Pascal triangle code example implemented by Java programming

Source program Secrets

Yang Hui triangle property:

The numbers in each line are symmetrical from left to right, gradually increasing from 1, then decreasing and returning to 1. The number of numbers in line n is n. The sum of the numbers in line n is 2 ^ (n-1). Each number is equal to the sum of the left and right numbers in the previous line. This property can be used to write the whole Yang Hui triangle. The first number in line n is 1, and the second number is 1 × (n-1), the third number is 1 × (n-1) × (n-2) / 2, the fourth number is 1 × (n-1) × （n-2） /2 × (n-3) / 3... And so on.

Algorithm principle 1:

A two-dimensional array yh[][] is used to store the data of Yang Hui's triangle, The size of rows and columns is the number of rows to be output row (row in this program is 10). Use the for loop to make the number of rows in Yang Hui triangle except the outermost layer (excluding the bottom edge of Yang Hui triangle) 1; use the statement YH [i] [J] = YH [I - 1] [J - 1] + YH [I - 1] [J] to make the data in column J of row I equal to the data in column (J-1) of row (i-1) and the data in column (i-1) (j) The sum of the data of the column, that is, each number is equal to the sum of the left and right numbers of the previous row.

Mode II

Method 3: recursive implementation

Please enter the number of rows:

6 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1

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result:

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 1 9 36 84 126 126 84 36 9 1

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