SPOJ - Find The Determinant III 计算矩阵的行列式答案 + 辗转相除法思想

SPOJ -Find The Determinant III

参考:https://blog.csdn.net/zhoufenqin/article/details/7779707

参考中还有几个关于行列式的性质。

题意: 

 计算矩阵的行列式答案

思路:

  计算行列式的基本方法就是把矩阵化成上三角或下三角,然后观察对角线的元素,如果其中有一个元素为0则答案为0,否则行列式的值就是对角线上各个元素的乘积。

#include <algorithm>
#include <iterator>
#include <iostream>
#include <cstring>
#include <cstdlib>
#include <iomanip>
#include <bitset>
#include <cctype>
#include <cstdio>
#include <string>
#include <vector>
#include <stack>
#include <cmath>
#include <queue>
#include <list>
#include <map>
#include <set>
#include <cassert> using namespace std;
//#pragma GCC optimize(3)
//#pragma comment(linker, "/STACK:102400000,102400000") //c++
// #pragma GCC diagnostic error "-std=c++11"
// #pragma comment(linker, "/stack:200000000")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
// #pragma GCC optimize("-fdelete-null-pointer-checks,inline-functions-called-once,-funsafe-loop-optimizations,-fexpensive-optimizations,-foptimize-sibling-calls,-ftree-switch-conversion,-finline-small-functions,inline-small-functions,-frerun-cse-after-loop,-fhoist-adjacent-loads,-findirect-inlining,-freorder-functions,no-stack-protector,-fpartial-inlining,-fsched-interblock,-fcse-follow-jumps,-fcse-skip-blocks,-falign-functions,-fstrict-overflow,-fstrict-aliasing,-fschedule-insns2,-ftree-tail-merge,inline-functions,-fschedule-insns,-freorder-blocks,-fwhole-program,-funroll-loops,-fthread-jumps,-fcrossjumping,-fcaller-saves,-fdevirtualize,-falign-labels,-falign-loops,-falign-jumps,unroll-loops,-fsched-spec,-ffast-math,Ofast,inline,-fgcse,-fgcse-lm,-fipa-sra,-ftree-pre,-ftree-vrp,-fpeephole2",3) #define lson (l , mid , rt << 1)
#define rson (mid + 1 , r , rt << 1 | 1)
#define debug(x) cerr << #x << " = " << x << "\n";
#define pb push_back
#define pq priority_queue typedef long long ll;
typedef unsigned long long ull; typedef pair<ll ,ll > pll;
typedef pair<int ,int > pii;
typedef pair<int,pii> p3; //priority_queue<int> q;//这是一个大根堆q
//priority_queue<int,vector<int>,greater<int> >q;//这是一个小根堆q
#define fi first
#define se second
//#define endl '\n' #define OKC ios::sync_with_stdio(false);cin.tie(0)
#define FT(A,B,C) for(int A=B;A <= C;++A) //用来压行
#define REP(i , j , k) for(int i = j ; i < k ; ++i)
#define max3(a,b,c) max(max(a,b), c);
//priority_queue<int ,vector<int>, greater<int> >que; const ll mos = 0x7FFFFFFF; //
const ll nmos = 0x80000000; //-2147483648
const int inf = 0x3f3f3f3f;
const ll inff = 0x3f3f3f3f3f3f3f3f; //18
// const int mod = 998244353;
const double esp = 1e-;
const double PI=acos(-1.0);
const double PHI=0.61803399; //黄金分割点
const double tPHI=0.38196601; template<typename T>
inline T read(T&x){
x=;int f=;char ch=getchar();
while (ch<''||ch>'') f|=(ch=='-'),ch=getchar();
while (ch>=''&&ch<='') x=x*+ch-'',ch=getchar();
return x=f?-x:x;
} /*-----------------------showtime----------------------*/
const int maxn = ;
ll a[maxn][maxn],mod;
int n;
void cal(){
ll ans = ;int sign = ;
for(int i=; i<=n; i++){ //当前行
for(int j=i+; j<=n; j++){
int x = i, y = j;
while(a[y][i]){ //利用gcd的方法,不停地进行辗转相除,达到消去其他行对应列元素的目的
ll t = a[x][i] / a[y][i];
for(int k=i; k<=n; k++)
a[x][k] = (a[x][k] - a[y][k]*t)%mod;
swap(x,y);
} if(x != i){ //奇数次交换,则D=-D'整行交换
for(int k = ; k<=n; k++){
swap(a[i][k], a[x][k]);
}
sign ^= ;
}
}
if(a[i][i] == ){ //斜对角中有一个0,则结果为0
puts("");
return;
}
else ans = ans * a[i][i] %mod;
}
if(sign) ans *= -;
if(ans < ) ans += mod;
printf("%lld\n", ans);
}
int main(){
while(~scanf("%d%lld", &n, &mod)){
for(int i=; i<=n; i++){
for(int j=; j<=n; j++)
scanf("%lld", &a[i][j]);
} cal();
}
return ;
}
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