Codeforces 837F Prefix Sums

Prefix Sums

在 n >= 4时候直接暴力。

n <= 4的时候二分加矩阵快速幂去check

#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ull unsigned long long

using namespace std;

const int N = 2e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const double eps = 1e-8;
const double PI = acos(-1);

const int MN = 3;
struct Matrix {
    LL a[MN][MN];
    Matrix() {
        memset(a, 0, sizeof(a));
    }
    void init() {
        for(int i = 0; i < MN; i++)
            a[i][i] = 1;
    }
    Matrix operator * (const Matrix &B) const {
        Matrix C;
        for(int i = 0; i < MN; i++)
            for(int j = 0; j < MN; j++)
                for(int k = 0; k < MN; k++) {
                    C.a[i][j] += 1.0 * a[i][k] * B.a[k][j] <= 2e18 ? a[i][k] * B.a[k][j] : INF;
                    C.a[i][j] = min(C.a[i][j], INF);
                }
        return C;
    }
    Matrix operator ^ (LL b) {
        Matrix C; C.init();
        Matrix A = (*this);
        while(b) {
            if(b & 1) C = C * A;
            A = A * A; b >>= 1;
        }
        return C;
    }
};

int n;
LL k;
LL a[N], b[N];
Matrix mat;
int Mat[3][3] = {
    {1, 0, 0},
    {1, 1, 0},
    {1, 1, 1}
};

int main() {
    for(int i = 0; i < 3; i++)
        for(int j = 0; j < 3; j++)
            mat.a[i][j] = Mat[i][j];
    scanf("%d%lld", &n, &k);
    for(int i = 0; i < n; i++) scanf("%d", &a[i]);
    int m = n; n = 0;
    for(int i = 0, flag = 0; i < m; i++) {
        if(a[i]) flag = 1;
        if(flag) a[n++] = a[i];
    }
    LL mx = 0;
    for(int i = 0; i < n; i++) mx = max(mx, a[i]);
    if(mx >= k) {
        puts("0");
        return 0;
    }
    if(n >= 4) {
        for(int o = 1; o <= 10000000 && mx < k; o++) {
            LL prefix = 0;
            for(int i = 0; i < n && mx < k; i++) b[i] = i ? b[i - 1] + a[i] : a[i];
            for(int i = 0; i < n && mx < k; i++) a[i] = b[i], mx = max(mx, a[i]);
            if(mx >= k) {
                printf("%d
", o);
                return 0;
            }
        }
    } else {
        for(int i = n - 1; i >= 0; i--) a[3 - (n - i)] = a[i];
        for(int i = 0; i < (3 - n); i++) a[i] = 0;
        LL low = 1, high = (LL)1e18, ans = high;
        while(low <= high) {
            LL mid = (low + high) >> 1;
            Matrix tmp = mat ^ mid;
            LL val = 0;
            for(int i = 0; i < 3; i++) {
                val += 1.0 * a[i] * tmp.a[2][i] <= 2e18 ? a[i] * tmp.a[2][i] : INF;
                val = min(val, INF);
            }
            if(val >= k) high = mid - 1, ans = mid;
            else low = mid + 1;
        }
        printf("%lld
", ans);
    }
    return 0;
}

/*
*/