榪欐槸涓秴綰уぇ姘撮錛屾垜澶矙鑼朵簡錛屾兂鍌諱簡N涔?#8230;…鍚庢潵鎵嶅弽搴旇繃鏉?#8230;…鎵浠ヨ鍐欎竴涓嬩綔涓鴻紺恒?br />
棣栧厛榪欎釜搴忓垪灝辨槸涓涓爢……
鍥犳錛岄棶棰樹篃灝辨槸璇碞涓粨鐐癸紝鏉冨煎垰濂藉彇閬?~N鐨勫爢鐨勬繪暟……
璁劇粨鏋滀負(fù)F[N]銆傝N涓粨鐐圭殑鍫嗭紝宸﹀瓙鏍?wèi)鏈塴涓粨鐐癸紝鍙沖瓙鏍?wèi)鏈塺涓粨鐐癸紙鏄劇劧鏈塴+r+1=N錛夛紝鍒欐湁
F[N]=C(N-1, l) * F[l] * F[r]
榪欎釜鐞嗚В璧鋒潵寰堝鏄撳洤……鍥犱負(fù)鏍圭粨鐐瑰彧鑳芥槸1錛屽乏瀛愭爲(wèi)鍜屽彸瀛愭爲(wèi)鏄劇劧涔熼兘鏄爢錛屽洜姝ょ浉褰撲簬鍦?~N涓彇l涓暟緇勬垚宸﹀瓙鏍?wèi)锛屽墿涓嬬殑鏁熬l勬垚鍙沖瓙鏍?#8230;…鍙堝洜涓轟笉綆″彇鍝簺鏁幫紝宸﹀彸瀛愭爲(wèi)鐨勭粍鎴愭柟娉曟繪暟閮芥槸F[l]銆丗[r]錛堝彧涓庢搴忔湁鍏籌級……榪欐牱灝卞緱鍒頒笂闈㈢殑寮忓瓙浜嗗洤……
C(N-1, l)=N! / l! / r!錛屽洜姝ら渶瑕侀澶勭悊鍑烘潵A[i] = i! mod P錛岀劧鍚庨櫎娉曠敤閫嗗厓?yōu)p浜嗗洤……
涓嶈繃錛屾湰娌欒尪涓寮濮嬫兂鎸夌収灞傛暟鏋氫婦錛岀劧鍚庣浉涔?#8230;…鑷劧鎼炰笉鍑烘潵鍥?#8230;…鍚庢潵鍙堢敤鏆村姏鎶奛<=15鐨勭粨鏋滄嬁鍑烘潵鍒嗘瀽錛屾兂鎵懼埌瑙勫緥……緇撴灉姣棤瑙勫緥……鍚庢潵鍙堢籂緇撲簡N涔呮墠鎯沖埌涓婇潰榪欎釜……鐪熸姣旇禌鐨勬椂鍊欏氨鎮(zhèn)插墽浜嗗洤……鎵浠ヨ璀︾ず涓涓?#8230;…
浠ｇ爜錛?br />
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
using namespace std;
#define re(i, n) for (int i=0; i<n; i++)
#define re1(i, n) for (int i=1; i<=n; i++)
#define re2(i, l, r) for (int i=l; i<r; i++)
#define re3(i, l, r) for (int i=l; i<=r; i++)
#define rre(i, n) for (int i=n-1; i>=0; i--)
#define rre1(i, n) for (int i=n; i>0; i--)
#define rre2(i, r, l) for (int i=r-1; i>=l; i--)
#define rre3(i, r, l) for (int i=r; i>=l; i--)
#define ll long long
const int MAXN = 1000010, INF = ~0U >> 2;
int n;
ll MOD, A[MAXN], F[MAXN], res;
void init()
{
cin >> n >> MOD;
}
void prepare()
{
A[0] = A[1] = 1; re3(i, 2, n) A[i] = (A[i - 1] * i) % MOD;
}
