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[Mathimatics-Numerical algorithms] hebingguozi DL : 0: 在一个果园里，多多已经将所有的果子打了下来，而且按果子的不同种类分成了不同的堆。多多决定把所有的果子合成一堆。每一次合并，多多可以把两堆果子合并到一起，消耗的体力等于两堆果子的重量之和。可以看出，所有的果子经过n-1次合并之后，就只剩下一堆了。多多在合并果子时总共消耗的体力等于每次合并所耗体力之和。因为还要花大力气把这些果子搬回家，所以多多在合并果子时要尽可能地节省体力。假定每个果子重量都为1，并且已知果子的种类数和每种果子的数目，你的任务是设计出合并的次序方案，使多多耗费的体力最少，并输出这个最小的体力耗费值。例如有3种果子，数目依次为1，2，9。可以先将1、2堆合并，新堆数目为3，耗费体力为3。接着，将新堆与原先的第三堆合并，又得到新的堆，数目为12，耗费体力为12。所以多多总共耗费体力=3+12=15。可以证明15为最小的体力耗费值-In an orchard, a lot has shot down all the fruit, and of different types of fruit into a different pile. Decided to put all the fruit of a lot of synthetic pile. Each merger, a lot can be merged together two piles of fruit, equal to two piles of physical consumption of fruit and weight. It can be seen, all the fruit through the n-1 times after the merger, on the left a pile of. When a lot of fruit in the combined strength equal to the total consumption of each of the merger and the physical consumption. Because these also make great efforts to move the fruit home, so when a lot of fruit in the merger as much as possible to save energy. Assume that each fruit weight is 1, and the number of species known to fruit and the number of each type of fruit, your task is to design a combined order of programs, so a lot of physical least cost and physical output of the minimum cost value. For example, there are three kinds of fruit, followed by the number 1,2,9. 1,2 heap can be first merged, the
Date : 2025-12-23 Size : 1kb User : yanSS
[Mathimatics-Numerical algorithms] SA_Ex DL : 1: 模擬退火是一種通用概率演算法，用來在固定时间内寻求在一個大的搜尋空間內找到的最優解。模擬退火來自冶金學的專有名詞退火。退火是將材料加熱後再經特定速率冷卻，目的是增大晶粒的體積，並且減少晶格中的缺陷。材料中的原子原來會停留在使內能有局部最小值的位置，加熱使能量變大，原子會離開原來位置，而隨機在其他位置中移動。退火冷卻時速度較慢，使得原子有較多可能可以找到內能比原先更低的位置。模擬退火的原理也和金屬退火的原理近似：我們將熱力學的理論套用到統計學上，將搜尋空間內每一點想像成空氣內的分子；分子的能量，就是它本身的動能；而搜尋空間內的每一點，也像空氣分子一樣帶有「能量」，以表示該點對命題的合適程度。演算法先以搜尋空間內一個任意點作起始：每一步先選擇一個「鄰居」，然後再計算從現有位置到達「鄰居」的機率。可以證明，模擬退火演算法所得解依機率收斂到全局最優解。 -Simulated annealing is a generic probabilistic algorithm used in a fixed period of time to seek in a large search space to find the optimal solution. Simulated annealing terminology from metallurgical annealing. Heating the material after annealing is cooled at a specific rate through the purpose is to increase the grain size, and reduce defects in the crystal lattice. Atoms in the original material will remain in the internal energy of a local minimum position, heating energy increases, atoms leave the original position, and move randomly in other locations. Annealing cooling rate is slow, so that atoms are more likely to be found within a position lower than the original. The principle is also simulated annealing and metal annealing approximation principle: We will apply the theory of thermodynamics to statistical would imagine every point within the search space of air molecules molecular energy is the kinetic energy of its own while searching for space every point, like air
Date : 2025-12-23 Size : 137kb User : Andrew Yeh