BigInt) with no floating-point step, so numbers above 2^53 such as 9007199254740993 are never rounded. Pasting thousands of lines is processed in linear time, usually within tens of milliseconds.

有大小限制吗？Are there limits?

「全是 1」最多拆 10000；「随机拆分」每个块在 1 到「随机块上限」之间（留空 = 不限，按整个数），整页输出最多 10 万项，超过时会提示把上限调大。位权展开没有限制，几十位的大数也能精确展开。All ones goes up to 10,000. In Random split each chunk is between 1 and Random chunk max (blank = no limit, up to the whole number), and the page outputs at most 100,000 terms; if a split would need more, you are asked to raise the limit. Place values has no limit and expands numbers with dozens of digits exactly.

随机块上限可以填多大？How large can the chunk max be?

任意正整数，大于 1e6 也照样生效（例如上限 1000000000 时，块可以超过一百万）；也可以写成 1e9 这样的科学计数（必须正好是整数）。0、负数或小数会提示错误。Any positive whole number; values above a million are honoured too (with a max of 1000000000 chunks can exceed a million), and scientific notation such as 1e9 is accepted when it is exactly a whole number. Zero, negatives or decimals give an error.

输入和输出是什么样的？What does the input and output look like?

例如在「把整数改写成若干数之和」中输入 123，输出为：123 = 100 + 20 + 3（⏎ 表示换行）。For example, the Rewrite Integer as Sum turns the input 123 into: 123 = 100 + 20 + 3 (⏎ marks a line break).

有哪些选项可以调整？What options can I adjust?

「把整数改写成若干数之和」的设置：「方式」可选 位权展开、全是 1、随机拆分（默认 位权展开）；「随机块上限（可选）」可留空；「种子（随机拆分）」可留空。改动任一选项后结果会按新设置重新生成。Settings in the Rewrite Integer as Sum — "Mode": Place values, All ones, Random split (default Place values); "Random chunk max (optional)" optional; "Seed (random split)" optional. Changing any option regenerates the result with the new setting.

「把整数改写成若干数之和」免费吗？需要注册吗？Is the Rewrite Integer as Sum free? Do I need an account?

「把整数改写成若干数之和」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Rewrite Integer as Sum is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.