void exgcd(ll a, ll b, ll &x, ll &y)
{
if (b) {
ll _x, _y; exgcd(b, a % b, _x, _y);
x = _y; y = _x - (a / b) * _y;
} else {x = 1; y = 0;}
}
void solve()
{
F[0] = F[1] = 1; int s = 1, l = 0, r = 0; ll x, y;
re3(i, 2, n) {
if (l == s) {
if (r == s) {s += s + 1; l++;} else r++;
} else l++;
F[i] = F[l] * F[r] % MOD; F[i] = F[i] * A[i - 1] % MOD;
exgcd(A[l], MOD, x, y); F[i] = F[i] * x % MOD; if (F[i] < 0) F[i] += MOD;
exgcd(A[r], MOD, x, y); F[i] = F[i] * x % MOD; if (F[i] < 0) F[i] += MOD;
}
res = F[n];
}
void pri()
{
cout << res << endl;
}
int main()
{
init();
prepare();
solve();
pri();
return 0;
}
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
using namespace std;
#define re(i, n) for (int i=0; i<n; i++)
#define re1(i, n) for (int i=1; i<=n; i++)
#define re2(i, l, r) for (int i=l; i<r; i++)
#define re3(i, l, r) for (int i=l; i<=r; i++)
#define rre(i, n) for (int i=n-1; i>=0; i--)
#define rre1(i, n) for (int i=n; i>0; i--)
#define rre2(i, r, l) for (int i=r-1; i>=l; i--)
#define rre3(i, r, l) for (int i=r; i>=l; i--)
#define ll long long
const int MAXN = 1000010, INF = ~0U >> 2;
int n;
ll MOD, A[MAXN], F[MAXN], res;
void init()
{
cin >> n >> MOD;
}
void prepare()
{
A[0] = A[1] = 1; re3(i, 2, n) A[i] = (A[i - 1] * i) % MOD;
}
void exgcd(ll a, ll b, ll &x, ll &y)
{
if (b) {
ll _x, _y; exgcd(b, a % b, _x, _y);
x = _y; y = _x - (a / b) * _y;
