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2023-06-09 18:52:05 +08:00
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commit 00282efd8b
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src/main/java/com/thealgorithms/maths/PascalTriangle.java
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@ -3,18 +3,19 @@ package com.thealgorithms.maths;
public class PascalTriangle {
/**
*In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises
* in probability theory, combinatorics, and algebra. In much of the Western world, it is named after
* the French mathematician Blaise Pascal, although other mathematicians studied it centuries before
* him in India, Persia, China, Germany, and Italy.
*In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that
*arises in probability theory, combinatorics, and algebra. In much of the Western world, it is
*named after the French mathematician Blaise Pascal, although other mathematicians studied it
*centuries before him in India, Persia, China, Germany, and Italy.
*
* The rows of Pascal's triangle are conventionally enumerated starting with row n=0 at the top (the 0th row).
* The entries in each row are numbered from the left beginning with k=0 and are usually staggered relative
* to the numbers in the adjacent rows. The triangle may be constructed in the following manner:
* In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is
* constructed by adding the number above and to the left with the number above and to the right, treating
* blank entries as 0. For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1),
* whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row. *
* The rows of Pascal's triangle are conventionally enumerated starting with row n=0 at the top
*(the 0th row). The entries in each row are numbered from the left beginning with k=0 and are
*usually staggered relative to the numbers in the adjacent rows. The triangle may be
*constructed in the following manner: In row 0 (the topmost row), there is a unique nonzero
*entry 1. Each entry of each subsequent row is constructed by adding the number above and to
*the left with the number above and to the right, treating blank entries as 0. For example, the
*initial number in the first (or any other) row is 1 (the sum of 0 and 1), whereas the numbers
*1 and 3 in the third row are added to produce the number 4 in the fourth row. *
*
*<p>
* link:-https://en.wikipedia.org/wiki/Pascal%27s_triangle
@ -51,7 +52,8 @@ public class PascalTriangle {
// First and last values in every row are 1
if (line == i || i == 0) arr[line][i] = 1;
// The rest elements are sum of values just above and left of above
else arr[line][i] = arr[line - 1][i - 1] + arr[line - 1][i];
else
arr[line][i] = arr[line - 1][i - 1] + arr[line - 1][i];
}
}