硬币找零问题
利用递归算法完成硬币的找零问题，得出找零的最优解
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>change</title>
</head>
<body>
<script>
function MinCoinChange(coins) {
var coins=coins;
var cache={};
this.makeChange=function (amount) {
var me=this;
if(!amount){
return [];
}
if (cache[amount]){
return cache[amount];
}
var min=[],newMin,newAmount;
for(var i=0;i<coins.length;i++){
var coin=coins[i];
newAmount=amount-coin;
if(newAmount>=0){
newMin=me.makeChange(newAmount);
}
if(newAmount>=0 && (newMin.length<min.length-1 || !min.length)&&(newMin.length || !newAmount)){
min=[coin].concat(newMin);
console.log('new Min'+min+'for'+amount);
}
}
return (cache[amount]=min);
};
}
//贪心算法遵循的是一种近似解决问题的技术，期盼通过每个阶段的局部最优选择，从而达到全局的最优
//最少硬币找零问题
function MinCoinChange1(coins) {
var coins=coins;
this.makeChange=function (amount) {
var change=[],total=0;
for(var i=coins.length;i>=0;i--){
var coin=coins[i];
while(total+coin<=amount){
change.push(coin);
total+=coin;
}
}
return change;
}
}
var minCoinChange=new MinCoinChange([1,3,4]);
console.log(minCoinChange.makeChange(6));
var minCoinChange1=new MinCoinChange1([1,5,10,25]);
console.log(minCoinChange1.makeChange(45));
</script>
</body>
</html>