} else {x = 1; y = 0;}
}
void solve()
{
F[0] = F[1] = 1; int s = 1, l = 0, r = 0; ll x, y;
re3(i, 2, n) {
if (l == s) {
if (r == s) {s += s + 1; l++;} else r++;
} else l++;
F[i] = F[l] * F[r] % MOD; F[i] = F[i] * A[i - 1] % MOD;
exgcd(A[l], MOD, x, y); F[i] = F[i] * x % MOD; if (F[i] < 0) F[i] += MOD;
exgcd(A[r], MOD, x, y); F[i] = F[i] * x % MOD; if (F[i] < 0) F[i] += MOD;
}
res = F[n];
}
void pri()
{
cout << res << endl;
}
int main()
{
init();
prepare();
solve();
pri();
return 0;
}
]]>
鏈矙鑼剁殑絎竴涓棤鍚戠幆濂楁爲(wèi)妯″瀷錛岀邯蹇典竴涓?#8230;…
鐜鏍?wèi)锛屾寚鐨勬槸姣忎釜杩為氬潡涓偣鏁伴兘絳変簬杈規(guī)暟鐨勬棤鍚戝浘錛堢О涓烘棤鍚戠幆濂楁爲(wèi)錛夋垨鑰呮槸姣忎釜鐐規(guī)湁涓斿彧鏈変竴涓墠瓚嬶紙縐頒負(fù)鍐呭悜鐜鏍?wèi)锛夋垨鍚幘lэ紙縐頒負(fù)澶栧悜鐜鏍?wèi)锛夌殑鏈夊悜鍥惧Q岀敱浜庤繖涓浘鐨勬瘡涓繛閫氬潡褰撲腑鏈変笖鍙湁涓涓幆錛堟敞鎰忥紝鍙兘鏄嚜鐜紝鍗抽暱搴︿負(fù)1鐨勭幆錛夛紝涓旇繖涓幆涓婄殑姣忎釜鐐歸兘鍙互褰撲綔鏍瑰紩鍑轟竴媯墊爲(wèi)錛屾墍浠ュ彨“鐜鏍?#8221;銆?br />
瀵逛簬鏃犲悜鐜鏍?wèi)锛屽厛灏嗘暣涓浘杩涜涓嬈FS錛屽綋涓鏋滃彂鐜版湁閫嗗悜杈癸紙榪欐潯杈圭涓嬈¤鍙戠幇蹇呯劧鏄綔涓洪嗗悜杈圭殑錛屼篃灝辨槸璧風(fēng)偣鏄粓鐐圭殑鍚庝唬錛夛紝灝辮鏄庢壘鍒頒簡榪欎釜鐜紝璁板綍鍏惰搗鐐瑰拰緇堢偣錛堟敞鎰忥紝濡傛灉鏈夊涓繛閫氬潡鐨勮瘽錛屼笉鑳介鍑猴紝瑕佺戶緇亶鍘嗗畬錛夛紝鍐嶄笉鏂笂婧紙鍥犳鍦―FS榪囩▼涓綋鐒惰璁板綍鐖惰竟浜嗗洤錛夛紝灝卞彲浠ユ壘鍒版暣涓幆浜嗭紝鐒跺悗鍐嶄互鐜笂鐨勭粨鐐逛負(fù)鏍瑰緩鏍?wèi)鍗冲彲锛寴q欐牱渚濇澶勭悊姣忎釜榪為氬潡銆?br />
瀵逛簬鍐呭悜鐜鏍?wèi)锛堝鍚懢c諱技錛夛紝鎵劇幆鏇翠負(fù)綆鍗曪紝鍙渶瑕佷換閫変竴涓偣錛屼笉鏂幓鎵懼畠鐨勫墠瓚嬶紝鍚屾椂璁板綍鎵懼埌鐨勭偣搴忓垪錛岀洿鍒版煇涓偣鍦ㄥ簭鍒椾腑鍑虹幇涓ゆ涓烘錛屾鏃惰繖涓偣浠ュ強搴忓垪涓畠涓ゆ鍑虹幇鐨勪綅緗腑闂寸殑鎵鏈夌偣錛屽氨鏄幆涓婄殑鐐癸紝欏哄簭涔熼『渚胯褰曚笅鏉ワ紝鐒跺悗鏍?wèi)涔熶笉鐢ㄥ晦Z簡錛岀洿鎺ュ湪鍘熷浘涓壘灝辮浜嗐?br />
瀵逛簬榪欓錛岀敱浜庢瘡涓偣閮芥湁涓斿彧鏈変竴涓悗緇э紝鎵浠ユ槸澶栧悜鐜鏍?wèi)锛屼笉杩囨湰娌欒尪鏇村懼悜浜庡畠鐨勫熀鍥撅紙鏃犲悜鍥撅紝鏄棤鍚戠幆濂楁爲(wèi)錛夛紝鐒跺悗灝辨槸涓涓狣P浜嗗洤……
浠ｇ爜錛?
