洛谷 #2822. 組合數問題

題意

t組數據，問當0≤i≤n，i<j≤m中，有幾組\(C_{i}^{j}\)能整除k

題解

依舊找規律，發現是\(\mathbb{YANGHITRIANGLE}\)

調試記錄

楊輝三角要加前綴和，不然會TLE

#include <cstdio>
#include <algorithm>
#define maxn 2005

using namespace std;

int T, k, c[maxn][maxn], sum[maxn][maxn];

void Install();

int main(){
    scanf("%d%d", &T, &k);
    Install();
    
    while (T--){
        int n, m;
        scanf("%d%d", &n, &m);
        m = min(m, n);
        printf("%d\n", sum[n][m]);
    }
    
    return 0;
}

void Install(){
    c[1][1] = 1;
    
    for (int i = 0; i <= 2000; i++) c[i][0] = 1;
    for (int i = 2; i <= 2000; i++){
        for (int j = 1; j <= i; j++){
            c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % k;
        }
    }
    for (int i = 2; i <= 2000; i++){
        for (int j = 1; j <= i; j++){
            sum[i][j] = sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1];
            if (c[i][j] == 0) sum[i][j] += 1;
        }
        sum[i][i + 1] = sum[i][i];
    }
}