The following problem is known as the dutch flag problem. in this problem, the task is to rearrange an array of characters r, w, and b (for red, white, and blue, which are the colors of the dutch national flag) so that all the r’s come first, all the w’s come next, and all the b’s come last. design a linear, in-place algorithm that solves this problem.

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Least square fit to polynomial write a function leastsquarefit3pol that solves a linear system of equations to find a least squares fit of a third order polynomial to an experimental data set given as two row arrays. the function leastsquarefit3pol must explicitly solve a set of linear equations and cannot use polyfit. there should be no restriction on the size of the problem that can be solved.

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