Recursion and Dynamic Programming: Uplevel Your Coding Interview by Wong Jack

Author:Wong, Jack [Wong, Jack]
Language: eng
Format: epub
Published: 2018-08-23T16:00:00+00:00

Approach 2: top-down dynamic programming (memoization)

Notice that there are some overlapping subproblems the above code repeatedly solves. We can improve the program run time by caching (saving) the result for quick reference, and therefore avoid the recomputation of the subproblem again. Here is the caching approach:

/**

@param {number} n - balance

@param {number []} denoms - coin denominators. [25, 10, 5, 1] in this case

@param {number} index - current denominator index (start with 0)

@param {Object} memo - the cache object for computed subproblems, where it is initialized to {}

*/

function findChange (n, denoms, index, memo) {

var memoKey = n + ':' + denoms[index],

denom = denoms[index],

ways = 0,

remainingAmount = 0;

if (memo[memoKey]) return memo[memoKey];

if (index >= (denoms.length - 1)) return 1;

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

remainingAmount = n - (i * denom);

ways += findChange(remainingAmount, denoms, index + 1, memo);

}

memo[memoKey] = ways;

return ways;

}

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