BZOJ4589: Hard Nim(FWT 快速冪)

自為風月馬前卒發表於2018-11-29

題意

題目連結

Sol

神仙題Orzzzz

題目可以轉化為從(leqslant M)的質數中選出(N)個(xor)和為(0)的方案數

這樣就好做多了

設(f(x) = [x ext{是質數}])

(n)次異或FWT即可

快速冪優化一下，中間不用IFWT，最後轉一次就行(然而並不知道為什麼)

哪位大佬教教我這題的DP怎麼寫呀qwqqqq

死過不過去樣例。。

#include<bits/stdc++.h>
using namespace std;
const int MAXN = (1 << 17) + 10, mod = 998244353, inv2 = 499122177;
inline int read() {
    char c = getchar(); int x = 0, f = 1;
    while(c < `0` || c > `9`) {if(c == `-`) f = -1; c = getchar();}
    while(c >= `0` && c <= `9`) x = x * 10 + c - `0`, c = getchar();
    return x * f;
}
int N, A[MAXN], B[MAXN], C[MAXN];
int add(int x, int y) {
    if(x + y < 0) return x + y + mod;
    return x + y >= mod ? x + y - mod : x + y;
}
int mul(int x, int y) {
    return 1ll * x * y % mod;
}
void FWTor(int *a, int opt) {
    for(int mid = 1; mid < N; mid <<= 1) 
        for(int R = mid << 1, j = 0; j < N; j += R)
            for(int k = 0; k < mid; k++) 
                if(opt == 1) a[j + k + mid] = add(a[j + k], a[j + k + mid]);
                else a[j + k + mid] = add(a[j + k + mid], -a[j + k]);
}
void FWTand(int *a, int opt) {
    for(int mid = 1; mid < N; mid <<= 1) 
        for(int R = mid << 1, j = 0; j < N; j += R)
            for(int k = 0; k < mid; k++) 
                if(opt == 1) a[j + k] = add(a[j + k], a[j + k + mid]);
                else a[j + k] = add(a[j + k], -a[j + k + mid]);
}
void FWTxor(int *a, int opt) {
    for(int mid = 1; mid < N; mid <<= 1) 
        for(int R = mid << 1, j = 0; j < N; j += R)
            for(int k = 0; k < mid; k++) {
                int x = a[j + k], y = a[j + k + mid];
                if(opt == 1) a[j + k] = add(x, y), a[j + k + mid] = add(x, -y);
                else a[j + k] = mul(add(x, y), inv2), a[j + k + mid] = mul(add(x, -y), inv2);               
            }

}
int main() {
    N = 1 << (read());
    for(int i = 0; i < N; i++) A[i] = read();
    for(int i = 0; i < N; i++) B[i] = read();
    FWTor(A, 1); FWTor(B, 1);
    for(int i = 0; i < N; i++) C[i] = mul(A[i], B[i]);
    FWTor(C, -1); FWTor(A, -1); FWTor(B, -1);
    for(int i = 0; i < N; i++) printf("%d ", C[i]); puts("");
    FWTand(A, 1); FWTand(B, 1);
    for(int i = 0; i < N; i++) C[i] = mul(A[i], B[i]);
    FWTand(C, -1); FWTand(A, -1); FWTand(B, -1);    
    for(int i = 0; i < N; i++) printf("%d ", C[i]); puts("");
    FWTxor(A, 1); FWTxor(B, 1);
    for(int i = 0; i < N; i++) C[i] = mul(A[i], B[i]);
    FWTxor(C, -1); FWTxor(A, -1); FWTxor(B, -1);    
    for(int i = 0; i < N; i++) printf("%d ", C[i]);
    return 0;
}

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