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11490: Just Another Problem

11490: Just Another Problem. ★★★☆☆ 題組： Problem Set Archive with Online Judge 題號： 1 1490: Just Another Problem 解題者： 蔡權昱 解題日期： 200 8 年 10 月 13 日.

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11490: Just Another Problem

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  1. 11490: Just Another Problem • ★★★☆☆ • 題組：Problem Set Archive with Online Judge • 題號：11490:Just Another Problem • 解題者：蔡權昱 • 解題日期：2008年10月13日

  2. 題意：假設有96個士兵排排站, 但是仔細數過後發現, 只要再補8個人就可以湊成一長方形(如右圖),題目會給你S, 問你還要多少人才可以湊成長方形.限制:1.只能把人補在中間, 且必須補成兩個等大的正方形.所以補的人數限制為2 * n22.在還沒補人之前的隊形, 必須每個地方的寬度都相同.如圖箭頭寬度皆為t.Ps. 輸出請modulo100000007

  3. 題意範例：Sample input 96102111000 Sample outputPossible Missing Soldiers = 8No Solution PossiblePossible Missing Soldiers = 553352Possible Missing Soldiers = 308898Possible Missing Soldiers = 45000Possible Missing Soldiers = 3528

  4. 解法：math另N=2*n2, 固定寬度為t依題意可知, S+N=(2t+n) * (3t+2n)=>S+2*n2=6t2+7*t*n + 2*n2=> S = 6t2+7*t*n (S,t,n皆為正整數) • =>S|t固可先將S質因數分解, 再由S的因數去求n. • 解法範例：96 => 可能的t為1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 • 令t= 3代入, 得n=2, 答2*22=8

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