Number of ways to reach ( X , Y ) in a matrix starting from the origin | C ++ implementation of the approach ; To store the factorial and factorial mod inverse of the numbers ; Function to find ( a ^ m1 ) % mod ; Function to find the factorial of all the numbers ; Function to find the factorial modinverse of all the numbers ; Function to return nCr ; Function to return the number of ways to reach ( X , Y ) in a matrix with the given moves starting from the origin ; Driver code
#include <bits/stdc++.h> NEW_LINE using namespace std ; #define N  1000005 NEW_LINE #define mod  (int)(1e9 + 7) NEW_LINE int factorial [ N ] , modinverse [ N ] ; int power ( int a , int m1 ) { if ( m1 == 0 ) return 1 ; else if ( m1 == 1 ) return a ; else if ( m1 == 2 ) return ( 1LL * a * a ) % mod ; else if ( m1 & 1 ) return ( 1LL * a * power ( power ( a , m1 / 2 ) , 2 ) ) % mod ; else return power ( power ( a , m1 / 2 ) , 2 ) % mod ; } void factorialfun ( ) { factorial [ 0 ] = 1 ; for ( int i = 1 ; i < N ; i ++ ) factorial [ i ] = ( 1LL * factorial [ i - 1 ] * i ) % mod ; } void modinversefun ( ) { modinverse [ N - 1 ] = power ( factorial [ N - 1 ] , mod - 2 ) % mod ; for ( int i = N - 2 ; i >= 0 ; i -- ) modinverse [ i ] = ( 1LL * modinverse [ i + 1 ] * ( i + 1 ) ) % mod ; } int binomial ( int n , int r ) { if ( r > n ) return 0 ; int a = ( 1LL * factorial [ n ] * modinverse [ n - r ] ) % mod ; a = ( 1LL * a * modinverse [ r ] ) % mod ; return a ; } int ways ( int x , int y ) { factorialfun ( ) ; modinversefun ( ) ; if ( ( 2 * x - y ) % 3 == 0 && ( 2 * y - x ) % 3 == 0 ) { int m = ( 2 * x - y ) / 3 ; int n = ( 2 * y - x ) / 3 ; return binomial ( n + m , n ) ; } return 0 ; } System . out . println ( n + m + " ▁ " + n ) ; int main ( ) { int x = 3 , y = 3 ; cout << ways ( x , y ) ; return 0 ; }