Divide and Conquer
Recursively breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly.
Definition
Problem
sub-problem
sub-problem
Simple Problems
- Number Classification
Complex Problems
Tower of Hanoi (河內塔)
- 將所有盤子從最左邊移到最右邊
- 大盤子不可疊在小盤子上
Tower of Hanoi
function hanoi(n, a, b, c) {
if(n === 1) {
return [{
from : a,
to : c,
}];
}
return hanoi(n - 1, a, c, b).concat(
hanoi(1, a, b, c),
hanoi(n - 1, b, a, c)
);
}
hanoi(3, 'A', 'B', 'C').forEach(function(move) {
print('盤從 ' + move.from + ' 移至 ' + move.to);
});T(n) = 2^n - 1
Tower of Hanoi
傳說在古老的印度，有一座神廟，據說它是宇宙的中心。在廟宇中放置了一塊上面插有三根長木釘的木板，在其中的一根木釘上，從上至下被放置了64片直徑由小至大的圓環形金屬片。按照規則移動，當這些金屬片全數被移到另一根木釘上時，世界就將毀滅。
需要次數：18,446,744,073,709,551,615 次
假設每秒搬一次不眠不休：約 584,942,417,355 年
To iterate is human, to recurse, divine
Sorting
Array.sort();- Chrome(V8): Quick sort + Insertion sort(len <= 10)
- Firefox/Mozilla: Merge sort
- Safari: Selection sort
- IE: Selection sort
Permutation
Q: 假設有10題題目，每題皆有2個答案，請產出所有答案組合
[
[0, 1], // Q1
[2, 3], // Q2
[4, 5],
[6, 7],
[8, 9],
[10, 11],
[12, 13],
[14, 15],
[16, 17],
[18, 19] // Q10
]
[
[0, 2, 4, 6, 8, 10, 12, 14, 16, 18], // A1
[0, 2, 4, 6, 8, 10, 12, 14, 16, 19], // A2
...
...
[1, 3, 5, 7, 9, 11, 13, 15, 17, 19] // A1024
]原始答案
答案組合
Permutation
Q: 假設有10題題目，每題皆有2個答案，請產出所有答案組合
function version1(args) {
return (
args.reduce((acc, curr) => (
_.flatten(acc.map(answerGroup => (
curr.map(answer => answerGroup.concat([answer])) // group length: acc * curr
)))
), [[]])
);
}[[0, 1], [2, 3] ... , [18, 19]]
[[]]
[[0], [1]]
[[0, 2], [0, 3], [1, 2], [1, 3]]
...
V1
Q: 假設有10題題目，每題皆有2個答案，請產出所有答案組合
function version2(args) {
const result = [];
const max = args.length - 1;
function permuteHelper(arr, questionIdx) {
if (args[questionIdx]) {
args[questionIdx].map((arg) => {
const tempArray = arr.slice(0); // clone arr
tempArray.push(arg);
if (questionIdx === max) {
return result.push(tempArray);
}
return permuteHelper(tempArray, questionIdx + 1);
});
}
}
permuteHelper([], 0);
return result;
}[[0, 1], [2, 3] ... , [18, 19]]
V2
Q: 假設有10題題目，每題皆有2個答案，請產出所有答案組合
[[0, 1], [2, 3] ... , [18, 19]]
0
1
2
3
4
5
4
5
2
3
.
.
.
.
.
.
permuteHelper([], 0)
permuteHelper([0], 1)
permuteHelper([1], 1)
permuteHelper([0, 2], 2)
permuteHelper([0, 3], 2)
permuteHelper([1, 2], 2)
permuteHelper([1, 3], 2)
Chrome (1024個解)
Firefox (1024個解)
Safari (1024個解)
Divide and Conquer
By Travor Lee
