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## Project Euler 82: Find the minimal path sum from the left column to the right column.

#### Problem Description

NOTE: This problem is a more challenging version of Problem 81.

The minimal path sum in the 5 by 5 matrix below, by starting in any cell in the left column and finishing in any cell in the right column, and only moving up, down, and right, is indicated in red; the sum is equal to 994.

 131 673 234 103 18 201 96 342 965 150 630 803 746 422 111 537 699 497 121 956 805 732 524 37 331

Find the minimal path sum, in matrix.txt (right click and ‘Save Link/Target As…’), a 31K text file containing a 80 by 80 matrix, from the left column to the right column.

#### Analysis

This is using the same technique that solved problem 18, 67, 81 & 83. We no longer have a fixed starting and ending point so we need to track the starting points to a vector. From there we “bubble” the minimum sums by moving from left to right.

#### Project Euler 82 Solution

Runs < 0.010 seconds in Python 2.7.

Use this link to get the Project Euler 82 Solution Python 2.7 source.

#### Afterthoughts

Project Euler 82 Solution last updated