#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
using namespace std;
#define re(i, n) for (int i=0; i<n; i++)
#define re1(i, n) for (int i=1; i<=n; i++)
#define re2(i, l, r) for (int i=l; i<r; i++)
#define re3(i, l, r) for (int i=l; i<=r; i++)
#define rre(i, n) for (int i=n-1; i>=0; i--)
#define rre1(i, n) for (int i=n; i>0; i--)
#define rre2(i, r, l) for (int i=r-1; i>=l; i--)
#define rre3(i, r, l) for (int i=r; i>=l; i--)
#define ll long long
const int MAXN = 1000010;
const ll INF = ~0Ull >> 2;
struct edge {
int a, b, pre, next;
} E0[MAXN * 3], E[MAXN << 1];
int n, m0, m, A[MAXN], stk[MAXN], st[MAXN], pr[MAXN], Q[MAXN];
ll F[MAXN][2], res = 0;
bool vst[MAXN], vst0[MAXN];
void init_d()
{
re(i, n) E0[i].pre = E0[i].next = E[i].pre = E[i].next = i; if (n & 1) m0 = n + 1; else m0 = n; m = n;
}
void add_edge0(int a, int b)
{
E0[m0].a = a; E0[m0].b = b; E0[m0].pre = E0[a].pre; E0[m0].next = a; E0[a].pre = m0; E0[E0[m0].pre].next = m0++;
E0[m0].a = b; E0[m0].b = a; E0[m0].pre = E0[b].pre; E0[m0].next = b; E0[b].pre = m0; E0[E0[m0].pre].next = m0++;
}
void add_edge(int a, int b)
{
E[m].a = a; E[m].b = b; E[m].pre = E[a].pre; E[m].next = a; E[a].pre = m; E[E[m].pre].next = m++;
}
void init()
{
scanf("%d", &n); int x; init_d();
re(i, n) {
scanf("%d%d", &A[i], &x); add_edge0(--x, i);
}
}
void sol0(int x)
{
Q[0] = x; int i, j, front, rear;
for (front=0, rear=0; front<=rear; front++) {
i = Q[front];
for (int p=E0[i].next; p != i; p=E0[p].next) {
j = E0[p].b;
if (!vst0[j]) {Q[++rear] = j; vst0[j] = 1; add_edge(i, j);}
}
}
rre3(z, rear, 0) {
i = Q[z];
F[i][0] = 0; F[i][1] = A[i];
for (int p=E[i].next; p != i; p=E[p].next) {
j = E[p].b; F[i][0] += F[j][0] >= F[j][1] ? F[j][0] : F[j][1]; F[i][1] += F[j][0];
}
}
}
void solve()
{
re(i, n) {vst[i] = vst0[i] = 0; st[i] = E0[i].next;} int x, y, tp, x0, y0; bool FF, FF2; ll tmp0, tmp1, tmp00, tmp01, res0;
re(i, n) if (!vst[i]) {
stk[tp = 0] = i; vst[i] = 1; FF2 = 0;
while (tp >= 0) {
x = stk[tp]; FF = 0;
for (int p=st[x]; p != x; p=E0[p].next) {
y = E0[p].b;
if (!vst[y]) {vst[y] = 1; stk[++tp] = y; pr[y] = p; st[x] = E0[p].next; FF = 1; break;}
else if (p != (pr[x] ^ 1) && !FF2) {FF2 = 1; x0 = x; y0 = y;}
}
if (!FF) tp--;
}
if (FF2) {
tp = 0; vst0[y0] = 1; while (x0 != y0) {stk[tp++] = x0; vst0[x0] = 1; x0 = E0[pr[x0]].a;} stk[tp++] = y0;
re(j, tp) sol0(stk[j]);
tmp0 = F[stk[0]][0]; tmp1 = -INF;
re2(j, 1, tp) {
tmp00 = (tmp0 >= tmp1 ? tmp0 : tmp1) + F[stk[j]][0];
tmp01 = tmp0 + F[stk[j]][1];
tmp0 = tmp00; tmp1 = tmp01;
}
res0 = tmp0 >= tmp1 ? tmp0 : tmp1;
tmp0 = -INF; tmp1 = F[stk[0]][1];
re2(j, 1, tp) {
tmp00 = (tmp0 >= tmp1 ? tmp0 : tmp1) + F[stk[j]][0];
tmp01 = tmp0 + F[stk[j]][1];
tmp0 = tmp00; tmp1 = tmp01;
}
res += res0 >= tmp0 ? res0 : tmp0;
}
}
}
void pri()
{
cout << res << endl;
}
int main()
{
init();
solve();
pri();
return 0;
}
