数学のめっちゃ計算する問題をC言語でやってみた

₃₀C₂₁(1/2)²¹(1/2)⁹ + ₃₀C₂₂(1/2)²²(1/2)⁸ + ... + ₃₀C₂₉(1/2)²⁹(1/2)¹ + ₃₀C₃₀(1/2)³⁰
を計算する問題（ではないけど）があったので、コンピュータにやらせちゃおうと思いました。

main.c

#include <stdio.h>
#include <stdlib.h>

void bunsu_tasizan(long,long,long,long,long*,long*);
void yakubun(long*,long*);
void C_keisan(long,long,long*,long*);
long yukurido(long, long);

int main() {
    long double shousu;
    int x = 30,y = 21;
	int kou_size = x - y + 1;
    long bunsi;
    long bunbo;
    long *kakubunsi = (long*)malloc(sizeof(long) * kou_size);
    long *kakubunbo = (long*)malloc(sizeof(long) * kou_size);
    long kekka_bunsi;
    long kekka_bunbo;
    long ni_sanjujou = 1;
    int i;

    for(i = 0;i < 30;i++){
        ni_sanjujou *= 2;
    }

    for(i = 0;i < (kou_size);i++){
        C_keisan(x,y + i,&bunsi,&bunbo);
        kakubunsi[i] = bunsi;
        kakubunbo[i] = bunbo * ni_sanjujou;
    }

    kekka_bunsi = kakubunsi[0];
    kekka_bunbo = kakubunbo[0];
    for(i = 0;i < (x - y);i++){
        bunsu_tasizan(kekka_bunsi,kekka_bunbo,kakubunsi[i+1],kakubunbo[i+1],&kekka_bunsi,&kekka_bunbo);
    }

    printf("%ld/%ld\n",kekka_bunsi,kekka_bunbo);

    shousu = (long double)kekka_bunsi / (long double)kekka_bunbo;
    printf("%.15Lf\n",shousu);

	free(kakubunsi);
	free(kakubunbo);

    return 0;
}

void bunsu_tasizan(long bunsi1,long bunbo1,long bunsi2,long bunbo2,long *bunsi,long *bunbo){
    if(bunbo1 != bunbo2){
        long a;
        a = yukurido(bunbo1,bunbo2);
		long tsubun_bunbo = bunbo1 / a;
        bunbo1 *= (bunbo2 / a);
        bunsi1 *= (bunbo2 / a);
        bunsi2 *= (tsubun_bunbo);
    }
    (*bunbo) = bunbo1;
    (*bunsi) = bunsi1 + bunsi2;
    yakubun(bunsi,bunbo);
}

void C_keisan(long n,long m,long *bunsi,long *bunbo){
	long bunsi2 = 1;
	long bunbo2 = 1;

    if(n - m < m){
        m = n - m;
    }
	int kou_size = m;
    long *bunsi1 = (long*)malloc(sizeof(long)*kou_size);
    long *bunbo1 = (long*)malloc(sizeof(long)*kou_size);

    for (int i = 0;i < m;i++){
        bunsi1[i] = (n - i);
        bunbo1[i] = (m - i);
    }
	for(int i = 0;i < m;i++){
		for(int j = 0;j<m;j++){
			if(*(bunsi+i) == 1){
				j = m;
			}
			else{
				yakubun(bunsi1+i,bunbo1+j);
			}
		}
	}
	for(int i = 0;i < m;i++){
		bunsi2 *= *(bunsi1+i);
		bunbo2 *= *(bunbo1+i);
	}

	free(bunsi1);
	free(bunbo1);

	yakubun(&bunsi2,&bunbo2);
	(*bunsi) = bunsi2;
	(*bunbo) = bunbo2;
}

void yakubun(long *bunsi,long *bunbo){
    long maxkouyakusu;
    maxkouyakusu = yukurido(*bunsi,*bunbo);

    (*bunsi) /= maxkouyakusu;
    (*bunbo) /= maxkouyakusu;
}

long yukurido(long x,long y){
    long temp;
    if(x < y){
        temp = x;
        x = y;
        y = temp;
    }

    long r = x % y;
    while(r != 0){
        x = y;
        y = r;
        r = x % y;
    }
    return y;
}

実行結果

22964087/1073741824
0.021386972628534

無駄な部分がめちゃくちゃ多いと思うけど、修正するの大変なので許してください。

今回コードを書いてみて、C言語のポインタの便利さがめっちゃわかりました。