js:数据结构笔记14--高级算法

动态规划：

递归是从顶部开始将问题分解，通过解决所有分解出小问题来解决整体问题；

动态规划从底部开始解决问题，将所有小问题解决，然后合并掉一个整体解决方案；

　　

function dynFib(n) {

	var val = [];

	for(var i = 1; i <= n; ++i) {

		val[i] = 1;

	}

	if(n === 1) {

		return 1;

	} else {

		for(var i = 2; i <= n; ++i) {

			val[i] = i * val[i-1];

		}

		return val[n];

	}

}



function iterFib(n) {

	var last = 1,

	    result = 1;

	for(var i = 2; i <= n; ++i) {

		result = last * i;

		last = result;

	}

	return result;

}

背包问题：

• 递归解决：

function max(a,b) {

	return (a > b) ?  a : b;

}

function knapsack(capacity,size,value,n) {

	if(n == 0 || capacity ==0) {

		return 0;

	}

	if(size[n -1] > capacity) {

		return knapsack(capacity,size,value,n-1);

	} else {

		return max(value[n - 1] + 

					knapsack(capacity - size[n - 1],size,value,n-1),

					knapsack(capacity,size,value,n-1));

	}

}



var value = [4,5,10,11,13],

	size = [3,4,7,8,9],

	capacity = 16,

	n = 5;

console.log(knapsack(capacity,size,value,n));

• 　动态规划：

function max(a,b) {

	return (a > b) ?  a : b;

}

function dknapsack(capacity,size,value,n) {

	var k = [];

	for(var i = 0; i <= capacity + 1; ++i) {

		k[i] = [];

	}

	for(var i = 0; i <= n; ++i) {

		for(var w = 0; w <= capacity; ++w) {

			if(i == 0 || w == 0) {

				k[i][w] = 0;

			} else if(size[i - 1] <= w) {

				k[i][w] = max(value[i - 1] + k[i - 1][w - size[i - 1]], k[i - 1][w]);

			} else {

				k[i][w] = k[i - 1][w];

			}

		}

	}

	return k[n][capacity];

}



var value = [4,5,10,11,13],

	size = [3,4,7,8,9],

	capacity = 16,

	n = 5;

console.log(dknapsack(capacity,size,value,n));