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
using namespace std;
#define re(i, n) for (int i=0; i<n; i++)
#define re1(i, n) for (int i=1; i<=n; i++)
#define re2(i, l, r) for (int i=l; i<r; i++)
#define re3(i, l, r) for (int i=l; i<=r; i++)
#define rre(i, n) for (int i=n-1; i>=0; i--)
#define rre1(i, n) for (int i=n; i>0; i--)
#define rre2(i, r, l) for (int i=r-1; i>=l; i--)
#define rre3(i, r, l) for (int i=r; i>=l; i--)
#define ll long long
const int MAXN = 1000010;
const ll INF = ~0Ull >> 2;
struct edge {
int a, b, pre, next;
} E0[MAXN * 3], E[MAXN << 1];
int n, m0, m, A[MAXN], stk[MAXN], st[MAXN], pr[MAXN], Q[MAXN];
ll F[MAXN][2], res = 0;
bool vst[MAXN], vst0[MAXN];
void init_d()
{
re(i, n) E0[i].pre = E0[i].next = E[i].pre = E[i].next = i; if (n & 1) m0 = n + 1; else m0 = n; m = n;
}
void add_edge0(int a, int b)
{
E0[m0].a = a; E0[m0].b = b; E0[m0].pre = E0[a].pre; E0[m0].next = a; E0[a].pre = m0; E0[E0[m0].pre].next = m0++;
E0[m0].a = b; E0[m0].b = a; E0[m0].pre = E0[b].pre; E0[m0].next = b; E0[b].pre = m0; E0[E0[m0].pre].next = m0++;
}
void add_edge(int a, int b)
{
E[m].a = a; E[m].b = b; E[m].pre = E[a].pre; E[m].next = a; E[a].pre = m; E[E[m].pre].next = m++;
}
void init()
{
scanf("%d", &n); int x; init_d();
re(i, n) {
scanf("%d%d", &A[i], &x); add_edge0(--x, i);
}
}
void sol0(int x)
{
Q[0] = x; int i, j, front, rear;
for (front=0, rear=0; front<=rear; front++) {
i = Q[front];
for (int p=E0[i].next; p != i; p=E0[p].next) {
j = E0[p].b;
if (!vst0[j]) {Q[++rear] = j; vst0[j] = 1; add_edge(i, j);}
}
}
rre3(z, rear, 0) {
i = Q[z];
F[i][0] = 0; F[i][1] = A[i];
for (int p=E[i].next; p != i; p=E[p].next) {
j = E[p].b; F[i][0] += F[j][0] >= F[j][1] ? F[j][0] : F[j][1]; F[i][1] += F[j][0];
}
}
}
void solve()
{
re(i, n) {vst[i] = vst0[i] = 0; st[i] = E0[i].next;} int x, y, tp, x0, y0; bool FF, FF2; ll tmp0, tmp1, tmp00, tmp01, res0;
re(i, n) if (!vst[i]) {
stk[tp = 0] = i; vst[i] = 1; FF2 = 0;
while (tp >= 0) {
x = stk[tp]; FF = 0;
for (int p=st[x]; p != x; p=E0[p].next) {
y = E0[p].b;
if (!vst[y]) {vst[y] = 1; stk[++tp] = y; pr[y] = p; st[x] = E0[p].next; FF = 1; break;}
else if (p != (pr[x] ^ 1) && !FF2) {FF2 = 1; x0 = x; y0 = y;}
}
if (!FF) tp--;
}
if (FF2) {
tp = 0; vst0[y0] = 1; while (x0 != y0) {stk[tp++] = x0; vst0[x0] = 1; x0 = E0[pr[x0]].a;} stk[tp++] = y0;
re(j, tp) sol0(stk[j]);
tmp0 = F[stk[0]][0]; tmp1 = -INF;
re2(j, 1, tp) {
tmp00 = (tmp0 >= tmp1 ? tmp0 : tmp1) + F[stk[j]][0];
tmp01 = tmp0 + F[stk[j]][1];
tmp0 = tmp00; tmp1 = tmp01;
}
res0 = tmp0 >= tmp1 ? tmp0 : tmp1;
tmp0 = -INF; tmp1 = F[stk[0]][1];
re2(j, 1, tp) {
tmp00 = (tmp0 >= tmp1 ? tmp0 : tmp1) + F[stk[j]][0];
tmp01 = tmp0 + F[stk[j]][1];
tmp0 = tmp00; tmp1 = tmp01;
}
res += res0 >= tmp0 ? res0 : tmp0;
}
}
}
void pri()
{
cout << res << endl;
}
int main()
{
init();
solve();
pri();
return 0;
}
]]>