Bzoj 3662: Clever Rabbit

原創 MintGreenTZ 2018-09-03 19:08

傳送門：http://www.lydsy.com/JudgeOnline/problem.php?id=3662
題意：
聰明的兔子定義了三個函數:
• g(x) 表示將 x 十進制表示中各位數字從高位到低位降序排列組成的數字。
• L(x) 表示將 x 十進制表示中各位數字從高位到低位升序排列組成的數字。
• f(x)=g(x)−L(x)
如果一個數 x 與 f(x) 相等，兔子們稱它爲幸運數。現在兔子們希望計算在所有的 n 位數字中，所有幸運
數的平方的和。結果對 p 取模後輸出，注意這裏數字可以包含前導 0 .
數據範圍： 1≤n≤30 ;1≤p≤2×109
題解： 一看數據範圍只有 30 就猜想是個打表題，30 個數 分成 10 類一共有 C930+9=211915132 種情況，再 O(n) 算一下感覺相當輕鬆嘛，然後就拿了個暴力打了個表（只用了7min多… ），然後用python算了一下平方水過。
打表程序：

#include<bits/stdc++.h>
const int N = 50;
int n, t[N], a[N], b[N], c[N], d[N];
void dfs(int dep, int last) {
    if (!dep) {
        for (int i = last + 1; i <= n; i++) t[i] = dep;
        for (int i = 1; i <= n; i++)
            a[i] = t[i], b[i] = t[n - i + 1];
        for (int i = n; i > 0; i--) {
            c[i] = a[i] - b[i];
            if (c[i] < 0) c[i] += 10, a[i - 1]--;
        }
        for (int i = 1; i <= n; i++) d[i] = c[i];
        std::sort(c + 1, c + n + 1);
        bool suc = 1;
        for (int i = 1; i <= n; i++)
            if (c[i] != b[i]) suc = 0;
        if (!d[1]) suc = 0;
        if (suc) {
            for (int i = 1; i <= n; i++)
                printf("%d", d[i]);
            printf("\n");
        };
        return;
    }
    for (int pos = last; pos <= n; pos++) {
        for (int i = last + 1; i <= pos; i++) t[i] = dep;
        dfs(dep - 1, pos);
    }
}
int main() {
    freopen("test.out", "w", stdout);
    for (n = 3; n <= 30; n++) dfs(9, 0);
    return 0;
}

表：

#include<bits/stdc++.h>
typedef long long ll;
const char a[240][50] = {
"495",
"6174",
"631764",
"549945",
"63317664",
"97508421",
"864197532",
"554999445",
"6333176664",
"9753086421",
"9975084201",
"86431976532",
"633331766664",
"975330866421",
"997530864201",
"999750842001",
"555499994445",
"8643319766532",
"63333317666664",
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"999999999999750842000000000001"};
const char b[240][100] = {
"245025",
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"99999999995061728400060966335988416399506172840000000001",
"99999999999501684000000620817089639999950168400000000001",
"7470721111110876588666666645227833333333698728888888907024",
"9754610821518672460874842432777320536381618350904130190521",
"9756807685941782561635232880109867998971687364770794348521",
"9757025234395929755579278721646108081993870227477187928521",
"9975323908212745026087240210779542783816405732413041274201",
"9975546054835220544139339478112097143919089321281637054201",
"7897280492642617530993995145896529355043466712689283604544",
"9997531019079683282606279990779765280164279683304349642001",
"9997553258324130675271732120112586791614442552385727442001",
"9999753088188352418236183990779790245843032772437186420001",
"9999755312339017349535791206315303088523341462992964420001",
"9999975308679439084679174610779819902851921685740864200001",
"9999997530864349946654475872780094473098613016308642000001",
"9999999753084199032827337998982837989147946075086420000001",
"401111111111109126666666666665743333333333341688888888888896",
"951275111111106299466666666193537333333334545288888888949241",
"955610519511067225483466623286846973334340994128889392696841",
"956005882963516118103719166220178030722965483017837047412841",
"956045036603062291365496452353512124149210421293882518572841",
"995072751111106189946666661753581733333345497288888894968401",
"995515705195066318548346219246887377343410345328939273724401",
"786138173831910098792108478505628118359032120952901738169344",
"995556054829195611410328006180218079669658834627705141684401",
"995560050321639073532162541193561018816548662272691861284401",
"999506727511106178994666617353586173333455017288889497284001",
"999551117051906227854830178846891417834103857333927412844001",
"999555160147851604740592493780222172740592394814518172444001",
"977659279190660179082799887471097567766383529192141285716321",
"999555560494816839713625189681653925886411160073986168444001",
"999950667275106177899466173353586617334550217288949732840001",
"999955107170474618785438574846891822781038977832741688440001",
"999955511561038084509654978580223463810332405495857284440001",
"997754570769684648996059171671120059416056647856348791852201",
"999995066672746177789941733353586661745502217294973328400001",
"999995510671660301878099414846891872254390227714172884400001",
"999995551111169941251321587460232410544213393630128844400001",
"999775343503472849388467082093144795732920270257281387422001",
"999999506666722577778945333353586666295022217897333284000001",
"999999551066672158623365502846891966988307215857328844000001",
"999999555110271258617135852348321481530715407060888444000001",
"999999950666662341777406133353586667834222278133332840000001",
"999999955106622277142292151646892874327966030173288440000001",
"999999995066661739412856613353586678830628301733328400000001",
"999999995510621777923029216526901943769451461772884400000001",
"999999999506661733344845661353586788355670661733284000000001",
"999999999551021768894395363014992642273635021768844000000001",
"308641975246913580243827160495061728395030864197524691358025",
"999999999950661732840608566153587883616350661732840000000001",
"999999999995061728400006096633598841639995061728400000000001",
"999999999999501684000000062081708963999999501684000000000001"};
int main() {
    int n, p, len;
    scanf("%d%d", &n, &p);
    ll ans = 0, t;
    for (int i = 0; i < 240; i++)
        if (strlen(a[i]) == n) {
            t = 0; len = strlen(b[i]);
            for (int j = 0; j < len; j++)
                t = (t * 10 + b[i][j] - '0') % p;
            ans += t;
        }
    printf("%lld\n", ans % p);
    return 0;
}
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