题目描述
小 C 数学成绩优异,于是老师给小 C 留了一道非常难的数学作业题:
给定正整数 ![[HNOI2011]数学作业 矩阵快速幂 BZOJ 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输入输出格式
输入格式:
从文件input.txt中读入数据,输入文件只有一行且为用空格隔开的两个正整数N和M,其中30%的数据满足![[HNOI2011]数学作业 矩阵快速幂 BZOJ 2326_#include_02](data:image/svg+xml,%3Csvg%20xmlns%3Axlink%3D%22http%3A%2F%2Fwww.w3.org%2F1999%2Fxlink%22%20width%3D%22525.015px%22%20height%3D%2230.087px%22%20style%3D%22vertical-align%3A%20-1.171ex%3B%22%20viewBox%3D%220%20-934.9%2025116.2%201439.2%22%20role%3D%22img%22%20focusable%3D%22false%22%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20aria-labelledby%3D%22MathJax-SVG-1-Title%22%3E%0A%3Ctitle%20id%3D%22MathJax-SVG-1-Title%22%3E1%E2%89%A4N%E2%89%A410000001%E2%89%A4N%E2%89%A410000001%E2%89%A4N%E2%89%A41000000%20%EF%BC%9B100%25%E7%9A%84%E6%95%B0%E6%8D%AE%E6%BB%A1%E8%B6%B31%E2%89%A4N%E2%89%A410181%E2%89%A4N%E2%89%A410%5E%7B18%7D1%E2%89%A4N%E2%89%A41018%20%E4%B8%941%E2%89%A4M%E2%89%A41091%E2%89%A4M%E2%89%A410%5E91%E2%89%A4M%E2%89%A4109%20.%3C%2Ftitle%3E%0A%3Cdefs%20aria-hidden%3D%22true%22%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-31%22%20d%3D%22M213%20578L200%20573Q186%20568%20160%20563T102%20556H83V602H102Q149%20604%20189%20617T245%20641T273%20663Q275%20666%20285%20666Q294%20666%20302%20660V361L303%2061Q310%2054%20315%2052T339%2048T401%2046H427V0H416Q395%203%20257%203Q121%203%20100%200H88V46H114Q136%2046%20152%2046T177%2047T193%2050T201%2052T207%2057T213%2061V578Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-2264%22%20d%3D%22M674%20636Q682%20636%20688%20630T694%20615T687%20601Q686%20600%20417%20472L151%20346L399%20228Q687%2092%20691%2087Q694%2081%20694%2076Q694%2058%20676%2056H670L382%20192Q92%20329%2090%20331Q83%20336%2083%20348Q84%20359%2096%20365Q104%20369%20382%20500T665%20634Q669%20636%20674%20636ZM84%20-118Q84%20-108%2099%20-98H678Q694%20-104%20694%20-118Q694%20-130%20679%20-138H98Q84%20-131%2084%20-118Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-4E%22%20d%3D%22M234%20637Q231%20637%20226%20637Q201%20637%20196%20638T191%20649Q191%20676%20202%20682Q204%20683%20299%20683Q376%20683%20387%20683T401%20677Q612%20181%20616%20168L670%20381Q723%20592%20723%20606Q723%20633%20659%20637Q635%20637%20635%20648Q635%20650%20637%20660Q641%20676%20643%20679T653%20683Q656%20683%20684%20682T767%20680Q817%20680%20843%20681T873%20682Q888%20682%20888%20672Q888%20650%20880%20642Q878%20637%20858%20637Q787%20633%20769%20597L620%207Q618%200%20599%200Q585%200%20582%202Q579%205%20453%20305L326%20604L261%20344Q196%2088%20196%2079Q201%2046%20268%2046H278Q284%2041%20284%2038T282%2019Q278%206%20272%200H259Q228%202%20151%202Q123%202%20100%202T63%202T46%201Q31%201%2031%2010Q31%2014%2034%2026T39%2040Q41%2046%2062%2046Q130%2049%20150%2085Q154%2091%20221%20362L289%20634Q287%20635%20234%20637Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-30%22%20d%3D%22M96%20585Q152%20666%20249%20666Q297%20666%20345%20640T423%20548Q460%20465%20460%20320Q460%20165%20417%2083Q397%2041%20362%2016T301%20-15T250%20-22Q224%20-22%20198%20-16T137%2016T82%2083Q39%20165%2039%20320Q39%20494%2096%20585ZM321%20597Q291%20629%20250%20629Q208%20629%20178%20597Q153%20571%20145%20525T137%20333Q137%20175%20145%20125T181%2046Q209%2016%20250%2016Q290%2016%20318%2046Q347%2076%20354%20130T362%20333Q362%20478%20354%20524T321%20597Z%22%3E%3C%2Fpath%3E%0A%3C%2Fdefs%3E%0A%3Cg%20stroke%3D%22currentColor%22%20fill%3D%22currentColor%22%20stroke-width%3D%220%22%20transform%3D%22matrix(1%200%200%20-1%200%200)%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2264%22%20x%3D%22778%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-4E%22%20x%3D%221834%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2264%22%20x%3D%223000%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(4057%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-30%22%20x%3D%22500%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-30%22%20x%3D%221001%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-30%22%20x%3D%221501%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-30%22%20x%3D%222002%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-30%22%20x%3D%222502%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-30%22%20x%3D%223003%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%223503%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2264%22%20x%3D%228338%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-4E%22%20x%3D%229395%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-2264%22%20x%3D%2210561%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(11617%2C0)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-30%22%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输出格式:
输出文件 output.txt 仅包含一个非负整数,表示 ![[HNOI2011]数学作业 矩阵快速幂 BZOJ 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输入输出样例
输入样例#1:
复制
13 13
输出样例#1: 复制
4
范围1e18,logn算法;
递推方程: f[ n ]= f[ n-1 ] * 10^( len(n) )+ n;
直接递推显然不行;
换成矩阵加速递推;
( fn,n,1 )= ( f(n-1),n-1,1 )( 10^(len) , 0 , 0
1 , 1 , 0
1 , 1 , 1 );
这里的 len 指的是 n 的位数;
那么我们每次枚举其位数进行计算即可;
这里我的快速幂参考了别人的封装;
#include
#include
#include
#include
#include
#include
#include
#include
EPFL - Fighting